Atomic Structure FULL CHAPTER | Class 11th Physical Chemistry | Chapter 2 | Arjuna JEE

So these topics, we will study them at the end, within the Principle of Atom. We will do them along with Redox. Structure of Atom is a very scoring chapter in itself. I keep telling you this again and again. So, it tells the probability of finding an electron inside any atom, which is psi squared. And the region where the psi squared value is maximum, where the probability of finding an electron is maximum, this region is called an orbital. When you fill electrons, electrons will be filled in increasing order of energy. Hello and welcome to all my dear students. How are you all? I hope everyone is doing very well. Once again, I welcome all of you. Today we are going to talk about Structure of Atom, a very lovely chapter, a very easy chapter. Yes, in some places it is written as Atomic Structure, Structure of Atom, it's the same thing. In the last session, we completed the Mole Concept all at once. Yes, and today we are going to complete Structure of Atom in one session. Okay. Then I was looking at some of your doubts, some comments. Some children wrote that sir, some topics are missing. I have intentionally kept some topics missing, as I have already told you, like Normality etc. These topics, we will study them at the end, within the Principle of Atom. We will do them along with Redox. But some people said that percentage purity has not been covered. Questions on percentage purity have been done, two or three, right? Only the heading was written as percentage purity. So if you see the session, you will find questions on percentage purity. Questions on percentage have been done, homework has also been given. Percentage purity, yes. The thing is, its separate topic is not written, right? Actually, it is not a separate topic at all. They have been made into topics. There is no separate topic. And because we have time limitations, it is one chapter, I have to finish it within 3 hours or 3.5 hours. So obviously, it is a bit difficult to teach a chapter extensively in that way. And this is also a backlog series, it is for you to complete your backlog. Right? So if you want to see the full detail, some people said sir, study like Manzil. Manzil series, brother, that is a different segment. The Manzil segment is different. Those are one-shot sessions in which we give 8-10-12 hour sessions. That is a different thing. That happens just before the exam. Yes, this is not that thing. This is different. In this, we finish a chapter in a concise way. Okay? So, brother, we have to complete the session with this thought. Okay, done. So, in my opinion, we should start the session now. Structure of Atom. Until this session is over, everyone sit in one place with great density. Take water, whatever you want to drink, with you and watch the entire session. Right? You will enjoy the session only then, and you will know which chapter, which topic is left, which is not left. Otherwise, at the end, you will comment that this was left, that was left. Right? Okay, done. Shall we start? Let's start the session. So, what are we going to do? So, okay, I have written the names, but today's target is that we have to finish the entire chapter very well. Alright? Let's start. First of all, from the introduction. See, in the introduction, the very first thing that comes is that when we talked, you were young, right? Then in class ninth, you used to study Dalton's Atomic Theory. Right? First of all, Mr. Dalton came. He said that the atom is indivisible. You cannot divide the atom any further. The smallest particle of matter is the atom. Then people came, radioactivity was discovered. People said, no, there is something smaller than the atom. And those smallest particles that are present inside the atom, what did we name them? Well, we didn't name them, whoever named them, what did they name them? Subatomic particles. Why am I writing orbital? Subatomic particles. Right. Okay, sir, there are many subatomic particles. Absolutely, there are. But which subatomic particles are in our syllabus that we have to study in this chapter? They are, brother, electron, then proton, and then neutron. Yes, we have to study about these three subatomic particles in this chapter. Let's move on and study about the discovery of subatomic particles. How were subatomic particles discovered? What happened? First of all, we are going to talk about the discovery of the electron. You know, Mr. J.J. Thomson discovered the electron. He did an experiment, the Cathode Ray Tube Experiment. Right? He did an experiment, the Cathode Ray Experiment, and from there he found out about this particle. Right? So, what is this Cathode Ray Experiment? See, in front of you, there is a glass tube. Yes. Inside this glass tube, you have filled air. But the air should be at very low pressure. At low pressure, and to maintain low pressure, a vacuum pump is installed here. Right? Here you have taken cathode and anode, two electrodes, and a very high voltage, a high voltage battery, you have connected here. Right? And between these cathode and anode, you have filled what? A gas. You have filled a gas. Right? And as soon as you applied high voltage, you noticed something. What did you notice? What did he do? He made small holes in this anode. Small perforations. He made a small hole. He noticed a very wonderful thing. He noticed a wonderful thing. And here he did what? He coated the anode with a substance like zinc sulfide. This is a substance that glows when a particle hits it. Right? So here, he noticed that as soon as he completed the circuit, he saw blue light here. Right? Then he thought, something is wrong. Right? Light can only come here if some particle comes and hits it with a certain velocity. Right? And that particle, he said, this particle is coming towards the anode. And the anode has a positive charge. This means that this particle must have had a negative charge. Right? And this negatively charged particle, this negatively charged particle that was moving from the cathode towards the anode, this negatively charged particle was named electron. Right? Very good. And these rays of negatively charged particles, stream of negative. No problem. Now, someone will ask, sir, where do these cathode rays come from? How are they generated? Where did this negatively charged particle come from? So, suppose you had hydrogen gas. Yes. Here you have applied very high voltage. Hydrogen will convert into H and this, due to high voltage, will break into H+ and negative. It will ionize. Yes. What will happen, brother? Ionization. It will break into ions. Not ionization, brother, ionization. It will break into ions. The hydrogen atom, brother, will become H+ and negative. A positively charged particle will form, a negatively charged particle will form. Today, we know this negatively charged particle as electron. Yes. And this negatively charged particle moves from here to here. And these rays of negatively charged particles have been named by us. Why? Because it seems they were coming from the cathode towards the anode. Yes. Now think, if you had filled oxygen gas instead of hydrogen gas, then brother, this negatively charged particle would remain the same, right? Electron is electron, right? Its charge will be the same, its mass will be the same, everything will be the same. This means that if you fill different gases here, then the properties of these cathode rays will not be affected. The properties of cathode rays are the same. Cathode rays mean electron rays. And no matter what the gas is, an electron is an electron, right? Its mass, its charge, everything remains the same. In my opinion, you have understood this. Yes. So, if we talk about the properties here, properties. If we talk about the properties of cathode rays, then a very wonderful thing is written, that these properties are independent of the nature of the gas. Take any gas, the properties remain unaffected. Right? And some other properties are also written here, that these cathode rays travel in a straight line from the cathode. And if you place a target in their path, they will cast its shadow. Yes. Their deflection is towards the positive electrode. Obviously, these rays will have charge. Cathode rays have electrons. Electrons have negative charge. So, they will be deflected towards the positively charged electrode, towards the plate. Right? Okay. If you place a small, light paddle wheel in their path, then these cathode rays will rotate that paddle wheel. Right? From this, it is known that the particle of the cathode ray has its own mass, it is hitting it with a certain velocity, transferring some momentum to it, and due to that, that wheel is rotating. Right? Did you understand my point? Yes. So, these are some properties. You can keep them in mind. But the most important property among them is this last property. See, it is shown here that when cathode rays are coming from here, if you apply a plus and minus plate, an electric field, then your cathode rays are going towards the positive plate. So, from here it is confirmed that this particle must have had a negative charge. Right? It had a negative charge. Okay. If we talk about the charge of the electron, then in my opinion, I don't need to tell you. The charge of the electron is -1.6 * 10^-19 Coulombs, and its mass is 9.1 * 10^-31 kg. Right? This is your absolute charge and absolute mass. This is its charge and mass. Now, as soon as this negatively charged particle was discovered, then it is common sense that when your atom ionized, a positively charged particle was formed, a negatively charged particle was formed. If your negatively charged particle is moving from cathode to anode, then the positively charged particle will move from anode to cathode. Yes. From where to where will it move? From anode to cathode. Yes. So, today, these rays of particles, which are moving from where to where? From anode to cathode. These rays were named what? Anode rays or Canal rays. What were they called? Anode rays or Canal rays. And these rays, the particle in them, must have had a positive charge. Right? Positively charged particle. Was it? Am I making sense? Clear? No problem here? Yes. And if you had filled hydrogen gas in it, if you had filled hydrogen gas in it, then the positively charged particle of hydrogen, H+, is called proton. Yes. It is called proton. Right? If you fill any other gas in it, like if you fill helium, then the positively charged particle of helium will not be a proton. What will you call a proton? When you fill hydrogen gas in it. Yes. For example, if helium is filled in it, then when it ionizes, its positively charged particle will be He2+? Now, He2+ and H+ have different masses. Their charges are also different. What will be called a proton? H+ will be called a proton when you fill hydrogen gas in it. Okay. Now, because it has a positively charged particle, it will move towards which electrode? Towards the negative plate. All properties are similar to the initial ones. Yes. The last property, the last property depends on the nature of the gas. Obviously, it will depend. Because when you change the gas, then brother, the positively charged particle's charge will also change, its mass will also change. And if both charge and mass change, then the specific charge will be different. Both charge and mass are different, so the properties of the anode will also be different. Right? So, this is a very important thing, that the properties of anode rays do not depend on, depend on the nature of the gas. The properties of cathode rays do not depend on the nature of the gas. Do not depend. Do not depend. Okay, done. Will remember this? Okay. See, this is also shown here. Right? That if you pass anode rays, they will be deflected towards the negatively charged plate of the electric field. So, from here it is confirmed that yes, the anode ray must have had a positive charge. Right? Done. Okay, one more thing. See one more thing. Understand. If I talk about proton, then the charge of proton is how much, brother? Charge of proton is +1.6 * 10^-19 Coulombs. And if you talk about mass, mass of proton is how much? Sir, mass of proton is 1.672 * 10^-27 kg. In my opinion, you know everything. You study these things in lower classes. So, there is one small term, there is one small term, which is called specific charge. What is specific charge, brother? It is called charge upon mass. Whether it is electron or proton. You don't need to remember the value. You can calculate the value of specific charge by dividing. Okay. Okay. Now, if I talk about relative charge, right? The relative charge of a proton, brother, is considered to be +1. And the relative mass is considered to be 1. Right? You write it as 1 amu, right? This is it. Relative mass is 1, and relative charge is +1. Right? The relative mass and relative charge of an electron are -1. No problem here. Very good. Let's move on. And now let's talk about the discovery of neutron, the last one. The discovery of neutron was done by James Chadwick. And how did he discover it? He took a beryllium sheet and bombarded alpha particles on the beryllium sheet. In my opinion, all of you know what an alpha particle is. Right? Helium nucleus. We call helium nucleus an alpha particle. It has a charge of 2 units positive. So, such a particle is called an alpha particle. When he bombarded alpha particles on beryllium, he got a particle that had no charge, but its mass was almost equal to the mass of a proton. Such a particle, what did Chadwick name it? He named it Yes. What did he name it, brother? Neutron. So, if I talk about the mass of neutron, right? Then the mass is, brother, approximately equal to 1.674. The mass will be positive. 1.674 * 10^-27 kg. And the charge, you know, if it is neutral, then it will have no charge. Yes. If you are asked, what is its relative mass? Then you will say, sir, the relative mass is 1. And its relative charge, sir, it has no charge at all. So, it will be zero. Yes. Relative charge will be zero. Yes or no? Say yes. Done. Okay. In my opinion, there is no problem here. So, this was the discovery of subatomic particles, the discovery of electron, proton, neutron. Although many questions can be asked on this, but it is not very important. I have told you the important things. One question is specific charge of cathode rays. The specific charge of cathode rays, that is, the charge to mass ratio, is always constant. What does this mean? It means that any particle, whether it is electron or proton, its charge. Okay. Let's see a question. This is a very easy question. You all look at it once. Yes. You all do it yourself. Yes. You do it yourself. And see, suppose there is another question. The specific charge of two particles A and B. The ratio of their specific charge is given as how much? That ratio is given as 2/3. It says, mass of A and mass of. See, you can write it like this, right? E_a / m_a and E_b / m_b. This is given as how much, brother? 2/3. Yes. So, now we are asked, what will be the value of E_a / E_b? So, E_a / E_b will be 2/3 * m_a / m_b. Right? Say yes. Okay. And m_a / m_b is given as how much? Sir, this is given as 2/3. m_a / m_b is given as 2/3. This means, what will be the ratio of their charges? 4:9. Tell me. Yes. Shall we move on? Okay. Then, next question. You will do this question yourself. It is a very easy question. Here we have to tell the order of specific charge. That is, E/M. What will be the ratio of charge and mass? You already know all the ratios of charge and mass. Okay. After this, as soon as these subatomic particles were discovered, people asked, tell us, what is an atom like? What is its shape? What is an atom like? From there, your atomic models were formed. How many atomic models do we have to study in the chapter? Four atomic models. Which ones? First will be Thomson's Atomic Model. Then will be Rutherford's Atomic Model. Then will be Bohr's Atomic Model. And the last will be the Quantum Mechanical Model. For your information, these two atomic models are more important. And the first two atomic models. Okay. We will study them. You have studied them before in lower classes, but this is not a very important part. Not important. Not important. Okay. So, let's come. Let's talk about Thomson. What did Thomson say? One day, Thomson had a dream at night. A dream of an atom. And whatever he dreamt, he just stuck it and made a rule. Right? That the atom is like this. What is the dream? That the atom is spherical. Okay. No problem. And he said that it is spherical, but along with that, the positive charge of this atom is uniformly distributed throughout the atom. And the distribution of negative charge is not uniform. He related his model to what? Or it is also called the watermelon model. Like in a watermelon, there are black seeds present. He said, similarly, negative charge is present inside the atom. And the edible substance, the red colored edible substance, like it is present in a watermelon. He said that your atom has what? It has positive charge. Right? So, because of this, this model was also called the plum pudding model and the watermelon model. Right? What is important to understand is that he called the atom spherical. With some calculations, he also said that the radius of the atom is. And he compared it with what? With a plum pudding or a watermelon. Right? I have told you this. It is important to understand this: the distribution of positive charge is uniform, the distribution of negative charge is not uniform. Who said this? Mr. Thomson said this. Right? This watermelon is in front of you. In this, as you can see the seeds, he compared these seeds with electrons. And the rest of the edible substance, he said, is the present positive charge. Right? Now, if someone asks you, what are its limitations? Oh, brother, it has all the limitations. It didn't say anything good about the atom. It didn't say anything good. Right? So, what to write? See, first of all, it is not known how the positive charge, if it is uniformly distributed, how it is held with the negative charge. Right? How positive and negative hold each other. From this, you cannot know about the stability of the atom. The nucleus is not mentioned anywhere in this entire story. What is the nucleus? Yes. And when Rutherford came, after this, Rutherford did an experiment, the Gold Foil Experiment. Everyone knows about it. Right? He took gold foil and bombarded alpha particles on it. Bombarded. And then he noted the deflection of alpha particles from that gold foil. And from the deflection, he drew some observations. Based on the observations, he drew some conclusions. And from there, his atomic model was formed. Right? So, let's see what things he said and what he said. See, understand. Here, the alpha particle is coming, brother. Right? A radioactive substance is emitting alpha particles. Alpha particles mean helium nuclei. Alpha particles come and hit this gold foil. They get deflected. You see, they are deflected at different angles. Right? Why are they deflected? We will understand the reason. And he has done what? He has put a film all around. A film, a screen. It is coated with zinc sulfide. So, as soon as any particle comes and hits it, it will glow there. And from that, it will be known at what angle this particle was deflected. Right? Why did he take gold foil? One reason is that gold is not cheap. Right? He could have taken iron, it is cheap. Gold is so expensive, damn it. Right? So, it's not that he was a very wealthy person. No. Right? But he took it because gold, brother, very thin sheets of gold can be made. If you take a thick sheet here, then it is possible that the alpha particle may not pass through that sheet. Right? So, for this reason, the sheet we had to take was thin. And for that, gold foil was the most suitable. We had to take a thin sheet, and that could be of gold, because very thin sheets of gold can be made. First thing. And the second reason was that the metal required here should be heavy. Right? Heavy metal means that its nucleus will have a lot of positive charge. And the more positive charge there is, the more it will deflect this alpha particle. So, the angle of deflection will be good, which will be easy to measure. Did you understand my point? Right? So, these were the reasons why he took it. Because gold itself is a heavy metal. Right? Done. Let's move on. What were his observations? They are written in front of you. Right? And all of you know the observations. The observation was that most of the alpha particles passed straight through without any deflection. Very few particles were deflected at some angle. And among them, very few alpha particles, one out of 18-20,000 particles, came back on the same path it went. 180-degree deflection. Right? Completely rebounded. It is called complete rebound. Right? But such particles were the least. Now, the number is also written here. That is, one out of 5000 came back. Some say one out of 20,000 came back. You don't need to remember that number at all. Just remember the observation. That maximum alpha particles will not be deflected. And some alpha particles will be deflected. What did he conclude? Now, think about it yourself. What is an alpha particle? It is a positively charged particle. What is it? Positively charged particle. Sir, if it is a positively charged particle, and if something can deflect it from its path, it means that it must also be positively charged. Right? Think about it. Positive charge is placed here. Your alpha particle is coming from here. It also has positive charge on it. So, brother, positive will repel. Right? Brother, in science, positive repels positive, positive attracts negative, negative repels. But in daily life, anything can happen. Any attraction, any repulsion, anything can happen. Nowadays, you can't trust anything. Right? But here, we know that the alpha particle is a positively charged particle. If a positive charge comes in its path, only then will the alpha particle be deflected. Now, think about it. If this positive charge was spread throughout the entire atom, then many alpha particles should have been deflected. But it was not so. Very few alpha particles were deflected. This means that the positive charge is not spread throughout the atom. Most of the alpha particles are passing through without any deflection. This means that the positive charge is in a very small, very small space. That is why it will not come in the path of most alpha particles. Right? And most alpha particles will pass straight through without any deflection. Some alpha particles will be deflected. Some more. This means that the distribution of positive charge is in a very small space. Right? And it is here, it is here that later he named it. He said that this small space where the positive charge of the atom is located, that space is called the nucleus. What did he name it? Nucleus. And by doing some calculations, he also told that the volume of the atom. Yes. The radius of the atom is 10^-10 meters. And the radius of the nucleus is 10^-15 meters. This means that the radius of the atom is quite large compared to the radius of the nucleus. So, here he also said that the volume of the nucleus will be negligible compared to the volume of the atom. Very less. Yes. Are you understanding my point? Right? Brother, our speed is a bit high here. The speed is high because you are learning all these things since childhood. Right? Very easy things. Yes. Now, after this, based on these observations and conclusions, he designed his atomic model. Right? So, first of all, he told about the nucleus. That brother, the nucleus is present in a very small space inside the atom. The distribution of positive charge is not uniform, as Thomson said. So, as soon as this experiment happened. Right? And it was found that the distribution of positive charge is not uniform, Thomson disappeared. Right? Haven't found him yet. Right? Come. Then what did he say? He said, brother, there is a nucleus, it has a positive charge, and the electrons are revolving around it in a circular path. And this circular path, what did he name it? He named it orbit. Right? So, this is also that brother, the electron will be attracted towards the nucleus, and there will be a centrifugal force outwards, which balances it. Due to which, this electron is continuously revolving in this circular path. Done. From here, he designed his atomic model in this way. But see, he designed the atomic model. He said that the nucleus of the atom is very small. Right? And the positive charge is present in the nucleus. And the electrons are revolving around the nucleus in a circular path. Right? The force of attraction acts from inside, the centrifugal force from outside balances it. But there is no shortage in the world, right? Meaning, people with different minds also found flaws in this. Right? And first of all, we have to study two flaws, which we study in the limitations of Rutherford's Atomic Model. Right? Okay. Among these limitations, the first thing is that this Rutherford cannot explain the stability of the atom. Someone will ask, how can he not explain? See, there was a brother named Maxwell. Right? He gave a theory. What did Maxwell say? That if any charged particle is accelerating, then it will emit some energy in the form of radiation. What does it do? It emits energy. So, as your electron is revolving around the nucleus, it means it is accelerating. So, it should emit radiation, emit energy. And if it keeps emitting energy, it will come closer and closer to the nucleus. One day will come when it will enter the nucleus. Yes. It will collapse into the nucleus. Does this ever happen? Have you ever seen an electron entering the nucleus? Have you seen it happening? If this happens, then your atom will not remain stable. But according to Maxwell, this should happen. Because the electron is revolving around the nucleus, and if there is acceleration, then all this should happen. But it does not happen. Why does it not happen? Rutherford had no answer for this. Right? And when there is no answer, then brother, atomic models are bound to fail. Right? The first reason was this. The second thing is, what did he say? He said that the electrons revolve around the nucleus in a circular path. People accepted it. They said, okay, they revolve. Someone asked, okay, tell me, will all electrons revolve in the same path? Or will two electrons revolve in different paths? Eight in different paths? Eighteen in different paths?

We will move to a different topic, and if it failed, man, I didn't even think about it. So, brother, when you don't think, the world will categorize you, right? So, in this way, this also has its limitations. Rutherford cannot explain both these things. He cannot explain how atoms are stable, why the electron does not collapse inside the nucleus, and he also cannot explain the arrangement of these electrons around the nucleus. The arrangement of electrons around the nucleus, he cannot explain this, okay? Did you understand what I said? Okay, brother. Now there is a question. In which year was it asked? JEE Mains 2011. Read this question carefully, what is it saying, understand it, and tell me its solution. Quickly, let's see. It says that if Thomson's atomic model were correct, what would happen in the experiment? Let's check. If Thomson's atomic model were correct, it would mean that the positive charge was spread throughout the atom. Positive charge, right? But a little bit, right? Because the positive charge has to spread throughout the atom, so its distribution is a little bit, its density is low. Alpha particles are coming from here. Alpha particles will say, "I have positive charge." This positive charge will say, "Son, I will deflect you." As the alpha particle comes closer, its speed will gradually decrease. Do you understand what I'm saying? Repulsion, yes, due to repulsion, due to positive repulsion, the speed will decrease. First thing. And the second thing, the deflection of alpha particles will also happen. Maximum alpha particles will be deflected, but at a very small angle. At a small angle, why? Because the positive charge will be distributed a little bit everywhere, right? The positive charge has to spread throughout the atom, so it will be present a little bit everywhere, right? And because of this, it will not be able to deflect the alpha particle much. In my opinion, this story is clear. Yes, very good. Atomic mass, mass number, what is it? In my opinion, there is no need to tell. Atomic mass, we represent atomic number by Z, and it is generally equal to the number of protons. Yes. And the mass number, we represent it by A, and what is it equal to, son? Number of protons plus number of neutrons. Right? It is equal to this. An element is A, right? Let's write M. An element is M, whose atomic mass is Z, and mass number is A. It is represented like this, right? This is its representation. You all know this. Now let's move on and talk about a small thing. What are isotopes, brother? Isotopes. If I talk about isotopes of hydrogen, like 1H, 2H, 3H. See, you all. Sir, the atomic number is the same. Sir, the mass number is different. Right? Atoms of the same atom, of the same element. The element is the same, hydrogen. Its different atoms have the same atomic number but different mass numbers. Such substances are called isotopes. Okay? Yes. Good. Let's calculate the neutrons. Let's do a question on this. See, in which year was it asked? 2020. Tell me, a question was asked on neutrons. Really. Come on, let's see. Its atomic number is 1, son. Proton 1, proton 1, proton 1, right? All three have one proton each because the atomic number is one. Now look, its mass number is 1, right? It means neutron plus proton is 1. So, it means neutron is 0. It has a mass number of 2. It means it has one neutron. Its mass number is 3. Yes, it means it has two neutrons. The question is, what will be the sum of neutrons? You will say it will be three. Look, the question is saying the same thing. If you don't believe it, read it. It is the same question that I just told you. Hydrogen has three isotopes. It says the number of neutrons of the respective ones are x, y, z, right? The chemical properties, the chemical properties depend on the number of electrons. They don't have much to do with the number of protons. So, the isotopes, isotopes, son, isotopes, son, look, it is written that isotopes have the same chemical properties because they have the same number of electrons. That's why isotopes have the same chemical properties. Okay? Tell me, what is correct? Yes, yes, very good, very good. Substances in which the same number of neutrons are present. What are the same number of neutrons present? Sir, give an example. Oh, take it, brother, take it. Look at this. And take this. If you calculate the neutrons here, you will get seven, right? And if you calculate the neutrons here, you will also get seven. Are these two each other? These two are each other's isotopes. What are isotones? They are each other's isotopes. Right? Keep this in mind. Isoelectronic species. In my opinion, there is no need to tell. You have read it many times. Its name is shouting at you. Iso means same. Electronic means electrons. Yes. And besides this, I can write Neon. 2F minus. If you check all of these, the number of electrons is how much, son? 10. Check it if you don't believe it. Right? And it is 10. It means all of them have the same number of electrons. Sir, how can these be? Isoelectronic. How can they be? Isoelectronic. Understood? A question. Let's see. In which year was it asked? Oh brother, 2023. And sir, this latest question. Do it, but finish it. Tell me what it is saying. It is asking for isoelectronic, right? What? Isoelectronic S2 minus. It has spoiled the game. How can they be? When can they not be? They can be. Mg2 plus. This is 2 plus. Where is it? It has 18 electrons. Look at K plus 18. Cl minus 18. Ca2 plus 18. S3 plus 18. Sir, the options have a lot of love for K. Right? It asks questions like this every time. So, keep in mind that knowing the question of isoelectronic is important. Yes. The pair in which isoelectronic. Homework, brother. Right? This is also from 2022. I was telling you, right? It has a lot of love. It was asked in 2022. Specific charge of proton and alpha particle. I have already told you about specific charge. You have to tell its ratio yourself. Come, let's see another type. Right? Although it is more useful in radioactivity. What are isodipers? Isodipers means neutron minus proton. Present. Like if you have Thorium 234 in front of you. So, here the proton is visible to me. Atomic number is 90, meaning proton is 90. And the number of neutron plus proton is 234. So, from here, you can do what? You can find the neutron. Subtract 90 from 234. You will get the neutron. And after getting the neutron, you have to find the value of neutron minus proton. Here also you can say, brother, the atomic number is 92. It means proton is 92. Yes. And the value of neutron plus proton is 238. So, from here, you can find the neutron. Subtract 92 from 238. And here also you will find its value. You will find the value of neutron minus proton. You will see that both these values are what, son? Same. So, such substances in which the value of neutron minus proton is the same. There is one more example. There is one more thing whose name is isosteres. What are they? It is written here. These are atoms, molecules, or ions whose size is approximately the same. Similar size containing the same number of atoms or valence electrons. Same number of atoms and valence electrons. For example, I have written O2, 2 minus, O2 minus, and Neon. Both have 6 electrons in their valence shell. You can check. Sorry, eight electrons in the valence shell. And both have the same number of atoms. One atom each. Like, suppose I wrote F minus and Neon. Both have the same number of electrons in their valence shell. Seven. Both their sizes are almost very similar. Right? And along with that, both have the same number of atoms. So, such substances, these are known as what? They are called isosteres. In my opinion, the story is clear up to here. There should be no problem. Tell me. These are very easy things that we have learned so far. Okay? Very good. So, after this, we will move forward and talk about, son, the dual nature of electromagnetic radiation. Right? Dual nature means what here? That your electromagnetic radiation shows a double nature. Right? Which ones? One is wave nature, and sir, the second is particle nature. Yes, sir. It shows these two natures. Wave nature and particle nature. Let's see what wave nature is and what particle nature is. But before that, before that, we will talk about what? Oh brother, what is electromagnetic radiation? Tell us that first. Right? So, electromagnetic radiation, look, son, what is electromagnetic radiation? Electromagnetic radiation is such radiation in which electric field and magnetic field both propagate perpendicular to each other, and both are also perpendicular to the direction of propagation. What does that mean, sir? Tell me again. Like, suppose there are three things. One is electric field, second is magnetic field, and third is direction of propagation. All these three things are perpendicular to each other. If the magnetic field is propagating in the X direction, the magnetic field is oscillating on the X-axis, then your electric field will do the same, and the direction of propagation will be Z. So, such radiation, radiation means a form of energy, in which the electric field and magnetic field oscillate perpendicular to each other, and they are also perpendicular to the direction of propagation. These are known as electromagnetic radiation. Right? And whenever a charged particle is under acceleration, it emits this radiation. What is written? That this electromagnetic radiation travels at the speed of light in a vacuum. What are you saying? Absolutely. At the speed at which light travels. Second, they do not need any medium to travel. Tell me, they can travel in a vacuum too. Very good. Yes. And what is in them? The electric field and magnetic field are perpendicular, perpendicular to each other, and also perpendicular to the direction of propagation. Yes, we already know this. And look, electromagnetic radiations can be different from each other. How? When their wavelength is different. When their frequency is different. So, electromagnetic radiations can be different from each other. Okay? Good. One thing comes, whose name is electromagnetic spectrum. What is the name? Electromagnetic spectrum, son. All the electromagnetic radiations you have, if you arrange them in an increasing or decreasing order. You will say, sir, increasing or decreasing what? So, son, you can take the increasing or decreasing order of their frequency. You can take the order of their wavelength. It's up to you, whatever you feel is right. Take the increasing or decreasing order of either of them. The arrangement that will be formed, that particular arrangement will be known as the electromagnetic spectrum. What is it called, son? Electromagnetic spectrum. Understood? And look, this order is written in front of you. I want you to remember at least this order. First gamma rays, then X-rays, then UV, then infrared, microwaves, radio waves, and finally long radio waves. Right? You need to know these things. They are important. And as you go from here to there, the frequency is decreasing, and the wavelength is increasing. Right? You notice one thing here, son. The ultraviolet region and the IR region. Between these two, who is present? The visible region. Right? Between UV and IR, what is present? The visible region is present. Right? That's right. So, after the electromagnetic spectrum, we need to look at some small, small things. Right? Like, suppose what is wavelength? What is wavelength, brother? This is your electromagnetic radiation, right? In this, in this, this maximum is called crest, and this minimum is called trough. The distance between two adjacent crests. Here, the distance between two troughs. You can call this lambda. You can call this wavelength. It is a kind of distance. Okay? What is frequency? Frequency is that in one cycle, in one second, how many cycles does your electromagnetic radiation complete? Sir, what does cycle mean? Oh, this is not that cycle, son. This is a cycle. It means this is a cycle. So, the number of cycles per second, whatever they are, will be called frequency. Frequency is represented by nu. Right? Frequency is represented by nu. Its unit is second inverse, or its more famous unit is what? Hertz. What is it? Hertz. Okay? There is a term called period. What does period mean? Like, suppose your electromagnetic radiation. To complete one cycle, one oscillation, the time it takes is called period. Right? And nu and T have a relation. Nu has a relation. You have to remember this. This is your time period. Right? Nu is equal to 1 by T. What does velocity mean? You already know. The relation is nu is equal to c by lambda. You have to remember this. Questions are asked on this formula. Yes. Here, what is C, son? Speed of light. Right? Speed of light. You can call this velocity. Come, there is a question given on your screen. Right? There is a question given on your screen. Look at this question carefully. What does it say? That a frequency modulated station, which is India Radio's Delhi broadcast at a frequency of, son, the frequency is given. Frequency is given. 1368 kilohertz. Meaning 10 to the power 3 hertz. Calculate the wavelength of the electromagnetic radiation emitted by the transmitter. Tell me, what to do now? Right? Wavelength is asked. The whole world knows that nu is equal to c upon lambda. Yes. So, you have the frequency. You have C. You need lambda. What will lambda be, son? 3 into 10 to the power 8 divided by frequency 1368 into 10 to the power 3. Right? And by solving this, you will get it in meters. Tell me, how easy it is. Yes, yes. Say something, brother. Frequency is defined for waves. Your lambda. Sir, all this is defined for waves. But there are some phenomena that you cannot explain with the wave nature of electromagnetic radiation. Sir, which phenomena are those? Black body radiation. You cannot explain. Photoelectric effect. You cannot explain. Variation of heat capacity of solids with temperature. This cannot be explained. And hydrogen spectrum. These are some phenomena that cannot be explained by the wave nature of electromagnetic radiation. And for that, we needed to assume the particle nature. Like diffraction, interference. These are some phenomena that can be explained by wave nature. You cannot explain them by particle nature. These are phenomena that require particle nature to explain. Wave nature cannot explain them. So, now what do we have to do? We have to read about these phenomena. But this thing, we don't need to read it here. Right? We will not read this thing here. Then, first of all, we have to talk about what? Black body radiation. What is it? Look, black body radiation. It is such an ideal body. Right? To which you give light of any frequency. It digests everything. And when it comes to emitting back, it can also emit back radiation of all frequencies. Such an ideal body is called a black body. And the radiation emitted by this black body is called black body radiation. Now, someone will ask, sir, why are you using the word ideal here? Because generally, such a body does not exist. Right? That can absorb light of all frequencies and also emit it. Such a body does not exist. Right? But still, a definition has been made. Here, a graph has been made. That the wavelength of this black body radiation and the intensity. At a particular temperature, in front of you. Look at this. What is this graph saying? This graph is saying that as you increase the wavelength, the intensity will increase. It will be maximum at a particular wavelength. And even if you increase the wavelength further, the intensity will gradually decrease with temperature. Now, the explanation of this graph has to be given only by particle nature. The wave nature of electromagnetic radiation cannot explain this graph. Right? Clear? So, there is no calculation part here. You will read more about this graph in physics. Yes. So, no calculation part is asked in black body radiation. So, this was about black body radiation. Now, after this, we have to talk about what? Planck's quantum theory. So, what does Planck's quantum theory say? Let's see. It is written about Planck's quantum theory in front of you. Right? What does Planck's quantum theory say? Very easy thing. Look, what did Planck say? He said that whenever an atom or molecule, meaning, I'll take one name, particle. Whenever a particle emits radiation, it emits energy. What does it do? It emits energy or absorbs energy. So, Planck said that this absorption of energy or emission of energy happens in the form of small packets of energy. No atom or molecule emits energy continuously. It does not emit radiation of all frequencies. It only emits small packets of energy. Right? And the smallest packet of this energy was given the name what? Quantum. What was the name given? Quantum. And if I talk about light, then in the case of light, the smallest particle of energy is known as a photon. Right? Like, suppose a photon is the smallest packet of energy, of 3 joules. Right? The smallest packet was of 3 joules. So, your atom, you know, can absorb how many joules of energy? It can absorb 3 joules if it absorbed one packet. It can absorb 6 joules if it absorbed two packets. It can absorb 9 joules if it absorbed three packets. It can absorb 12 joules if it absorbed four packets. So, this absorption of energy is always not continuous, but in the form of packets. And this energy of the photon, he also did calculations. He said that the energy of a photon is directly proportional to the frequency of light. Yes. And if you remove the proportionality sign from here, you will use a constant, H. You have named this H as Planck's constant. Yes. Planck's constant. Its value you know, 6.62 into 10 to the power minus 34. Yes. This is the energy of one photon. Right? Here, you can also write C by lambda instead of nu. Right? So, this is the energy of one photon. Right? Energy of one photon. Now, if someone asks you, sir, suppose there are N number of photons. Then, son, the energy of N photons, you can calculate it very easily. If this is the energy of one photon, then to find the energy of N photons, what do you do? Multiply it by N. Yes, yes. Is that clear? You can multiply it by N. That's it. Now, numericals are formed on this, which are asked in exams. Right? Come, then let's look at those questions, those numericals. In front of you is a question from 2022 JEE Mains. Right? Look at this question. What does it say? It says, tell me the energy of one mole of photons. Right? The value of H is given to you in the question beforehand. And the value of wavelength is given, son. Wavelength is given as 300 nanometers. Convert it into meters. 300 into 10 to the power minus 9 meters. This is done. Now you can also write it as 3 into 10 to the power minus 7 meters. You have got the value of lambda. Calculate the energy of one photon. You said, sir, the energy of one photon, one photon, how much will it be? It will be, sir, HC by lambda. And what is asked from us? What is asked from us is one mole of photons. Right? So, energy of one mole of photons. One mole means Avogadro's number. So, multiply this energy by Avogadro's number and be happy. Just calculation. So, you have to do it yourself. Right? You expect me to solve it? No. Right? The value of H is given to you in the question. C, we already have C, 3 into 10 to the power 8. Right? And the value of lambda is also here. Just solve this and get the answer in power. I have heard that your calculations are excellent. Right? You will finish this easily. Right? So, see its solution. It will be one of these questions. But what I want to tell you is that such simple questions are asked. Nothing complicated. This chapter is a very easy chapter. Although it is a bit lengthy, a big chapter, but easy questions are asked from it. It is not actually a difficult chapter. Right? So, you also have to study this chapter in the same way. And very simple questions. Even if you look at JEE, Mains, Advanced, from this chapter, you will find very easy questions. Right? Let's move on. Let's do one more question. The ratio of photo energy. Energy is HC by lambda. So, I can write it as energy is inversely proportional to lambda. So, if I have to write E1 by E2, it will be lambda 2 by lambda 1. Yes. Oh, son, you have to say it. Yes. You have to say it, son. So, your lambda 2 is how much? 4000. And lambda 1 is how much? 200. 200. This is gone. Sir, it is not found here. 200 is not there. Then it is 2000, brother. Now make it 2000. So, you will get, sir, 2 by 1. Right? What will be the ratio of energy? 2 by 1. Here is option number D, correct. Right? Very simple questions come from this. And look, let's do some more questions. Here, what do you do? Let's assume. Let the number of photons be, son, let's assume N. Let the number of photons be N. 4000 picometers means 4000 into 10 to the power minus 12 meters. Which, after calculation, will be 4 into 10 to the power minus, what will it be, brother? 10 to the power minus 9. Yes. So, brother, it has become very easy now. What will be the energy formula? E is equal to NHC by lambda. Yes. Energy is with me. 1 joule. We don't know the value of N. The value of the number of photons. The value of H. The whole world knows it. The value of C is 3 into 10 to the power 8. And the lambda will be, sir, 4 into 10 to the power minus 9. Yes. Solve it and find the value of N. Be happy. That's it. Right? So, these are the kinds of questions. These are your NCERT questions, but very good questions. Questions like these can be asked. Right? So, son, this was Planck's quantum theory. Now, after this, we are going to read about another very wonderful concept. And the name of this concept is what? Photoelectric effect. What is it? Very easy thing. Like, suppose you have a metal surface. This metal surface will have many metal atoms. Atoms will have many electrons. Here, when you shine light of a certain frequency. Right? What are you doing? You are shining light on its surface. Right? But by shining light of a certain frequency, you have noticed one thing. That this metal surface ejects its surface electrons. The metal surface ejects electrons. And the ejection of electrons from any metal surface, those electrons are called photoelectrons. And this phenomenon is known as the photoelectric effect. What is this phenomenon called? Photoelectric effect. Very easy, simple thing. Right? This shows this. You have a setup like this. Right? Light is coming from here. As this light hits this metal surface, electrons will come out from here. These electrons will move from here to here. The circuit will be completed. And here, in the ammeter, there will be a deflection. As there is deflection in the ammeter, it means current is flowing. Current is flowing, so it can only be possible when some particle comes from here to here and completes the circuit. Meaning, ejection of electrons has happened. Now, the question is, why does it happen? The story behind it is very simple. Very easy thing, brother. Look, like, suppose this is the nucleus, and the electron is revolving around it. Right? You have shone light of a certain frequency from here. Right? A photon of light will come, and it will hit this electron. It will absorb that photon. And then what will happen? Look, think about it. This is an electron, and this is negative and positive. The world attracts each other. Right? In chemistry, plus and minus always attract each other. So, there is attraction between these two. And what have you done? You have not seen this attraction. You don't see attractions in the world, right? So, the world will try to break this attraction. Yes. And to break this attraction, what do you have to do? You have to give energy to this electron. Yes. Right? You have to give energy to this electron. In chemistry, whenever you have to break the force of attraction, you have to give energy. So, you have given so much energy to the electron that this electron will break this force of attraction and run away from here. It will go out of this metal surface. But remember, if this electron does not have enough energy to break this force of attraction, then this electron will not come out of the metal surface. That is why I said that light of a certain frequency has to be shone. Meaning frequency means energy. Yes. Frequency is directly proportional to energy. Energy is directly proportional to frequency. Yes. So, if the frequency is less than a certain frequency, then it will not come out of the metal surface. If the frequency is more than a certain frequency, then that electron will come out of the metal surface. And this minimum frequency, which is used to eject any electron from the metal surface, son, that minimum frequency is called threshold frequency. What is it called? Threshold frequency. Yes. So, the electron will never come out of the metal surface before the threshold frequency. This is its first observation. Yes. This frequency, the minimum frequency required to eject any electron from the metal surface, what do we call it? Threshold frequency. Yes.

This is shown by the new note, okay? First, this was a metal surface. This electron came. This, sorry, photon came, and the photon is hitting this electron from here, right? And this photon has enough energy to make this electron come out. So it won't be like the photon will come, say hello to it, right? And this electron will absorb this photon, and say, "Let me have some tea and water and then I'll go out." It doesn't happen like that, brother. As soon as this photon hits it, the electron will come out from here. There is no time lag in this photon hitting this electron. Remember this point, okay? So, no time lag.

Second point you need to remember is, no time lag. If a photon with sufficient energy hits this electron, then your electron will come out of this metal surface. One more thing was observed: the number of photoelectrons that came out of the metal surface is directly proportional to the intensity of light. That means the number of photons. So, the more intense the light, the more photoelectrons it will eject. And a very important thing is, it is independent of the frequency of light. It is independent of the frequency of light. Whatever the frequency of light, it will not affect the number of photoelectrons. This is a very important thing. If I draw a small graph in front of you, okay? If I draw a small graph in front of you, here, I have written the number of photoelectrons. And here I am writing the frequency. Here I have written the frequency. Now, understand, I want to draw two graphs in front of you. The first graph is this one. What does this graph tell you? This graph tells you that until the frequency reaches this point, no photoelectrons will be ejected. The first photoelectrons are being ejected at this frequency. So, this frequency is the threshold frequency. At this frequency, this many photoelectrons have been ejected. And now, if you increase the frequency further, increase the frequency, it will not affect the number of photoelectrons. This is what is understood from here. These number of photoelectrons do not depend on frequency to eject the electron. But after that, if you increase the frequency, it will not affect the number of photoelectrons. Yes, let's assume this light was for low intensity. Okay, let me increase the frequency slightly, sorry, intensity. So, when I increased the intensity, I observed this: the graph I got this time is this. Even now, photoelectrons will be ejected at this frequency, but here this is high intensity light. This light is high intensity light. That means when I used light with more intensity, I got more number of photoelectrons. This was the first observation, and the second was that it has no dependency on frequency. This is a very important thing. Then I wrote, what will the kinetic energy of the photoelectron depend on? So, I noticed that the kinetic energy is directly proportional to the frequency of light. Yes, it is directly proportional to the frequency of light. And it is independent of what? It is independent of what? It has nothing to do with the intensity of light. Yes, it has nothing to do with the intensity of light. Yes, for example, if you want to draw a graph between kinetic energy and intensity, okay? Between intensity and kinetic energy, okay? Brother, this graph will be like this. Increase the intensity, decrease it, the kinetic energy doesn't change. But if you draw a graph of kinetic energy, kinetic energy is directly proportional to frequency, right? So, the graph that will be formed here is kinetic energy, and here is frequency. So, brother, the graph that is going to be formed will be like this. From this frequency onwards, the electron will not be ejected. So, the kinetic energy will be zero. Here, for the first time, the electron is ejected at this frequency. So, I am going to name this frequency as threshold frequency. Do you understand what I am saying? Yes, yes. So, these are the observations. And based on these observations, there was a gentleman whom the world knows as Albert Einstein. He observed and explained this photoelectric effect. He said that the total energy you are giving through the photon, yes, the total energy you gave, this total energy does two jobs. This total energy does two jobs. First, it will eject that electron from the metal surface, and the energy required for that is called the work function. And second, if some extra energy is left, if some extra energy is left, then it will convert into kinetic energy. So, the total energy, which is received through the photon, will do two jobs. First, it will eject that electron from the metal surface, and the energy requirement will be known as the work function. And here, the remaining extra energy will be converted into its kinetic energy. So, from here, I can write the total energy as h-nu. The work function will be phi. So, from here, you can write the formula for kinetic energy as h-nu minus phi. Okay? Here, nu naught means what is nu naught? It is the threshold frequency. Hey, do you understand what I am saying? Yes, yes. And this h-nu naught is what is called the work function. Where h is Planck's constant. Okay? Now, the questions that are asked are based on this formula. For example, here is a question on your screen. What is this question asking? The question tells me that light of wavelength, okay, wavelength is given, brother. Wavelength is 4000 Angstroms. Wavelength is this much. That is, lambda naught is also given as 5420 Angstroms. And what is asked? Work function. Oh, brother, work function is asked, right? Work function is denoted by phi. It is h-nu naught. And instead of nu naught, I can write c upon lambda naught. You know the value of h, you know the value of c, lambda naught is in front of you. Solve this, and you will get the energy, or the work function. You can call it either. It's your choice, your wish. You can call it either. Is the story clear up to here? Okay, let's move on. Let's see one more question. What is it asking? Work function is given, right? Work function is given, meaning h-nu naught is given as 3.2 * 10 to the power minus 19 Joules. Kinetic energy is asked. So, what's the problem with this? What is the formula for kinetic energy, brother? H-nu minus phi. The value of phi is already there, and I have the value of nu. So, multiply by h. 6.62 * 10 to the power minus 34. And nu is 8 * 10 to the power 14. This is the value. Solve this. You will get the kinetic energy. Tell me, is there any problem with this? No, it's a very easy question. Okay, let's move on. In which year was this question asked? It was asked in 2019. What is the question asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H Z square (1 upon n1 square minus 1 upon n2 square). Where R H is the Rydberg constant, and its value is 109677 per centimeter. Z is the atomic number. n1 is the lower energy level, and n2 is the higher energy level. So, if you want to find the wavelength of the emitted radiation, you can use this formula. And if you want to find the frequency, then frequency is equal to c upon lambda. Okay? Now, you have noticed that the spectrum of hydrogen has many series. Which series are there? Some groups of lines are called series. And what is the meaning of those series? And which group of lines will be called? For example, if I talk about the Lyman series, the Lyman series means that for this, the value of n1 is always 1. The electron always comes to the ground state. And the value of n2 can be anything, 2, 3, 4, up to infinity. Okay? Yes. Okay, now these lines of the Lyman series, brother, are in the ultraviolet region. You should know this. After Lyman comes Balmer. Right? The lines of the Balmer series are called those lines for which the value of n1 is 2. And the value of n2 will be from 3, 4, up to infinity. These lines are in the visible region. This question is often asked. Then comes Paschen. Right? The value of n1 is 3, and the value of n2 is 4, 5, up to infinity. This is in infrared. After Paschen comes Bracket. Right? Then comes Pfund. Right? Then comes Humphreys. Now you must have understood what it is, right? Bracket means n1 is 4, and n2 is 5, 6, 7, up to infinity. It can be anything. Here, the value of n1 will be 5. Here, the value of n1 will be 6. Here, the value of n2 will be 6, 7, 8, up to infinity. And here, the value of n2 will be 7, 8, up to infinity. So, you should know about these lines. Second thing, all these lines will be present in the infrared region. These lines are present. Okay? If, for example, the question asks you that the first line of the Lyman series. The question asks you that the first line of the Lyman series. This means the electron is coming from 2 to 1. The answer you want is that the electron is coming from 3 to 1. If it says the ultimate line, the last line of the Lyman series. This means it is coming from infinity to 1. So, the value of n2 is infinity, and the value of n1 is 1. Okay? If, for example, the question says the first line of the Balmer series. This means the electron is coming from 3 to 2. But the line means it is coming from 4 to 2. And the last line means it is coming from infinity to 2. So, the second type of question that is asked on this topic is this. What other questions can be asked? And that question is, you might be asked that, brother, in the Lyman series, what will be the transition of the electron corresponding to the least energy? Least energy, by obvious logic, will be when the electron comes from 2 to 1. Lambda max means minimum energy. And the transition corresponding to the least energy in the Lyman series is from 2 to 1. Is the point clear? Yes. Okay? You might be asked that what will be the transition corresponding to the maximum energy? So, you will say maximum means it is coming from infinity to 1. So, it will emit the most energy. And I max means lambda minimum. I might also ask you to tell the transition with the minimum wavelength. So, the transition with the minimum wavelength will be from infinity to 1 for the Lyman series. Okay? If I talk about the Balmer series, and if I ask you about the minimum wavelength, minimum wavelength means maximum energy. And maximum energy means from infinity to 2. If I ask you about the maximum wavelength, it means minimum energy. And minimum energy means from 3 to 2. So, these are the second types of questions that are asked. This question is asked in which year? 2019. What is it asking? Write the question. Which of the graphs shown below does not represent the relationship between incident light and electrons ejected from the metal surface? First, kinetic energy and energy. Absolutely correct. This graph is absolutely correct. Kinetic energy has nothing to do with intensity. This graph is also correct. Number of electrons does not change with frequency. This graph is also correct. And here, the graph of kinetic energy and frequency is started from zero. It will not start from zero. The graph starts from further ahead, from the special frequency. So, it says, give any frequency, and the electron will come out. That's wrong, brother. It will not start from here. It will start from here. The incorrect one is asked. The last option will be correct. Okay? Let's move on after the effect. And that is, yes, we will talk about what is a spectrum. You must have studied it in physics. For example, if you have a prism, white light comes from here, and this prism splits the white light into seven different radiations, seven different colors. And this you have written is in increasing order of lambda. Red has a higher lambda. So, in a way, you have arranged different radiations on a photographic film. And this arrangement is known as, what is it called, brother? Spectrum. Now, this spectrum you are seeing is a continuous spectrum. Why continuous? Because you see, one color merges into another, the second into the third, the third into the fourth, the fourth into the fifth. There is no discontinuity anywhere. So, this type of spectrum is known as continuous. Actually, there are two types of spectrum, brother. Continuous. See, here from here to here, there is no discontinuity in between, right? This is a continuous spectrum. This one is also continuous. This one is also continuous. And what is this continuous spectrum? You can call it discontinuous or line spectrum. Look at your screen. There is light from here to here. In between, the light is missing, right? There is discontinuity here. Then, after that, again, you have wavelengths in front of you. In between, the wavelengths are missing. Then there are wavelengths, then missing, then there are. So, these examples are examples of discontinuous spectrum. Continuous means that light of every frequency is present in a certain range. And discontinuous means some frequencies of light are not present there. Now, this discontinuous spectrum is also of two types. Which ones? One is emission, and the other is absorption. Which ones? Emission and the other is absorption. Okay? So, what do we need to talk about? Emission line spectrum. What will we talk about? Emission line spectrum. Why is it called that? You can see it, right? Because when I am talking about the discontinuous spectrum, see, you can see lines in between, right? It looks like lines, yes. Many times, the lines are dark, and these lines are bright. So, many times, the lines can be dark or bright. It depends on the type of spectrum. So, if I talk about emission line spectrum, then what is emission line spectrum? Understand it a bit. Understand it a bit. For example, if you have a sample, and you heat it intensely. So, this sample will have many atoms. Those atoms will have many electrons, right? So, that electron, let's assume, was present in its ground state before heating. When you heated it, this electron got energy, and it jumped from here and went to the excited state, to the state with higher energy. Now, you know that no electron is stable in a higher energy state. So, what will it do? It will realize its mistake and try to come back to its ground state, to the state with lower energy. Yes. Now, when it comes to the lower energy state, when will it come? Only when it emits some radiation, only then can it come to its lower energy state, right? So, the radiation it emitted, the energy it emitted, energy in the form of radiation. And these radiations it emitted, you passed them through a Nicol prism, and after passing through the Nicol prism, you made a spectrum of them on a photographic film. [Music] So, on this photographic film, you will get how many lines? You will get four lines. You will see lines here. From this, you will know that this sample of yours emitted which radiations, which wavelengths of light, right? And because you have put the emitted wavelengths into the spectrum, so this spectrum is known as emission. What is it called? Emission spectrum. And why is it called emission line spectrum? Because you can see lines. Do you understand what I am saying? Yes, very good. Okay, in this, you can also write a small formula for stopping potential. You can write a relation for stopping potential. Kinetic energy equals potential. This formula you can write. Kinetic energy and stopping potential. Stopping potential means that potential at which the movement of your electron will stop. The electron will stop. It will be stopped. And that negative potential is called stopping potential. So, this is a small story that you need to remember. Now, if I talk about hydrogen, then the spectrum of hydrogen, brother, is an emission spectrum, right? And the hydrogen atom was in its ground state. Yes, it was in its ground state. And when it went to the excited state and came back. Right? If, for example, you want to find the wavelength of the radiation emitted, what is the wavelength of the radiation emitted? So, there is a formula that you need to remember: lambda is equal to R H Z square. Yes. And Z is the atomic number. Z is the atomic number. Along with that, n1 is the lower energy state, and n2 is the higher energy state. So, the wavelength of the emitted radiation is given by 1 upon lambda is equal to R H

Atomic number, let's look at one more thing, Dada. What do we need to see? We know that sir, one electron volt is equal to 1.6 * 10 to the power of -19 Joules. So if I convert this into Joules, it will be -2.18 * 10 to the power of -80 * z² / n² Joules per atom. And if you want to convert it into calories, we know that one calorie is equal to 4.18 Joules, right? You can write this as approximately 4.2 Joules. So, divide this by 4.2, you will get the value in calories, right? But this formula, this formula is very, very important. Yes, this formula for energy, Dada, this formula is very important. There are quite a few questions on this that you get, that have been asked, and will continue to be asked in the future, that's our guarantee. And look, and look, if suppose, talking about this formula, talking about this formula, and if I calculate the energy of the first orbit from here, then you all calculate it, you will get -13.6, right? For hydrogen, right? We are doing this calculation for hydrogen, and we are doing this calculation for hydrogen because the value of z becomes one, right? If you look at the energy of the first orbit, the energy of the first orbit, e1, how much will you get? -13.6 * z² / n². How much did you get? -13.6 electron volts. Yes. If I calculate the energy of the second shell, -13.6 * z² / n², n² means 2², it will be -3.4 electron volts. If I calculate the energy of the third shell, it will be -13.6 * 1 / 3², z² this will be -1.52 electron volts. Okay? Now, if you calculate the energy of the fourth orbit, keep calculating like this, keep calculating, keep calculating. What is important that you need to keep in mind? What is important is that the energy of the fourth orbit will be more than the third, the third will be more than the second, and the second will be more than the first. This story will continue, meaning as you move away from the nucleus, as you move away from the nucleus, the energy is increasing, the energy is increasing, and the second important thing is that the value of 2 - e1 will be the maximum, then after that e3 - e2 will come, then after that e4 - e3 will come, right? This will continue like this, i5 - e4 will come. The meaning is that as you move away from the nucleus, the energy difference between two shells will gradually decrease. The energy is increasing, but the energy difference between two orbitals, between two shells, will gradually, gradually decrease. This is very important that you need to keep in mind. Yes, will you remember? Right? There is one or two more things. Suppose if I ask you, there is a term, right? There is one or two more things. So, where did this come from? Where did this come from? Right? Yes, let's write it on this side. Let's remove this homework. What's the matter? There is a term which is called what? It is called ionization energy. Dada, what is it called? Ionization energy. What is it called? Ionization energy. Its formula is, my brothers, what is the formula? Ionization energy is i infinity minus e1. To remove an electron from the first shell and take it to infinity. How much energy will be required? Yes. Now, the energy at infinity is zero, and the energy of the first shell is -z² / n², meaning 1 electron volt per atom. So, the direct formula you need to remember here, brother, for ionization energy, you should know it. Plus, plus 13.6 * z² electron volts per atom. This is a very important formula. Everyone will remember this formula and keep it in mind. Questions can be asked on this. Yes, will you remember? What do I have to say? Okay, Dada. Now, suppose what is similar to this? It's its sister, separation energy. Yes, separation energy, brother. Separation energy, what is it? An electron is there. Yes, it is revolving in some shell. Yes, it is revolving in some shell. You have to remove it from there and throw it to infinity. Right? To send the electron from the nth shell to infinity, the amount of energy required will be called what? Separation energy. And this is zero minus 13.6 * z² / n² electron volts per atom. Right? So, from here, you can also solve this and write the formula for separation energy as 13.6 * z² / n² electron volts per atom. Tell me, tell me, are you understanding, Dada? Yes. These are some formulas, you know. In physical chemistry, work cannot be done without formulas. So, it won't work here either. Okay, then after that, remember one more small formula. Maximum number of maximum number of spectral lines. How many maximum spectral lines can be formed? Suppose the electron is transitioning. Suppose the electron is transitioning, brother, from n2 to n1. The electron is coming, and how many maximum, how many maximum spectral lines can it form? The formula is, Dada, n2 - n1 * n2 - n1 + 1 / 2. Remember this formula and be happy. Yes, yes, will you remember this? This is a very easy formula, right? n2 - n1 + n2 - n1 * -11 + 1 / 2, right? With this formula, your question will not be wrong. You can also directly calculate the spectral lines if you want, right? You can also directly calculate if you want, but if you use this formula, your question will not be wrong. This is the direct formula. You can also calculate manually, right? You can also calculate manually and find out how many spectral lines we are getting in this. So, this was about what. Now we are going to talk about, after this, we will practice some questions on Bohr's atomic model. Okay, let's start. So, look at the first question written on your screen. Let's check it quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was -13.6 * z² / n² electron volts per atom. Yes, in z² / n² electron volts per atom. So, let's calculate the energy of the third orbit. It will be 1/9, right? And solving this, how much will you get? -1.51. Option number A is correct. Will it be? Tell me, is there any problem? No, right? So, this was an energy question. This is a radius question. Questions like this can be asked. Look, do this yourself. Then we have already done an energy question. Right? Do this yourself. Let's move on. Let's look at a question about speed. Very simple questions come in this. Straightforward questions. Nothing is asked by twisting it up or down. It says, the speed of the electron in the first orbit. The speed in Bohr's first orbit is X. So, tell me, what will be the speed of the electron in the third orbit? Nothing is given, so assume it is hydrogen. Right? Hydrogen is given here. Now, I told you the velocity is directly proportional to z / n. Remember the formula: 2.19 * 10^6 * z / n meters per second. Yes. So, here, look, I can say that the velocity is inversely proportional to n. Can you say that? So, you can write it like this: Velocity in the first orbit, v1, and velocity in the third orbit, v3. So, it will be n3 / n1, right? It is inversely proportional to n, right? So, the velocity in the first orbit is X. The velocity in the third is asked, sir. 3, and write 1. Sir, how much will v3 be? It will be x/3. Yes, yes. Tell me, tell me, can I say that? Option number B is correct. Finished. Velocity is equal to velocity. The most important thing in this is, if you don't remember the formula, if you don't know the formula, then brother, you will keep wandering around the question. The questions will not be solved. The formula is straightforward. Just remember the formula directly. There will be no problem in any question. It's as simple as that. Done. Okay, Dada. Now, you will have PYQs in front of you. And when all these PYQs, all these PYQs, you have to do them yourself. Right? Look at this question. It is written on your screen. Let's check quickly. What needs to be written? Look, the question is very simple. It is written: The ratio of the radius of which of the following orbits is the same as that of the first orbit of Bohr's hydrogen atom? Right? So, let's check for a moment. What is it trying to tell us? We had written the formula for the radius of the first orbit of hydrogen. Look, 529 * n² / z. And if I talk about hydrogen, n=1 is given, z will also be 1. So, the radius of the first orbit of hydrogen will be 0.59. The question is asking us, what is such an orbital whose radius is coming out to be 0.529? Right? So, you can do it easily. Look, Beryllium 3+. Yes, Beryllium 3+ is given. When n=2 is given. The z of Beryllium is 4. If you apply the formula for r, the radius of the second orbit is 0.59 * 2². And its atomic number will be 4. Yes. So, this is also coming out to be 529. And the radius in both of these is exactly the same. So, option number D will be correct. Finished. Yes. Let's move on to the next question. The radius of Bohr's first orbit of Helium+ is X. The radius of Bohr's second orbit of hydrogen is. Yes. Such questions are asked quite a lot. When you do PYQs, you will also know. Look, when you write the formula for radius, how do you solve such questions directly? You should know this formula. I can say that the radius will be directly proportional to n² / z. Tell me, can you write it? So, you can write it like this: Radius of Helium+ divided by Radius of Hydrogen is equal to n² / z for Helium+ and n² / z for Hydrogen. What's the problem? n² is given as the first orbit for hydrogen and Helium+. So, n1 will be there. And the z of Helium is 2. Okay, very good. And here, for the second orbit of Bohr's hydrogen, so second orbit means n=2 is given. Yes, 2² will be 4, divided by the z of hydrogen is 1. Whoever solves this will get 1/8. Now, what is given here? It is given as X. What is given? It is given as X. So, tell me, what will be the radius of hydrogen? You will say, sir, it will be 8X. Finished. What's the problem in this? Yes, there is no problem. Right? So, such questions are comparison questions. These are also asked quite a lot. Come, look at one more question. It says, for a hydrogen atom, an electron in the ground state. Right? Hydrogen atom is given. The value of z is 1. Ground state means the first, n=1. And the energy is given as -13.6 electron volts. We know this, right? Right? And it asks for the energy of the second excited state. Oh, look, this is the ground state. Yes. Ground state means n=1. When I say first excited state, first excited state means n=2. And when I say second excited state, it means energy = 3s. So, it is asking for the radius of the third orbit. Right? So, we had the formula for its energy, which was

You can use this formula in this question. Apply your mind and solve it. I will give you the homework anyway, okay? Look at this homework. 2016 BYES. Think about it yourself. If the value of M is very large, then the value of your lambda will be very small. Yes. So if it is a microscopic particle, and if I write it the other way around, right? When M is very small, lambda will be quite large. When it is a small particle, sir, its mass will be less, its lambda will be good enough that it can be measured, that you will get an appreciable value. But on the other hand, if, say, there is a microscopic particle, yes, and microscopic particles, microscopic particles, right? So sir, there the mass will become very large, and if the mass is very large, then sir, the value of lambda will be very small. It will be so small, so insignificant, that it will not be possible to measure it. Yes, or you will get an insignificant value, a very small value, right? So for this reason, it is said that this de Broglie wavelength of yours is significant for microscopic particles only. Yes, for small particles like electrons, protons, neutrons, alpha particles, gas molecules, for them only, for them only, the de Broglie wavelength is defined. If it is a large particle, a cricket ball, you, me, and any other large particle, there is no significance of de Broglie wavelength for it, right? So similarly, many of you might have a question in your mind, you will say, sir, we are also particles, yes, so some associated with us should also be there if we are moving. It happens, but it is a very insignificant value that we do not consider. Tell me, is it clear? Have you understood de Broglie? Is it clear? These four-five formulas are the de Broglie wavelength. Keep them in mind, no question will be wrong, I guarantee it. Let's move on. Then another gentleman came, his name was. He created a lot of tremendous uproar. He said a very wonderful thing. What did he say? His saying was that if, say, a particle is moving, then the position of that particle and the velocity of that particle, what am I saying? The position of the particle and its velocity, you can never measure with 100% accuracy, 100% accuracy. You can never tell both things with 100% accuracy simultaneously. If you tell one with accuracy, then the accuracy in the other will increase a lot. If you increase the accuracy in the second, then it will decrease in the first, right? This is what Heisenberg's Uncertainty Principle said. And here he also gave a relation. He gave a relation that the uncertainty in the position of an electron and its momentum, beta, will be equal to or greater than h/4π, right? This is what the principle said. This is the equation on which numerical problems will be formed, which you will have to solve and come. Uncertainty, uncertainty in position. In what? Uncertainty in position. So the multiplication of uncertainty in these two will be equal to or greater than p, right? Now, if, say, I talk about p, what is p, beta? It is m * v. So delta p will be m * delta v. There is no uncertainty in mass, right? Mass is fixed. So m * delta v. Put it here, the formula becomes: dx * m * delta v is greater than or equal to h/4π. Yes, greater than or equal to h/4πm. There are quite a few numerical problems on this, which will be yours. I am telling you again, you will make a mistake here again. What mistake will you make? That you will write the mass in grams, because in the first chapter we are used to keeping the mass in grams, right? Beta, it will not be in grams, it will be in kg. In what should it be written? In kilograms. Tell me, is it clear? Have you understood the बात? No problem, right? It will not be, in my opinion. It is a very simple thing, a very easy thing, right? There are some different forms of it too, but they are of no use to us here, right? Our numerical problems will be formed from this only. Nothing else matters. Look, sometimes there is also a sign like this, beta, right? What does it mean? h/2π, right? What does it mean? h/2, right? If you see such a sign somewhere, then, right? Okay, if you see it. Now, now think for yourself. Yes, now think for yourself that when your, let's talk about significance first, okay? Let's talk about significance. Look, I have written the relation, delta x. Think for yourself, if your particle is microscopic, understand again. If your particle is microscopic, then in the case of a microscopic particle, the mass will be very large. And if the mass is very large, then look, the uncertainty in your position and the uncertainty in velocity will be very small, right? You will get insignificant values. But on the other hand, if, say, your particle is small, how is it? If it is small, then in the case of a microscopic particle, its mass will be quite less. The uncertainty in its measurement, in position and velocity, will be quite high, which you can measure. You will get a good value, a significant value, right? Yes, like if someone says, if sir, say I am moving on a path, then can my position and my velocity not be told simultaneously? Yes, it can be told. Right? Because we are microscopic particles, our position, our uncertainty, our mass is very large, so the value of delta x and delta v will be very small. But on the other hand, if you talk about an electron, an electron is moving on a path, right? An electron is a microscopic particle that is moving. When it is moving, you cannot tell its position and its velocity with 100% accuracy. So the first thing is this, you will also write this that it is significant for microscopic particles only. Understood the बात? Significant for microscopic particles only. Tell me. [Music] You said, brother, the electron's position is here, and it is moving in this direction at 5 meters per second. Only then can you tell where it will be after 5 seconds? Then you will say, sir, the electron's position is here, and it is moving in this direction at 10 meters per second. So tell me, where will the electron be after 10 seconds or 5 seconds? Yes, do you understand what I am saying? So when can this be told? The path of the electron can be told only when you know both the position of that electron and its velocity with 100% accuracy at a particular time. And Heisenberg said, you cannot find it out, right? When you cannot find it out, then how did you tell one thing? This Bohr of ours, Niels Bohr, he told everything about the path, the path. The electron will move on a path around the nucleus. He also gave the energy of the path. First, second, third, fourth energy level, what not, he gave everything. And this Heisenberg completely ruined his dreams. He said, brother, you cannot tell the path, right? When you cannot tell the path, then there will be no orbit, nothing like a fixed orbit can be told, right? That it will move only here. And if this is not the case, then the radius etc. that were calculated have no use, right? So this was the thing that was a contradictory statement of Bohr's Atomic Model by Heisenberg, right? Because Bohr did not consider all these things, right? And that later became the reason for his failure, right? About which we will talk in a little while. Okay? Then came some questions on this. Look, what is it saying? What kind of questions can be asked on this? Very easy type, very similar, very simple questions. Look, what is it saying? Uncertainty in velocity is to be found, brother, delta v value is to be found. Okay, sir. And it says, if the uncertainty in position is of what order? Tell me, you know the formula. Delta x. Who are we talking about? We are talking about an electron. So the mass is 9.1 * 10^-31 kg. Write it. Everything else is with you. Delta x is with you. Solve it and find the value of delta v. Tell me, can you find it? I heard, brother, you are very skilled in calculations. Then let's move towards another question. What does the next question say? It's a question about a microscope, so brother, it's the same question, it's already done. What to do? Let's see the question. And the question is written on your screen. It came in grams. Convert it to kg, otherwise it will be wrong right there. 10^-3 kg. 4 * 10^-2. Okay, dad. And it says its velocity is 45 meters per second, right? Many people write delta v. No, this is velocity. Delta v is not given to us yet. Look further. What does it say? If the speed can be measured with an accuracy of 2%. If the accuracy is 2% of the velocity of any electron, of a golf ball, then obviously, what can be the maximum uncertainty in its velocity? Tell me, what is 2% of 45? This is how much? Do you understand what I am saying? Many people here will do what? Here it is said, sir, this is the accuracy given, 2%. Sir, the uncertainty will be 98%. Brother, write 98, the question will be wrong. Right? I gave an example earlier. You can locate the position of an electron within 1 kilometer. Think about it. The probability of finding an electron, the probability of finding an electron, let's say in an area of 100 meters, then what will be the maximum uncertainty in its measurement? It will also be 100, right? It will not be found outside 100. So what is the maximum certainty in its measurement? It is 100. Yes, it says the maximum accuracy is 2%. You can find its velocity with only 2% accuracy. So the uncertainty will be within 2%, it will not be outside. Yes, so this 2% uncertainty is given, beta. Keep that in mind, otherwise the question will be messed up, you will do it wrong. Now these were three types of questions. If you have solved them, then you can easily handle the rest of the questions. Your homework is, right? Okay, sir. This is also your homework. Do it. This is also your homework. Do it, right? Let's talk about what? The reason for the failure of the atomic model. Why did it fail? Oh, it failed because de Broglie says that the electron has a dual nature. Yes. Bohr said the electron has particle nature. Brother, what you said, he did not consider the dual nature of the electron. Yes. When you do not consider dual nature, yes. We read that. Bohr, Bohr, what things could Bohr not explain? Right? We wrote those things. G.M. Fact, Stark's Fact, and Duplet Plate. Why? Because it does not consider wave nature, it only considers particle nature. So the problem started there itself. Yes. So the first thing is this. Second, second, now Heisenberg's Uncertainty Principle. He completely tore apart Bohr. Bohr said the electron is moving. It will move on a path. Its name is orbit. It is an energy level. And as long as it moves on a path, its energy will not change. Neil said, brother, such a path is not possible. Right? So you are fooling the world. Yes. So Neil Bohr was not right. Neil Bohr contradicted Heisenberg's Uncertainty Principle. He proved his point, gave everything. So it was proven. The things that were said, right? So he was made fun of. And these Einsteins, everyone, what are you talking about? Why can't we do it? When all this happened, a new model was made. A new model was made, and that model was named what? Quantum Mechanical Model. Yes. This Quantum Mechanical is that model. This is that model which considers the dual nature of the electron, right? That the electron will have wave nature and also particle nature. This model, this, this model based on dual nature, that was the Quantum Mechanical Model, right? Where the electron was considered as a 3D wave, right? Where it would have some energy, some velocity, and along with that, some coordinates in a three-dimensional space, right? And who gave this? And how big a task was this, you can estimate from this that they gave an equation, right? Which is called the wave equation, and the Schrödinger equation, and that entire Quantum Mechanical Model was based on this, this equation, right? And for that equation, [Music] comes, right? So you can understand how big a deal it was, how big a thing it was, that for what they are getting a Nobel Prize, what was it? Let's see for once. d²ψ/dx² is the wave equation, right? Where, where the electron was considered a three-dimensional wave, and x, y, z were its coordinates, right? Beta, what were the coordinates? Right? Here M is mass, everything is told to you. E, beta, E, is the total energy, right? And this V written here, many people say it is velocity. No, this V is beta, this is your potential energy. What is it? Here V is. A new thing came in this, which is called Psi. What is Psi called? Wave function. What is it called? Wave function. This was the equation. Think about how it was derived, what happened to it. We don't need to talk about it at all. It is outside our scope, right? We will not see that. Now, here, this equation can also be broken down into a small equation. Hψ = Eψ. Both these things are the same, right? Both these things are the same. Many people will say, sir, cancel Psi from Psi. Oh, foolish person, it doesn't happen like that. This Psi, this H, what is it? It is an operator, right? It is an operator. Which one? Hamiltonian operator. What is it called, beta? Hamiltonian operator. Yes, Hamiltonian operator. And this Psi, Psi cannot be canceled out from Psi. Clear? You have to keep this equation in mind. So here, something came, which is called Psi. Significance of Psi. It is written on your screen. Look, if I ask you, does it have any physical significance? You will say no, right? Psi has no physical significance. This Psi is a wave function. All the information related to the electron will be found in the wave function of that electron. It has a physical significance. It is called probability density. Yes. What is it? Like, look, Heisenberg said that brother, you cannot tell the fixed position of the electron, right? You cannot tell the fixed position, but what can you do? You can tell the probability that, brother, the probability of finding the electron here is more, right? And the space inside the atom, that place where the probability of finding the electron is maximum, this place is given a name, Orbit. Yes, right? Maximum possibility of finding an electron. This is a region around the nucleus where the probability of finding an electron is maximum, it is called a properitor, right? So what did you do? Like, say, this is the nucleus. At a certain distance from this nucleus, if you calculate the value of Psi², it means you have defined the probability of finding the electron at this certain distance x from the nucleus. What is the probability of finding an electron at a certain distance? Who defines it? Psi defines it. So, the probability of finding an electron inside any atom is told by Psi. The region where the probability of finding an electron is maximum is called an orbital. Clear? Did you understand the बात? Tell me. Now, the important thing here is Quantum Numbers, right? These quantum numbers, brother, are quite important. Quantum numbers are quite important. You will say, sir, what are quantum numbers? First of all, tell me, right? So look, brother, quantum numbers are a set of four numbers. How many numbers? A set of four numbers. And all the information related to electrons, you can tell with the help of those four numbers. It is said that you can tell the address of the electron, right? Some people write, you can also tell the address of the electron, right? There are four quantum numbers. Which ones? First of all, you have heard their names: Principal Quantum Number, denoted by n. Azimuthal Quantum Number, denoted by l. Yes. Magnetic Quantum Number is denoted by m. And the fourth is Spin Quantum Number, denoted by s or sometimes also written as S. It's all the same, right? Tell me, tell me, is it clear? These are the four quantum numbers. Among these, among these, these three quantum numbers above, they came from solving the de Broglie equation. Oh, why am I repeatedly saying de Broglie? Where do these values come from? They come from solving the wave equation. And this beta, spin, the spin quantum number has been defined separately, right? These three above, they are found in the solution of the Schrödinger wave equation. Alright. Let's look at each quantum number one by one. First of all, let's talk about the Principal Quantum Number. What does it tell? The Principal Quantum Number tells about the shell. In which shell is the electron? When I say the value of the Principal Quantum Number for an electron is one, it means the electron is in the first shell. When I say the value of the Principal Quantum Number is two, it means the electron is in the second shell. It's a very easy thing, right? So who tells about the shell? Which quantum number tells which shell the electron is present in? The Principal Quantum Number. It can also tell the energy of the electron. Why? We had read that as you move away from the nucleus, the energy increases, right? So if you know which is the electron's quantum number, the Principal Quantum Number, then you will know in which shell the electron is. And if it is in a shell, then accordingly you can estimate the energy. Energy is directly proportional to what? To the Principal Quantum Number. And similarly, if I talk about the size of the shell, then the size, beta, will also be directly proportional to which shell? Look at the size of the first shell. Look here. This is the nucleus. First shell, tiny. Second shell, bigger. Third shell, even bigger. Fourth shell, even bigger. Fifth shell, even bigger, right? And as you move away from the nucleus, your shell will increase, its size will increase, right? So you can also estimate the size of the shell. There is a formula in front of you. You used to read in childhood that in one shell, what is the maximum number of electrons that can be present? n² electrons can be present. And where this n is, what is n, beta? It is the Principal Quantum Number. Suppose your n is 1, the first shell, then the maximum number of electrons that can come in it is two. Suppose you have the value of n as 2, the second shell, then the maximum number of electrons that can come is eight. If the value of n is 3, then the maximum can be 18. You can solve these things yourself. Yes. Tell me, any problem? Now, in one shell, in one orbital, what is the maximum number of electrons that can be present? There is also a formula for that, n². Where n is the Principal Quantum Number. Yes. Like, suppose n is 1, the first shell, then the maximum number of orbitals will be? Then you will say, sir, it will be one only. Right? If, say, n is 2, then the maximum will be four. If n is 3, then the maximum will be nine. According to this, your story will continue. So this was the Principal Quantum Number, which tells you in which shell the electron is present. Let's move on and talk about the Azimuthal Quantum Number. It is also called the orbital angular momentum quantum number, or it is also called the subsidiary quantum number. It does not tell about the shell. It tells about the subshell. In which subshell is the electron present? And its values, beta, are from 0 to n-1. Right? From 0 to n-1. The value of l can never be equal to the Principal Quantum Number. Right? It can never be equal. So, like, suppose, like, suppose n is 1, right? The first shell. Then for the first shell, the value of l will be only one, which is zero. Right? The value of l is zero. What is the value of l being zero called? It is called s. Assumption. If, say, the value of l is 1, wherever you find it, the value of alpha is 1. It means it denotes the p subshell. If the value of the principal azimuthal quantum number is 2, it means it represents the d subshell. And if, say, your azimuthal quantum number is beta 3, then sir, it represents the f subshell. Right? So from this, you get to know the subshell. Right? What do you get to know, beta? The subshell. You can also tell the shape. That the s subshell is spherical. Yes. How is it? Beta, spherical. The p is dumbbell-shaped. How is it? Dumbbell-shaped. And the d is double dumbbell-shaped. Yes. Double. Do you understand what I am saying? Yes, yes, yes, you have to say. Tell me, any problem? Right? These are all very easy things. Like, suppose, like, suppose I write n is 1, the first shell. Zero. It means there will be only one subshell, which is the s subshell. But when someone says the second shell, then for the second shell, the value of l can be two. Zero to n-1, meaning zero and one. Two are possible, right? So it means this tells about what? This tells about 2p. Zero tells about the s subshell. One tells about the p subshell. And which shell is the p subshell from? The second shell. So it is written as 2p. Similarly, if I talk about n=3, then beta, l can have three values. Zero, one, and l can have one more value, two. If the value of l is zero, it means it tells about the s subshell. The s subshell is from which shell? The third shell. So this becomes 3s. This tells about the p subshell. Which shell? The third shell. L=2 tells about the d subshell. And from which shell? The third. Are you understanding what I am saying? From here, one more important thing to understand is that the d subshell does not exist in the first shell. The d subshell does not exist in the second shell. Yes. The p subshell starts from the second shell. The d subshell starts from the third shell. So this is very important. Azimuthal quantum number is written. If you feel like it, you can remember it. That the maximum number of electrons in a subshell. What is the maximum number of electrons that can be present in a subshell? The formula is written. Like, suppose it is an s subshell. It is an s subshell, beta. If in this, s subshell means l=0. And if you ask for electrons in this, put the value of l as zero. What is the maximum number of electrons that can be formed? Only two electrons can come. Suppose it is a p subshell. So for the p subshell, what is the value of l, beta? It is one. And if you put one here, you will get six electrons. Yes. Suppose it is a d subshell, beta. And if you put the value of l as two in the d subshell, then you will get 10 electrons. Yes. And if it is an f subshell, and if you put l equal to three in place of l, then how many will you get? 14 electrons. Right? So these are the maximum number of electrons that can be present in a subshell. Earlier, we read the formula 2n², that formula was about the maximum number of electrons that can be present in a shell. A small formula you have to keep in mind is that the orbital angular momentum of an electron is under root l(l+1) h/2π. A straight formula. Here, l is the same, right? Which one is it? Beta. Is the बात clear? You have to say yes, yes, yes. Tell me. Magnetic Quantum Number. What does it tell? The magnetic quantum number tells how many orbitals are present in a subshell. How many orbitals are present? And these spectral lines, they split in the presence of a magnetic field. It could not explain it much. So this quantum number can explain it. Right? You can also say it like this, how many orbitals are present in an electron? You can also say it like this, that how many orientations are possible for an electron? It's all the same thing. Right? And its value, its value, look, I will explain to you. Its value, beta, the value of m, the value of m is from -l to +l. Right? Including zero. Yes. Including zero. And as many values of m are there, that many number of orbitals are present. As many values of m are there, beta, that many number of orbitals are present. Right? So, like, suppose I take the first example. l was zero, right? l was zero, meaning it was an s subshell. And if the value of l is zero, then there will be only one value of m, which is zero. Yes, -l to +l. So the value of m is zero, which means there will be only one orbital present in it. There is only one orbital present in the s subshell, which you know by the name of s orbital. Right? Relate this. This is a very good thing. Like, suppose I write l=1, beta. Then it will be a p subshell. And if it is a p subshell, then there are three possible values for m: -1, 0, and +1. -l to +l, right? From -1 to +1 including zero. This means there are three values. So this means how many orbitals will come in it? Three orbitals will come. Yes. These three orbitals, one is called px, one is called py, and one is called pz. No problem, in my opinion. Yes, yes. Like, suppose the value of l is written as 2. Then it means, sir, it is a d subshell. And if it is a d subshell, then how many possible values for m will there be? -2, -1, 0, +1, +2. Sir, five values are possible. Five values means how many orbitals will be in it? Sir, there will be 5 orbitals. Do you understand what I am saying? Yes. There are five orbitals in the d subshell. Their representation is dxy, dyz, dzx, dx²-y², and dz². Right? This is the representation. Do you understand what I am saying? Tell me. Yes. And if the value of l is 3, the value of l is 3, meaning it is an f subshell. Sir, it is an f subshell. This means there are -3, -2, -1, 0, +1, +2, +3. Seven values are possible. Seven values are possible. This means, sir, there will be 7 orbitals present. Tell me, is the thing correct? How many orbitals will be present? 7 orbitals will be present. So you can estimate how many orbitals are present in a subshell from the magnetic quantum number. Tell me. Finally, your spin quantum number comes. And this spin quantum number tells about the speed of the electron, right? It is said that the electron, it revolves around the nucleus, and along with that, it also revolves on its own axis. Just like the Earth revolves around the Sun, similarly, and it also revolves on its own axis. Similarly, the electron will revolve around the nucleus and also on its own axis. Right? So its spin can be defined in two ways. Brother, it can spin in a clockwise direction on its own axis, or it can spin in an anti-clockwise direction. There are two possibilities. So its spin, the electron's spin, has been defined as either +1/2 or -1/2, right? In this way, the electron's spin has been defined. Many times it is also shown like this, right? Like this also, spin up and spin down. You can write these two spins. +1/2, sir, for this, will it be +1/2 or -1/2? It can be anything. For this, will it be +1/2 or -1/2? It can be anything. If you are calling this +1/2, then this is -1/2. If you are calling this -1/2, then this is +1/2, right? There is no such rule that for anti-clockwise it will be minus, or for clockwise it will be plus. There is no such rule, right? Keep this in mind, there are two spins. Done. Okay, one more thing to keep in mind. What? That sir, in one orbital, in one orbital, a maximum of two electrons can come. In one orbital, a maximum of two electrons can come. The spin of these two electrons will be opposite. With opposite spin, right? With opposite spin. So, like, we just said that there is an s orbital, yes, yes, s subshell. Sorry, s subshell. In the s subshell, brother, there is only one orbital. In the s subshell, there is only one orbital. A maximum of two electrons can come in the s subshell. That is why there are two electrons in the s subshell. Yes. We wrote that the p subshell, in the p subshell, there are three orbitals. How many? Three orbitals. So this means a total of six electrons can come in it. A maximum of two electrons can come in one orbital. If there are five orbitals, two electrons in one orbital, then 10 electrons in five orbitals.

Tell me, did you understand my point, everyone? Yes, did you understand my point, everyone? You will have to answer yes or no. Speak, speak. Did you understand my point? Yes, yes, yes. Okay, so this whole story is related to each other in this way. Here's a question from 2023: What is the maximum number of electrons that can be accommodated in a shell with n=4? Just put n=4 in the formula 2n², and you will get the answer. It's a 2023 question. Now, what can I say? Tell me, how many subshells will there be where n=4 and beta, n=4 means the 4th shell, n=4 and m=-2? How many such subshells will there be, right? Who tells us about subshells? Which quantum number tells us about subshells? Tell me. The azimuthal quantum number tells us about subshells. Yes, no, sir, not magnetic, sir, azimuthal, right? So, we just need to tell this: when n=4 and m=-2, how many such subshells will be present? How many such subshells will be present, right? So, try to solve this question for once, right? So, look, it's a straightforward question. n=4, beta. So, from here, I can say that the value of l can be 0, 1, 2, and 3. Say it, right? Now, think about it. When l=0, l=0, then m will also be 0. So, we needed a subshell with m=-2. It's not here. Yes. Now, think, if l=1, then m will be -1, 0, +1. Here too, we are not getting any subshell with m=-2, right? l=3, so sorry, 2, then m will be -2, -1, 0, +1, and +2. Sir, we got one subshell here. And if l=3, then m will be -3, -2, -1, 0, +1, +2, and +3. Sir, here too, there is one with m=-2. So, how many such subshells are there where m=-2? Sir, there are only two subshells. This means option number B is correct. It was a straightforward question that we solved. Let's look at one more question, right? The number of orbitals associated with the quantum number, how many with quantum number n=5 and s=? Here you have to tell about the number of orbitals. Okay? Look, this should not be the number of orbitals, in my opinion, it should be the number of electrons. S tells us about electrons, right? It tells us about electrons. So, this means if they are asking for orbitals, they are asking me how many total orbitals are there in n=5. So, use the n² formula, the answer will be 5², which is 25. Are you understanding? No problem. Okay, then. Now, some questions, beta. Let's look at this question once more. What is it asking? For the electron, the value of the orbital angular momentum is how much? This question was asked in 1997. Orbital angular momentum, I told you the formula: √[l(l+1)] * h/2π. And if it's a d-electron, then for this electron, l is 2. Just put 2 in it, and it's done. It will be √6 * h/2π. These are very simple questions. Now, we will talk about what? We will talk about a plot, a graph. The graph is between psi and r, which is called the radial wave function. The graph between psi and r. These are very simple graphs. You will find them in your NCERT. For example, let's say the graph of psi and r. Yes, I told you to draw it for 1s. There's a logic to these as well. I will tell you how these graphs are made. Psi and r graph. I told you to draw it for 2s. Psi and r graph. Psi and r graph. I told you to draw it for 2p or 3s. Let's say you were asked for 3s. Done. And the graph of psi and r. Let's say someone asks you to tell about the graph of psi and r for 2p. Tell me about the graph of psi and r for 3p. Okay? So, look, there is a trick to doing these graphs. The trick is, first of all, the graph of s, right? Always remember this: the graph of s always starts from the top. Like this. The graph of s always starts from the top. Okay? And if we talk about 2s, the graph of s starts from the top, goes down once, plus minus. See, the graph of 1s will only be in the positive. The graph of 2s is plus minus. Then 3s comes. Start from the top. Plus minus plus. Bring it back to plus. Plus minus plus. If they asked for 4s, it would go down again. Sir, what is this logic? You will know the logic now. The logic is: always remember, the graph of p always starts from here. Start in the positive. Plus minus. Plus and minus. If, for example, it was 4p, 4p, 4p, then what would happen? Plus minus plus. Here's the logic. Plus minus plus. This is how it would be for 4p. So, always remember, the graph of s starts from the top, and the graph of p starts from the origin. Done. Now, one thing you need to understand here is one more small thing. And that is a node. Yes, what is it, beta? Node. You need to understand the node. What are nodes? A node is a region, right? A node is a region around the nucleus where the probability of finding an electron is zero. Okay, who tells us about the probability of finding an electron? So, if the probability of finding an electron is zero, it means the value of psi is zero. Tell me, can I say that there are two types of nodes, beta? One is a radial node. Yes. This is a nodal plane or a nodal surface. Done. It is also called an angular node. Now, the formula for radial node is. If you want to find this, it means a circular ring around the nucleus. Like a circle where the probability of finding an electron is zero. That will be a radial node. The second is this nodal plane or angular node. What is this? This is a node that passes through the nucleus. It passes through the nucleus, and in which the probability of finding an electron is zero. Yes, it passes through the nucleus, and in which the probability of finding an electron is zero. That is a nodal surface, a nodal plane. You can call it a nodal plane. I am good. The formula for calculating radial nodes is. The number of radial nodes is equal to n - l - 1. It's just a formula. It will be like this. For example, if I tell you, listen. I told you, here is your. I told you, 2s. How many radial nodes will there be in 2s? You said, n - l - 1. n is 2. l is 0 for this. This means it has one radial node. And how many angular nodes are there? l is 0 for this. This means 2s has only one node, beta. And that node is the radial node. Clear? So, in this way, you can do all these calculations. For example, if they ask you about 1s, how many radial nodes are there in 1s? Then you will say, n - l - 1. There are no nodes in this. No nodes. This means the value of psi² will never be zero for this. Yes, the value of psi² will never be zero. The graph will start from the top and go like this. Done. Psi² is always positive. I don't need to tell you this because it's squared, and square is always positive. Done. This is for beta, 1s. Now, for example, if I give you one more graph like this, and I ask you to draw the graph of psi² and r for 2s. Then you said, in 2s, there is one node, and that too is radial. So, what do you have to do? Start from the top. One radial node means the graph will be zero once. Plus plus, because it's psi², so both values will go in the positive. And this position, see this place, at this place, psi² is zero. This means this is your node. Do you understand? Yes, clear. In 3 orbitals, there are 3 orbitals. This means the probability of finding electrons is only present on the x-axis. Right? If, for example, this is the y-axis, I called this the y-axis, then p means the probability of finding electrons is only present on the y-axis. And when I say pz, pz, if this is the z-axis, it means the probability of finding electrons is only present on the z-axis. This is your present. This is the double, not double shape. P subshell, beta, is dumbbell-shaped. How is it? Dumbbell-shaped. Do you understand? Okay? Now, look, if you talk about nodes here, if you talk about nodes here, then your nodal plane. Catch this plane. Understand this plane. This plane, like this, this plane, this plane, which is passing through pz, beta, this plane. This plane, which is passing through the nucleus, and in which the probability of finding electrons is zero. So, this plane, I can say that this is this. This is the angular node. This is the nodal plane. And which plane is this? If this is pz, the plane behind it is which plane? It's the xy plane. So, for pz, the nodal plane will always be the xy plane. Okay? If I ask you about py, then which plane is this? This plane, this plane, which is this? This is the x and z axis. So, this will be the xz plane. And here, this plane, which is passing through here, or passing through here. This plane. Yes, this plane, beta. This plane is the xy plane. This plane is the xy plane. Oh, sorry, sorry, I reversed it. This is the y-axis, right? So, if this is the y-axis, then which plane is this? If this is the x-axis, then which plane is this? This is the yz plane, right, beta? How is it the xy plane? This plane is which plane? This plane is which plane? YZ. See, this is the y-axis and the back is the z-axis. So, this will be the yz plane. So, you can keep this in mind: if it's px, then the yz plane. Remove x. If it's py, then remove y. Xz plane. And if it's pz, then remove z. Xy plane. So, these are the nodal planes. Which are x, y, px, py, pz. Now, whether it's 2px, 3px, it doesn't matter because the formula for the nodal plane is l. Normal planes are l. And if the normal plane is l, then whether it's 2px, 2py, 3px, 3py, or 2px, 3px, l will always be 1. For all of these, the number of nodal planes will always be 1. Keep this in mind. Okay? For example, let's talk about 2p, beta. In 2p, how many radial nodes will there be? The formula for radial nodes is n - l - 1. Sir, n is 2, l is 1. This means it has no radial nodes. And how many angular nodes are there? Angular node is l. It has one angular node. Where does the angular node form? Tell me quickly. Sir, where does the angular node form? At the nucleus. So, it will form here. Yes, it will start from here. If you have only one nodal mode, and it's this. This means it's a nodal plane because no plane passes through the nucleus. I said, draw the graph for 3p. Draw the graph of psi² and r for 3p. So, it's very easy. Again, you have to check the nodes. You said, in 3p, there is one angular node, or one normal plane. It will form at the nucleus. Sir, it also has a radial node. How many? n - l - 1. Sir, it also has one radial node. This means it has a total of two nodes, beta. One radial and another nodal plane. Do you understand? If there are two planes, if it has two nodes, one is formed here, so it means one more will be formed. It's just like this. So, it has to touch twice. It will be zero twice. Psi² will be zero twice. Once here, and once here. But which node is this? Radial node. Which node is this? Nodal plane. Do you understand? Speak. So, in this way, you can draw the graphs. For example, if I tell you to draw it for 4p. Then in 4p, the total nodes, beta, will be 3. Total nodes will be 3. But out of these, two will be radial nodes, and the other nodal plane will be one. The nodal plane always forms here. It will be zero three times. Here's the logic. It will be zero three times. Here's the logic. Once, twice, and three times. Radial node is zero. Clear? Understand? So, in this way, in this way, you can draw the graphs for this. And look, if I talk about its shape, what are we talking about? We are talking about the shape. It's double dumbbell, right? Double dumbbell. Look, in this, there are five orbitals. Five orbitals are dx², dy², dz², dx²-y², and dz². Sir, what's the difference between all these? It's very easy. Look at the shape. Okay? Look at the shape. Yes, if it's the x-axis and y-axis, it means in dxy, the probability of finding electrons will be between the x and y axes. Right? If, for example, this is the y-axis and this is the z-axis, then your dyz, beta, in that, the probability of finding electrons will be between the y and z axes. Okay? So, and if, for example, this is the x-axis and this is the z-axis, then if I talk about the zx, then the probability of finding electrons will be between the z and x axes. Right? If we talk about dx²y², this is the x-axis, this is the y-axis, and if the probability of finding electrons, the probability of finding electrons is on the x and y axes, then it will be called dx²y². Similarly, this is the z-axis, and the probability of finding electrons is only on the z-axis. But look, look, here the electron density is also present around the nucleus. Like this. This is dz². So, dz² never has a double dumbbell shape. You can see it. It's a dumbbell, but not a double dumbbell. Sir, there will be a possibility of finding electrons around the nucleus. Double dumbbell shape, except, for example, if I talk about dxy, beta, then in dxy, what will be the nodal planes? Yes, what will be the two nodal planes? Tell me, what will be the two nodal planes? Look, this is dxy. So, one node is here. Which plane is this? This is the xz plane. And one node is here. One node is here. Which plane is this? This is the yz plane. Right? So, you know how to remember this? Dxy, z is left. So, its two nodes will be xz and yz. Okay? In this way, you can remember. If you talk about dyz, then x is left. So, for this, your angular nodes will be xy and xz. Okay? And here, if you talk about dxz, then y is left. So, it will be xy and yz. Okay? And in this way, you can find it here. And remember, dz² has no nodal plane. dz² has no nodal plane. Why doesn't it have it? Because you cannot pass any plane through the nucleus in such a way that you don't find electron density. Look, if, for example, you take this plane, then electron density is coming into it. If you take this one, due to this circular ring, you will not find any plane in which the electron density is zero. Right? So, it has no nodal plane. It has a special type of plane. No doubt, who is present? It has what? Cone. It's like this. Like this, a cone will form above, a cone will form below. Like a damaru. Have you seen the damaru of Shivaji? That kind of two, one above, one below. It forms here. Nobel cone. It forms here, beta, Nobel cone. It has no nodal plane. Okay? Keep this in mind. Right? So, we have talked about what? Shapes, etc. How the d orbitals, s orbitals are shaped. If you want to do questions based on this, you can do questions. For practice, one or two questions. For example, look, such questions are asked directly. Right? Tell me, how many radial nodes are there? What is the total number of nodes? What is their ratio? I have given you the formula. Right? It's asking, tell me, how many angular and radial nodes are there in the 4d orbital? There are questions like this that are asked directly in the exam. Look, this was in 2021. No angular nodes and two radial nodes. Angular nodes are not there, radial nodes are there. So, these are very easy questions. You just need to know the formula. If you know the formula, you can solve the questions very easily. Okay? Look at one more. For example, all these questions are like this, beta. All these questions are like this. You can solve these types of questions very easily. Look, it asked for the graph of psi² and r in 2019. We can do this very easily. We just made it a little while ago. Okay, one more graph is left. One more graph is left. Between 4πr²psi² and r. This graph is left. Graphs like this can also be asked. For 1s, 2s, 3s, 3p, 2p, for anything. There is also a method to solve these types of questions. There is a way. How do we solve them? How do we draw the graphs? I will tell you this too. Look, if I talk about 1s, then this kind of, every graph, every graph, this 4πr²psi² will also be there. Every graph, beta, will start from here. Where will it start from? From here. Done. Yes, the graph will start from here. Why? Because at this point, the value of r is 0. The value of r is 0. So, this entire term will be 0. And then, as many radial nodes as there are, touch it. For 1s, there are no radial nodes. If there are no radial nodes, then this graph will never touch zero. Done. And look, look, look. For example, if I talk about 2s. Then this graph, beta, this graph will start from here. And in 2s, there is one radial node. There is one radial node. So, the graph will touch it once. It touched it once. And in this, the size of the node will always increase. What will happen? It will increase. Because here, psi² is coming. The effect due to psi² will be more. Yes. For example, if I talk about 2p. If I talk about what? 2p. Yes, 2p. Then, beta, in 2p, in this graph of 4πr²r, you only have to check the radial node. Start the graph from here. Because the angular node was to be formed here, it has been formed. If I talk about 2p, then beta, it has zero radial nodes. Yes, radial nodes are zero. So, the graph will start from here and end here. It will not be zero again. Okay? Done. If, for example, it was 3p. In this, you only have to see the radial node. If I talk about 3p, it has one radial node. So, the graph will start from here and touch it once. Plus plus, like this. In this way, you can also solve this question. In my opinion, you should not have any problem with this. Tell me, is there any problem? Yes, yes. So, based on this, this question is here. Look, what is it asking us? It's asking us to draw the graph for 1s electrons with 4πr²dr and r. Right? And the graph of 1s. We have already made the graph of 1s. There are no radial nodes in 1s. There are no radial nodes. This means this value will never be zero again. So, if you do these questions with this trick, you can solve them very easily. 2016 JEE Advanced question. You solved the question within seconds. Yes, always remember what to remember. The graph will start from here. Because at this point, the value of r is 0. The value of r is 0. So, this entire term will be 0. And then, as many radial nodes as there are, touch the graph that many times. There are two radial nodes. Formula for radial node is given to you. So, it has one radial node. It touched once. If, for example, there were two radial nodes, it would touch twice. If there were three radial nodes, it would touch three times. Right? So, you can design and draw this graph very easily for anything like this. Very good. So, after this, after this, if we talk about the energy of atomic orbitals. We will talk about the energy of atomic orbitals. First, for hydrogen and hydrogen-like species. Hydrogen-like species means single electron species. For single electron species, you need to tell the order of energy. So, always remember, the energy, the energy of the orbital depends on what? Depends on the value of n, the principal quantum number, only and only. It depends only on n. For example, if I talk about 1s and 2s, then 2s will have more energy because its n is more. If I talk about 2s and 2p, then both will have the same energy because for both, n is the same. Then, if I talk about 3s, 3p, 3d, all three, then their energy will also be the same. But when will this happen? Only when there is only a single electron. Single electron species. Sir, if there is more than one electron, then it's a multi-electron species. Then this is useful for us. Then the value of energy, beta, will depend on both n and l. It will depend on both values. Right? So, here comes a rule called the n+l rule, or the Bohr-Bury rule. First of all, this rule says that for which orbital the value of n+l is more, beta, its energy will also be more. Right? For example, if I ask you, between 1s and 2p, which one has more energy? Then you will say, sir, here n=1, l=0, so n+l=1. Here n=2, l=1, so n+l=3. So, sir, its energy will be more. Simple. Do this. Check n+l. Whichever is more, its energy is more. Now, it can also happen that the energy of two orbitals, the n+l of two orbitals can be the same. If n+l is the same, then whose n is more, its energy is more. Its energy is more. Sir, give an example. For example, if I write 3s and 2p, beta. In 3s, the value of n is 3, the value of l is 0. So, n+l=3. And here, the value of n is 2, the value of l is 1. So, n+l=3. The value of n+l is the same in both. In that case, whose n is larger, its energy is greater. Its energy is greater. So, by doing this, you can arrange all the orbitals in increasing order of energy, very easily. It will be like this. Then 3d will come. Then 4f will come. 4p will come. 5s will come. 4d will come. The story will continue like this. Yes. Check the value of n+l. Whichever is more, its energy is more. And if, for example, the n+l of two orbitals is the same, then check whose n is larger, its energy is more. Okay? So, these were the two things that you needed to keep in mind. For example, this question is here. Right? It's asking us for the decreasing order of energy. Asked in 2023. Whichever is more, its energy is more. And if n+l is the same, then what to do? Similarly, a question was asked in 2022. Exactly similar question. Exactly similar question. Asked in 2022. One more question was asked. Hasn't it been repeated? No, this is from different shifts, right? This was asked in different shifts. So, there are questions like this. Done. Which can be asked of us. Very easy. Just need to check the value of l+l, and accordingly, our question will be solved. Now, we have found out what is the order of energy of the orbitals. If we know the order of energy, then we are going to fill the orbitals. With what? With electrons. How many? Very simple. Right? We fill it with electrons. And for that, there are some rules. And the first rule among them is the Aufbau principle. Very simple principle. This Aufbau is not someone's name. Aufbau means to build. So, build up. And what did it say? That when you fill electrons, electrons will be filled in increasing order of energy. In which orbital the energy is less, put the electron there first. In which orbital the energy is more, put the electron there later. That's the rule. Simple story of the Aufbau principle. Clear? Done. Okay. Then, another principle came, whose name is the Pauli Exclusion Principle. What did Pauli say? What was Pauli's statement? That in an orbital, two electrons with the same spin can never come. Right? This is not possible. Two electrons will come in an orbital with opposite spins. Because if two electrons come in an orbital with the same spin, then for them, the value of all four quantum numbers will be the same. And which is not possible. That's why it's the Pauli Exclusion Principle. Then, another rule came, whose name is Hund's Rule of Maximum Multiplicity. It said that when you fill electrons in degenerate atomic orbitals, degenerate means those whose energy is the same. Right? When you fill electrons in degenerate atomic orbitals, then beta, first of all, put one electron in each orbital. Like, you put one electron in all three. Degenerate means you understand, right? Those orbitals whose energy is the same. Like, the three orbitals of 3p, 3px, 3py, 3pz. Their energy is the same. Right? First, when filling, put one electron in all three. After that, you have to pair the electrons. The fourth electron will come here. This is allowed. Right? Don't do it like this. Don't do it like this. Pairing of electrons will not happen until one electron reaches every degenerate orbital. Done. Clarity? Right? So, this was also a very simple story. We have also noted it down and seen it. Now, if we know how many electrons are in an orbital, yes, and how to fill them, then we can write the electronic configuration very easily. Atomic electronic configuration. We can write it very easily. For example, if I ask you, write the electronic configuration of Lithium. Sir, the atomic number is 3. Sir, we have to fill three electrons in the orbitals. So, do it. First electron will come in 1s. How many? Two. And after that, in 2s, how many? One. Done. We know that s can hold two electrons, p can hold six electrons, d can hold ten electrons, and f can hold fourteen electrons. We already know this. Right? So, we can solve the questions very easily. Right? And look, after Lithium, let's say someone asks about Nitrogen. The atomic number of Nitrogen is 7. Sir, we have to fill 7 electrons. 1s², 2s², 2p³. Two, four, and three, seven. Done. If they ask you about Sodium, then z will be 11. This means we have to fill 11 electrons. Two will come in 1s. Then two in 2s. After 2s, whose energy comes? 2p. How many can come in it? Six. That's ten. After 2p, whose energy comes? 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After 2s, it's 3s. How many can come in it? Two. That's twelve. After