Structure of Atom in ONE SHOT || All Concepts, Tricks & PYQ || NEET 2026

Hello children, how are you all? Myself Amit Mahajan and I welcome you all on this incredible platform of Physics Wallah. So, what's up, brother? I welcome all of you. Today, in our last lecture of Physical Chemistry for 'Umeed', the chapter is named 'Atomic Structure' or you can also say 'Structure of Atom'. This is the smallest chapter. If you look at it, it can compete with Redox Reactions. Although Redox Reactions are slightly smaller than this. Okay? But yes, it's a theoretical chapter. It's not a very tough chapter. It's not like Chemical Kinetics, like Electrochemistry, like Thermodynamics, like Equilibrium. Okay? You can say the theory portion is a bit more. Right? Good evening. Good evening. Good evening. We will keep the duration short, children. We will keep its duration short. Okay? We have worked on the PPT for this reason in 'Umeed' because if you look at the content, it is similar to any previous 'Umeed'. Okay? It's almost similar. But here we have worked on the PPT because each 'Umeed' has its own thing, what do you call it? The demand is different. When the demand is different, then obviously the supply should also be different. Everything has to be covered. But obviously, it has to be covered in a concise time. We will keep the time short, children. Yes, finish what you have started, right? We will try our best to finish it within two and a half hours, let's see what happens. Let's see how things will take off. It is more important for you to understand than whether it takes two or two and a half hours. Shall we start then? Let's start. Right? Yes, absolutely, absolutely. We will meet our crocodiles in the celebration. Please come. JEE Main results came yesterday. Many interviews were conducted with many students. Many JEE students will also be meeting at the result celebration. Similarly, when your NEET results come, you will also meet at the NEET result celebration. Why wouldn't you? Overthinking is happening. It happens with everyone at this time. At this time, the mind always focuses on the wrong things. It focuses on bad things. It will never remind you of the joy if you get selected. It will always remind you of what will happen if you don't. Okay? This is the moment when you open a book, you will feel like you know everything. And as soon as you close your copy, close the book, you will feel like you don't know anything. It happens with everyone. Everyone. There's nothing to say about it. Okay? But yes, if you don't focus in the last 10-12 days. Okay? Then things will go downwards. Okay? It's happening with everyone. It's happening with the one who is scoring 200 marks. It's happening with the one who is scoring 600 marks, brother. Okay? Yes, you must be feeling anxious. Absolutely, absolutely, absolutely. I will not say at all that why are you feeling anxious? How is this happening? Didn't you study the whole year? No, children, even if you studied, you might still be feeling anxious. This is a fact. It means we are not in denial mode. Okay? The stakes are high. You are in a very high-pressure zone. I don't know how you are managing your mental health right now. Which should be the top-most priority for any person. Right? NTA has tweeted. Right? I haven't read much. But one or two students sent it. Okay? Look, brother, their job is to conduct the exam. And they are talking about themselves. Our job is to prepare you for the exam. We will talk about ourselves. Your job is to prepare for the exam. You should focus on yourself. Okay? It doesn't matter. If the paper is easy, the cutoff goes very high. Students still cry. Oh, I have to drop even at 650. So what? Is this life? This is a ruined life. Tell me. I have to drop even at 650. Okay? And if the paper is difficult. Okay? And the child scoring 550.5 gets selected. Then it is said that, oh, why make the paper so difficult, so difficult? Okay? So these things, well, these will keep happening. Okay? If you ask me personally. Okay? As a teacher, with which framework would you prefer to stay? I think it is better to stay with the framework where the paper is moderate to tough. Because having to drop at 650, I am telling you the truth, it's a very bad situation, very bad. The child doesn't have the courage to drop. You scored 550 marks. Okay? You feel, oh, there's still a gap of 170 marks. 170 marks is approximately equal to 25%. Okay? So you need more hard work, and you need more hard work, so you can obviously do it. When you have to drop at 650 marks, it hurts a lot. It pains you a lot. I am telling you the truth. Let's start, children. Today, Atomic Structure, as you know, we are starting with the discovery of the electron, or what we used to call cathode rays. See, let's talk about before electrons. Let's talk about before electrons, protons, neutrons. Before that, what existed? That is, the atom was talked about. And who gave it? Dalton's Atomic Theory gave it. He said that the smallest particle of any particle will be called an atom. And it is indivisible. It cannot be broken down into smaller parts. But then the discovery of subatomic particles began. That is, electrons, protons, neutrons. Among them, the first thing we have to study is the discovery of the electron. And how did that discovery happen? Let's study it in a little detail on the next page. Okay? Look at this. First, a CRT, that is, Cathode Ray Tube, was taken. This one that you see is called a Cathode Ray Tube. We connected it to a battery. Here we placed two metal electrodes and connected them to a battery. This is connected to the negative terminal of the battery, which is called the cathode. The one connected to the positive terminal of the battery is called the anode. And here we placed any gas. It's not necessary that it should be air. It can be hydrogen gas, nitrogen, oxygen, chlorine. Any gas can be there at very low pressure. Okay? Now, as you see, nothing will happen right now. Nothing will happen. But as you see, with the help of this vacuum pump, you will keep decreasing the pressure here. And with the help of this battery, you will keep increasing the voltage. Two things need to be done. One is to increase the voltage. And one is to decrease the pressure. Sir, why do we need to do both these things? Tell us the reason behind it. You know that gases are very bad conductors of electricity. That's why we are decreasing the pressure, removing the gas. That is, if the quantity of gas is less, it will be easier to conduct electricity through it. Sir, why are we increasing the voltage? If this voltage increases, you know what is the tendency of metals? To lose electrons. Look carefully. This metal, the cathode one, will lose electrons. Because you are increasing the voltage, this electron that is coming out will have a lot of energy. Now, whatever gas you have kept inside, whatever it is, if you have kept hydrogen. Let's say you kept hydrogen. Let's say you kept air, so there will be oxygen and nitrogen. Okay? Let's say you kept carbon dioxide. Any gas can be kept. I've assumed hydrogen. This electron that came out of the metal will strike the hydrogen gas because the voltage is very high, so it will have a lot of energy. As soon as it hits it, it will break it down into two isolated atoms. Okay, sir, then? Then again, it will strike it. The energy is still so high. It will strike it again, and it will ionize it. It will ionize it. I have written an equation for this. It will ionize it. Now, the electron that came out of the metal, and the electron that came out of the hydrogen gas. These two will move straight ahead, keep moving, keep moving. They move in a straight line. There will be small holes in between. And they will come out through these holes. We have placed some fluorescent material behind. Sir, what is this? Fluorescent material. A material that, if any energy strikes it, it emits light. Sir, what are you saying? We have never seen such a material. Oh, your cheek is somewhat like that. Not exactly. How? Sir, I don't believe it. I don't believe it. Oh, look, brother. I don't want to do such an experiment with you. But if you find a stupid friend, you can do the experiment with him. What will you do? Make your friend stand in front of you and show him the fluorescence experiment. Slap him hard on the cheek. As soon as you slap him, you will see that his cheek will start to turn red after some time. Yes. The same is happening here. These electrons that are coming, where did these electrons come from? One came from the metal, and one came from the gas. They will come out from between the anode. We have placed ZnS behind. Okay? This is the same material that emits light when struck. So, when these electrons strike here, light will be emitted from here. They strike, light is emitted. They strike, light is emitted. Okay? These particles that are coming and colliding are named cathode rays. Today, we call cathode rays electrons. All these things are written here. Pressure will be very low. Voltage will be very high. Gas molecules will be ionized. They are indeed being ionized. Electrons are coming out. They are being ionized. Okay? And these negatively charged particles, electrons, which were called cathode rays, go to the other side of the tube, and what is placed there? The same fluorescent screen, coated with ZnS. These electrons. Okay? What will they be called? That is, cathode rays. Right? Remember, the next time you meet your stupid friend, you have to do this experiment. What are the properties of cathode rays, electrons? Okay? First of all, they have a mechanical nature or particle nature. I will explain. I will explain. What is particle nature? Let's explain that first. In the world, only one thing can exist in one place. Okay? Like all the things you can see with your naked eyes around you. Almirah, book, pen, copy, fan. Okay? All the things you can see have particle nature. Only one thing can exist in one place. Like there is another way too. See, when two things have particle nature, they collide with each other, and energy is exchanged between them. Okay? Now, we don't have to see its experiment. Otherwise, brother, grab your stupid friend again and slap him hard on the cheek. You will see that when your hand goes to his cheek, energy will be exchanged. Energy will be transferred from your body to his body. Okay? This is an example of particle nature. You have particle nature. If your stupid friend also has particle nature. That's why energy was exchanged. Okay? The same is happening here. These cathode ray particles were coming from here. You placed a mica wheel in the path. Mica is not red, that's you. Mica wheel. What is a mica wheel like? Like you made that in 10th class in childhood. A pinwheel. Right? The one that spins round and round. Yes. These electrons will come, and this mica wheel will be placed in the path, so it will start rotating. Oh, it will only rotate if it gets energy. And electrons have energy. That's why it will get it. So, what is the nature of electrons? Particle nature. When they strike the mica wheel, they are rotating it. Okay? Secondly, they have a negative charge. How do we know? See, without deflection, if we talk about nothing being placed, they would go straight, absolutely straight. But as soon as you place an electric field in their path, where the negative plate is upwards. The positive plate is upwards. You will see that instead of going straight, they will deflect towards the positive one. Oh, only that will be attracted towards the positive which is itself negatively charged. Right? That will be it. Deflected towards the positive, proving that it has a negative charge. Okay? Another very important thing. Whenever cathode rays or electrons, it's the same thing. Strike a metal whose atomic mass is very high, then X-rays are emitted from it. What is emitted? X-rays are emitted. Let me repeat. Electrons or cathode rays, whenever they strike a metal whose atomic mass is very high. Then after striking, what is emitted from it? It is written here, that is, X-rays are emitted. Electrons are moving charges. You know that moving charges have electric fields and magnetic fields. Are they deflected by electric fields? Yes. Will they also be deflected by magnetic fields? Absolutely. See, if nothing was placed, then cathode rays would come out from here and strike straight ahead. But look at the top, what is held in the hand? A horseshoe magnet. As soon as the horseshoe magnet is placed, you will see that these rays will be attracted towards it. And why would that happen? You already know. Brother, this charge will have an electric field, a magnetic field. The south of its magnetic field and the north of this horseshoe will be coming towards each other. That's why they will be attracting each other. That's why it will be going towards it. Okay? Let's talk about some other properties. Cathode rays ionize gases. See, this was already discussed. On the very first page, we did this. This is also a cathode ray that came from the metal. This is also a cathode ray that came from the gas. But has the gas been ionized? Yes, sir, absolutely, electrons have come out of it. So, we already discussed this, there's no need to worry about it. Specific charge of cathode rays. Let me tell you something different. Wherever you see the word 'specific'. Okay? Then understand that first of all, it is a ratio. Secondly, the denominator will be mass. It's a ratio, and the denominator will be mass. Like specific dash of cathode rays. Then you see, the denominator will be the mass of cathode rays. Sir, what will be in the numerator? Since it's a ratio, whatever is written, if it's specific charge, then charge will come. If it's volume, volume will come. If it's density, density will come. Whatever is written, children, that's what will come. Okay, sir. So, specific charge of cathode rays, understood? Yes, sir, understood. That is, charge of cathode rays divided by mass of cathode rays. Everyone knows. What is the charge on an electron? -1.6 * 10 raised to the power -19 Coulombs. What is the mass of an electron? 9.1 * 10 raised to the power -31 kg. And if you want to find the specific charge, that is, what do you have to do? What will you put on top? Charge. What will you put at the bottom? Mass. You will divide both. So the answer will be 1.76 * 10 raised to the power 11 Coulombs per kg. Okay? The specific charge will not change when the gas is changed. This is very important. This can be asked in the exam. Sir, why will it not change? You tell me, what is a cathode ray? Sir, it's an electron. Suppose instead of hydrogen gas, you kept chlorine gas here, then, children, it would become Cl. It would become Cl, Cl, Cl, Cl positive. But electrons would still come out. Oh, yes, sir. Electrons are coming out of the metal. Whether it's chlorine gas or hydrogen gas, electrons will come out. When you know that electrons are the same for everything. The same. So obviously, its charge will also be the same. Mass will also be the same. That's why the specific charge will also remain the same. Even if you change the gas, the specific charge of cathode rays will not change. Will not change. Will not change. Okay? The color will not change on changing the gas. We have already explained that because you know the specific charge itself is not changing. Its energy is not changing. So obviously, the color will also not change. Questions can be asked on these two points. Let's talk about Millikan's oil drop experiment. You also study it in physics. I know. Okay? But what is it used for? What is it used for? That is, to find the charge on an electron. How is it done? I will tell you. Okay? Below is the chamber. The chamber has two parts. One upper, one lower. Okay? In the upper part, you have an oil dispenser. From that oil dispenser, very small droplets of oil will come out. Very small droplets will come out. Okay? They will come down through this small opening. Okay, sir. In the lower hole, you have taken these two metal plates. And you have connected them to a battery. And from here, you are passing rays. What are you passing? Rays. Which rays will ionize this air? What will they do? Ionize. I will tell you what will happen. Whatever X-rays etc. are emitted. Okay? They will ionize the air. Will they do it? Yes, they will do it. They will do it. We, yes, we will do it. And what will come out? Electrons. Since these oil droplets are coming down, will these electrons stick to these droplets? Yes, sir, they will stick. How many electrons will stick? Sir, now that is unknown. Maybe five, or two, or three, or four, or one, or twelve, or fifteen, whatever sticks. That will be an integer. Right? It's not possible that 13.4 electrons stick. Can this happen? Absolutely not, sir. What are you talking about? Okay? Either 13 will stick, or 14, or 12, or 18, or 2 lakhs, or 5 lakhs. But it's not possible that 12.4 sticks. Right? 13.7 sticks. 21.3 sticks. This is not possible. Not possible, not possible. Okay? Okay? This is not possible. So what will happen? That's why electrons are sticking here. The total charge on them will be equal to that is, ne. Here, n is the number of electrons. e is the charge.

Inside on one electron that is -1.6 * 10 to the power of -19 Coulombs. That is what is written here. Okay? When the oil drop comes down, it will adsorb these electrons, and the voltage, meaning its voltage, has been kept in such a way that the oil drop becomes stationary. What happens? It becomes stationary. Then from there, we will find out the charge. How much charge will be there, that is, ne, all those things I have told you here. Okay? Just like when the discovery of the electron was known, that there is some negatively charged particle inside the electron. Since then, everyone started thinking that perhaps there must be some positively charged particle inside it as well. Now, that was talked about. The same cathode ray tube was taken again. The only difference this time is that here they have shown the cathode as perforated. Perforated means that there will be small holes in between. Okay? Sir, what we read earlier about the cathode ray tube, was the anode in that not perforated? It is absolutely perforated. It is not written here, it is just not written. That does not mean that it is not perforated there. That is also perforated. Look here, what is this? That is perforated. What is it? That is the cathode. And what is here along with it? That is the anode. The cathode is obviously negatively charged. The anode is positively charged. There is nothing to explain. Then again, the same thing has to be done. What has to be done, sir? What has to be done to the pressure? Decrease with the help of a vacuum pump. And what has to be done to the voltage? Increase with the help of this battery. You will see that first, electrons will come out from this metal. What will these electrons do? Whatever gas you have kept here. Suppose you have kept hydrogen gas. Sir, you are starting to teach the same thing again, that these electrons, these electrons that came out of the metal, will first convert it into isolated atoms. Then what will they do? They will ionize them. Sir, you have already told us these things in cathode rays. You are absolutely right. The only difference is this. This time, these H positive ions. These positively charged particles will now come out from here and strike at the back. Here too, there will be some fluorescent or phosphorescent material present, on which it will strike and emit energy. Okay? And this, this is your anode ray this time. I am saying a statement to you. Tell me if it is true or false. If I say that cathode rays come out of the cathode, is that statement absolutely correct? Yes sir, what are cathode rays? Electrons. Where did those electrons come out from? One from this metal and where did they come out from? From the gas. So they come out of the cathode, that is absolutely correct. But if I say the same thing to you here, that anode rays come out of the anode. Then that is absolutely rubbish. Why? Because what are anode rays? Whatever gas you took, its positively charged part or its cation, whatever you want to call it. For example, if you took hydrogen, then it is H positive. If you took oxygen, then it can be O positive. If you took nitrogen, then it can be N positive. If you took chlorine, then it can be Cl positive. So anode rays never come out of the anode. But cathode rays do come out of the cathode. Okay? They come out. Okay? So that is what is written, that m positive will go towards the cathode. Okay? They pass through the perforations. Here it is, here it is, it will pass through these perforations. Okay? We will study its properties too. Similarly, it also travels in a straight line, just like cathode rays did. And if an object comes in its way, it will cast its shadow. It will also have particle nature, brother. If you keep a mica wheel in its path, it will rotate it. It will be positively charged. Sir, how did you know? How did you know? Although it was moving straight, you applied an electric field in its path. You applied positively charged and negatively charged terminals. They were attracted towards the negatively charged terminal. So, only that will be attracted towards the negative charge which has a positive charge on it. They are deflected by electric field. Just told you, magnetic field, obviously, right? Because it is a moving charge. This is a moving charge, so it will have an electric field and a magnetic field. So obviously, both the magnetic field of the magnetic field and the magnetic field applied from outside. Both will interact with each other. It is possible they will attract. It is possible they will repel. But they will definitely do so. Okay? The specific charge on anode rays is very, very important. These last three points are quite important. Questions can come from these in the exam. That is, charge of cathode ray / mass of cathode ray. Do you know? If I am writing gas here. I am writing anode ray here. Let's assume I kept hydrogen gas. So, you know the anode ray is H positive. Suppose I kept chlorine gas. So the anode ray is Cl positive. Suppose I kept nitrogen gas. So maybe it is N positive. Right? Are you understanding? Although the charge on all of them is the same. If we talk about one positive, one positive, one positive. But the mass of all of them is different, right? Its mass is 1 amu. Its mass is 35.5 amu. Its mass is 14 amu. So obviously, this will be different. For this reason, the specific charge will change on changing the gas. Because the mass of every anode ray is different. Okay? The color will also change. Because the energy of each ion will be different, so the color will be different. The very first model of the atom, inspired by these discoveries, was which one? Thomson's model of the atom. What did he assume? That the atom is like a watermelon. The red part, the red part, is showing. That is the positively charged part of the atom. And these seeds visible in the middle, black black, represent the negatively charged particles of the atom. Okay? So why did it fail? Everyone said, if this is positive and this is negative, then they should attract each other. Because opposite charges do what? They attract each other. Okay? They attract each other. So if they attract each other, then they should attract. That is, the atom should be unstable. But the atom is stable. So when these things were asked to Thomson, he could not explain the atomic stability when tested by collisions, nor could he explain the hydrogen spectrum. Okay? So when these things were asked to him, he said that he does not know anything about it. Now let's look at some questions based on what we have studied, and tell me the answers quickly. First, select the correct statement from the following. Atoms of all elements are composed of two fundamental particles. No sir, there are three fundamental particles: electron, proton, and neutron. So this statement is wrong. Mass of the electron is 9.103 939 10 - 31 kg. Yes, it is 9.1 10 - 31 kg. Clear? All isotopes of any element have the same chemical properties. Yes, they are the same, brother. Physical properties are different. Like H2, D2, and T2. Their melting point will be different, their boiling point will be different. But the physical properties will be the same. Okay? Protons and electrons are called nucleons. No sir, we have studied all this in basic concepts of chemistry. The things found inside the nucleus are called nucleons. That is, protons and neutrons. Dalton's atomic theory regarded the atom as an ultimate particle of matter. Dalton's atomic theory assumed that the atom is the ultimate particle of matter. Yes, absolutely. So which ones are correct? Option number one, that is B, C, and D. The specific charge of cathode rays, tell me, what does it depend on? Does it depend on the gas? Does it depend on the material of the discharge tube? Does it depend on the potential difference applied to the cathode and anode, or is it a universal constant, not depending on anything? Cathode rays are what? Just said, electrons. What is its specific charge? That is, charge of cathode rays upon mass of cathode rays. Do you know this ratio is constant? This is also fixed. This is also fixed. So what will be the answer? The answer will be fourth. It is a universal constant. Right? Which of the following statements is incorrect? Brother, whatever you see in the exam, correct or incorrect, always underline it first. Okay? So, which of the following statements is incorrect? We have to tell the wrong statement. Cathode rays are emitted from the cathode. Yes, they come out from the gas and also from the cathode. So this statement is correct. Cathode rays travel in a straight line. Yes, they travel in a straight line, brother. Absolutely. If no electric or magnetic field is applied in their path, they travel in a straight line. Anode rays are heavier than cathode rays. Absolutely. What are cathode rays? Electrons. And the anode rays are the cation of any gas. Whether it is of hydrogen, chlorine, helium, or any other. Obviously, its mass will be much greater compared to it, maybe thousands or millions of times greater, depending on which cation it is. So this is also correct. So only this must be wrong. But let's check anyway. Anode rays are emitted from the surface of the anode. Absolutely wrong, sir. Cathode rays are emitted from the cathode. Anode rays are not. Anode rays are the gas, which is its cation in the middle. Okay? So option number D is the correct answer. Next, on what does the charge/mass ratio of anode rays depend? Charge upon mass ratio, what is this called? It is called specific charge. It is called specific charge. Tell me. Just explained a little while ago. I want you to do this as homework. Just explained a little while ago. I am telling the truth. We have worked very hard this year on the PPT. A lot of effort has gone into condensing so many classes, more effort than in the classes themselves, I swear. Next is Rutherford's model of the atom. Okay? Rutherford's model of the atom was based on Rutherford's experiment. Now, what was Rutherford's experiment? Let's talk about that first. What did Rutherford take? He took some radioactive particle from which alpha rays were being emitted. Sir, what are alpha rays? It's nothing, brother. It is the nucleus of helium. The nucleus of helium, here it is. H2, not H2 positive. Helium has lost two electrons. Only the nucleus of helium will remain, which will have two protons. Two neutrons. Okay? These are coming out from here. Alpha rays are coming out. Okay? They travel in a straight line. Everyone knows this too. Nothing to explain. Okay? In front of it, he had placed a very thin gold foil. Okay? And he wanted to know that there will be gold atoms inside this gold foil. What will be the structure of those atoms? What kind of things will they be made of? Okay? What did he find? And behind it, a screen was placed. What was the coating on the screen? Again, ZnS. Understood? What kind of material is ZnS? It is a material. It is a material on which, when struck, light will be emitted. Okay sir. Okay. Okay. What happened? Alpha rays came, and maximum alpha rays passed straight through. That is, they passed directly through the atoms of gold. So he found, okay, maximum alpha rays are going straight. This means that as I am able to walk straight here. Tell me, if I can walk straight, what does that mean? Sir, it means that there is nothing else in the path. This is what he found, that if maximum alpha rays are passing straight through, then it means that most of the space inside the atom is empty. Then he found that there were very few alpha rays that were being deflected at some angle. Deflected by an angle theta. Their rays, meaning they were going straight. Okay? And something appeared in their path, and they changed their path. Okay? This must have happened because there is some positively charged particle inside. Listen carefully. There will be a positively charged particle. Whose mass will be very high. But it will occupy very little space. Sir, prove both these things. The mass will be very high. Okay? And it will be positively charged, and it will occupy very little space. Prove all three things. I will prove all three things for you. See, first of all, what charge do the alpha rays coming have? Positive. So, what will repel it? Positive. So, this much is known, that where deflection is happening, some positively charged particle is coming in its path. Okay? Secondly, its mass will be very high. How do you know this? Oh brother, the mass of helium is 4 amu, right? So obviously, whatever is deflecting it, its mass will also be very high. It cannot be as light as an electron. Okay? Thirdly, it will occupy very little space. How do you know this? Because most of the alpha rays passed straight through, didn't they? There was no one to stop them. So from these things, it is clear that whatever space it occupied, it must have occupied very little space. And very, very few particles struck and came back. Out of millions, only one particle, right? This is all written here, that what are we projecting? Alpha particles. Onto what? A gold foil. And the thickness of just 1000 atoms. Okay? If Thomson's model was correct, then heavy alpha particles would pass straight through, and there would be minimum deflection. But that was not the case. That was not the case. Look at this. What do you see? Maximum passed straight through. What does this tell us? All space is empty. Okay? Some deviations occurred at small angles. So what was learned about the atom? There must be some positively charged particle. Some out of thousands or millions struck and came back. So it became clear that whatever is causing the deflection, it is concentrated in a very small area. Okay? Another very significant finding was that n, meaning here, the number of alpha particles scattered. This is n. This is n. This is n. This is not n. This passed straight through. Okay? The number of alpha particles scattered is directly proportional to z². What is z? Its atomic number. Its atomic number, obviously, sir, you know the atomic number of these alpha particles? That is 2. It will depend on its z. Sir, why will it depend on its z? Oh brother, what is repelling it? Sir, its protons are repelling it. So how many protons will there be? The higher the atomic number, the more. So that's what I've written. What French have I written? Right? The higher the atomic number, the more they will be deflected. There will be more alpha particles. Okay sir. Okay? That is, if I reduce its atomic number here. If I put copper instead of gold, then these deflected particles will decrease. Okay? No sir, if I put something with a higher atomic number than gold, then they will increase. Simple. Okay? Another thing, the number of deflected particles is inversely proportional to sin⁴(θ/2). What is θ? This is the angle of deflection. It was going straight. It got deflected at some angle. This is that θ. This is that θ. May God save you from such a situation. Right? As soon as it strikes at the back, where it strikes, scintillation will be observed. What is scintillation? Here, see. Live example of scintillation. Live example of scintillation. Unfortunately, perhaps last year you saw this live example when the results came out. God willing, I pray that this year you do not have to see a live example of scintillation. You do not have to see it. Yes, if it happens to your bad friend, that's fine, but it should not happen to you. I wish this from the bottom of my heart. Right? What is scintillation? As soon as alpha particles strike somewhere, light will come out from there. Okay? Mom is doing the same thing. Mom is holding her hair first, and as soon as Mom hits anywhere, say on this leg, you will see that this leg will become red after some time. Right? Yes, yes, yes. Everyone is understanding, brother. Right? 1 minute, I am coming. In 1 minute. Okay sir, okay, okay, okay. Yes, yes, yes, yes, yes. This is Rutherford's model of the atom. In the center, there is the nucleus, and inside it, there will be protons. Neutrons were not discovered at that time. That is why I have not told you about the discovery of neutrons yet. Outside, electrons will be revolving. See, the size of the atom is 10⁻¹⁰ meters, and the size of the nucleus will be? 10⁻¹⁵ meters. That is, if, let's say, an entire football field is considered the size of an atom, then I think the size of the nucleus will probably be a football, or even smaller. Right? How much? 10⁵ times smaller. 10 raised to the power of minus. Nucleus is good, right? A marble. Absolutely. The nucleus will be a marble. Okay? If the atom is considered a football stadium at a distance of 50 yards, then a small pebble or stone will be the size of the nucleus. So you can see how small it is. Okay, tell me one thing. If its size, the size of the nucleus, is 10⁻⁵ times smaller than the size of the atom, meaning 10⁵ times smaller, then tell me one thing, how small will the volume be? How small will the volume be? How small will the volume be? Tell me that. The size has become 10⁵ times smaller. How small will the volume be? 10¹⁵ times. Right? Because the volume will be equal to 4/3 πr, if you cube r, if you cube 10⁵ times, how much will it be? It will be 10¹⁵ times smaller. It will be 10¹⁵ times smaller. Okay? Let's do some questions on Rutherford's model of the atom. Rutherford's experiment showed that there is a nuclear model of the atom. What did he use in it? What did he use? What beta particles, gamma rays, nucleus of helium atom? Answer is nucleus of helium. Many children will read helium atom and choose the third option as the answer and will not read the fourth option. This should also be a lesson for you for the final exam, that we must read all four options, even if the first option is correct. Okay? Not helium atom, nucleus of helium. Helium atom is He. Alpha rays are He²⁺. Okay? Which of the following conclusions could not be drawn? Could not be drawn from Rutherford's alpha ray particle scattering experiment. Most of the space in an atom is empty. Yes, absolutely, Rutherford said this. Radius of the atom is 10⁻¹⁰.

The nucleus will be 10 to the power of -15 meters, and the nucleus will be 10 to the power of -15 meters. Yes, this was also said just now, I just read it. Electrons will move in a circular path of fixed energy called orbits. This point was not told, brother. Who told this? Bohr told this. Right? Electrons and the nucleus are held together by electrostatic force of attraction. Yes, that is true. The nucleus is positively charged due to the presence of protons. Electrons are negatively charged. Both will be attracting each other. Very good question. It's a very fresh question. Listen carefully, hear, understand. Alpha particles are projected towards the nucleus of following metals with the same kinetic energy. Okay, the alpha particle is going towards the nucleus of these four metals. The kinetic energy is the same. Towards which metal will the distance of closest approach be minimum? Okay, this alpha ray is going. It's going. To whom will it be able to reach the closest? Right? Distance of closest approach means to whom will it be able to reach the closest? Tell me, sir. It will reach closest to the one that repels the least, right? Didn't you see in class there are many types of ladies. Okay? Some are such that you sit three benches away, or your smelly friend sits three benches away, and they start acting like this. "Ugh, I can smell something, I don't know what kind of people come without bathing." As soon as she says "without bathing," you start thinking it's about you. Right? So you stay a little away from her. Okay? And there's another one. Okay? Who feels pity for you. Okay? Even if you are sitting on benches in front and behind, she doesn't say anything. But as soon as you go to her bench, dare to sit on her bench, then she starts talking. Right? The stench of your smelly friend is so much. Okay? So then, right? Tell me, where will the distance of closest approach be? Sir, the one that repels the least. Who repels the least? Protons are repelling it. Protons are equal to what? Whatever the atomic number is. Here the atomic number is 29, 47, 79, 20. Sir, here the protons are the least, the repulsion is the least. So it will be able to reach closest to the nucleus. Right? Did everyone understand? Did you understand? Some children are saying, "Sir, how did you get footage of our school?" Right? Come on, come on, come on. Limitations of Rutherford's model of atom, I am explaining what is written. You must know the name of a scientist, Maxwell. Do you know what Maxwell said? Any charged particle. What kind of particle? A charged particle. A charged particle always emits energy. Okay? If it is in accelerated motion. Maxwell is asking Rutherford, "Tell me, what does your model of the atom look like?" He says, "Sir, it looks like this. Look, look, it looks like this. The nucleus is in the center, which has protons inside, and electrons are revolving outside." He says, "Oh, the electron is charged." He says, "Yes, yes, it is negatively charged." He says, "Oh, oh." He says, "This path, the path, it's accelerated motion. At every moment, at every instant, acceleration is shown in it. The velocity is changing." He says, "Yes." He says, "Oh my god, if this electron of yours is in accelerated motion, then its energy must be decreasing. It must be emitting energy." See, energy is emitted. It's not a Wi-Fi signal. Energy is being emitted, so its energy will keep decreasing. If its energy keeps decreasing, decreasing, decreasing, decreasing, decreasing, decreasing, decreasing, then it will fall into the nucleus. Okay? This means the atom is unstable, but the atom is stable. Tell me why? He says, "I don't know anything about this." So Maxwell declared, brother, then the model of the atom failed. I made it fail. Okay? In the previous question, the sir asked for the minimum. In the question. Distance of closest approach. The distance will be minimum. Yes. So the distance of closest approach will be minimum. So it will be minimum right here, son. Right? It will sit closest to it. Right? So the distance of closest approach will be minimum right here. The distance will be the least. It will go closest to the nucleus. This one will be farthest. It will be driven away from afar. This is the same. That nagging girl, right? Who sees you and your smelly friend and says, "Yes, yes, he hasn't bathed again today." Right? So your distance from her will always be more. Come on, everyone is talking in their regional language. That's good. You should. Okay? It's a good thing to relax the mind. You should do it. See, I am explaining some terms. Okay? Although you might have read them in inorganic, but I'll tell you anyway. What are isotopes? They have the same atomic number. Different mass number. The example is written in front of you. What are isobars? Okay? They have different atomic numbers. What is the mass number? Same. Like look at the atomic numbers of carbon and nitrogen, they are six and seven. But the mass number, we took the isotope of carbon which is 14. Nitrogen is normally the 14 one. What are isotones? They have the same number of neutrons. And how were neutrons calculated? Mass number minus atomic number. 31 - 15 = 16. 32 - 6 = 16. This will also be 16. In isodiaphers, okay? a - 2z is the same. That is, mass number minus twice the atomic number. These two are the same. Okay? And isoelectronic means those in which the number of electrons is the same. Like look at this, nitrogen should have had seven electrons. But why seven? Why? Because its atomic number is seven. But it has gained three electrons, so it will have 10. Oxygen should have had eight. But it has gained two, so it will have 10. Fluorine will have nine. It must have gained one more, so it will have 10. Sodium should have had eleven. But it has lost one, so it will have 10. Magnesium's atomic number is 12. It should have had 12. It must have lost two, so it will have 10. Aluminum has 13. It must have lost three, so it will have 10. So these will be called isoelectronic species. Okay? Next, we are going to talk about waves. What is a wave? First of all, sir, tell us about it. Okay? What is a wave? Okay? Look, a wave is a disturbance by which we transfer energy from one place to another without any transfer of matter. Without any transfer of matter. Matter has not been transferred from one place to another. Okay? But energy has been transferred. Okay? That is called a wave. Sir, no sir, I didn't understand. Look, son, if you have to explain something to mothers, right? They explain it with particle nature. Right? Mothers explain it like this. They explain it like this. Right? My mother also explained many things to me. And she explained it like this. She explained it like this. Sir, is this you? In our time, there was no mobile, otherwise we would have had many such pictures. Right? And the pictures would have been like this. Part one, part two, part three, part four, and sometimes such pictures would be released two or three times a day. Breakfast, lunch, evening tea, dinner. We were beaten up so many times by our mother like this. Okay? So explaining to mothers is like this. They transfer energy from their body to your body. But they also transfer matter along with it. Right? You don't understand things when they talk nicely. They hit you, only then you understand. This is particle nature. Wave nature, you know what it is? Energy will be transferred from one place to another. But there will be no transfer of matter. No. No. Sir, how, how, how? You tell me, like if you are doing some stupid thing. Okay? Suppose you went to a wedding. Okay? And you brought a full plate of food. In which a rasgulla is floating under the pickle. Okay? Papads are stuck inside the rasgulla. Okay? And there, four of your father's friends are standing. Right? And right there, and right there, you come to your father and say, "Look, Dad, you said to collect the entire 'shagun' (auspicious gift). Look, look, is anything missing? If anything is missing, tell me." And you say softly, "Dad, I brought an envelope. Should I put it in there?" Right? Then the father feels very embarrassed, thinking, "Is this my blood? Is this my blood?" But he can't hit you there. The wedding is going on. Your father's friends are standing around. So how do they explain things? They explain with their eyes. With their eyes. Right? If they have to say anything, they do this. They take off their glasses and do this. Like this. Just now, energy is being transferred. When you look into their eyes, you understand that you are doing something stupid. I shouldn't have done this. Yes, you feel that you are doing something wrong. That's it, that's it. Energy is being transferred without the transfer of matter. If mothers have to transfer, they will explain by hitting you with slippers, using particle nature. If fathers have to transfer, they explain with their eyes, with their eyes. Right? My father also used to explain with his eyes. My father also used to use particle nature. But I knew that if I said the next line, you would understand. I knew that if I didn't understand these things through wave nature, then they would explain it to me through particle nature. So it's better that I understand it through wave nature. Right? So I used to understand. I used to understand through wave nature. Brother, understand. Okay. Yes, sir, true, sir, true, sir. Right? A hint is enough for the wise. Absolutely. Absolutely. That's it, that's it, that's it. Okay. So that's it. This is good. How do these waves travel? Right? They are in the form of, you can say, if yes, if the wave is propagating in this direction, then it is called crest, trough. Crest, trough. Crest, trough. Okay? Good. Now, what is wavelength? The distance between two consecutive. Consecutive means continuous. The distance between two consecutive crests and troughs will be called what? Wavelength. Like look here. The distance from one trough to another trough. This will be called wavelength. Or you can also say the difference from one crest to another crest, this will also be called wavelength. Since it is a distance, its unit will obviously be meters, centimeters, nanometers, picometers, angstroms. And you know how to convert all these things into meters. Okay? Well done, Kamlesh. I am so proud of you. You have reached MBBS college. That's very good. Okay? Let's talk further. Okay? So obviously, I have told you their distance. I have also told you the unit. Okay? You know these things. Like if you want to convert angstrom to meters, it's 10 to the power of -10 meters. If you want to convert nanometers, it's 10 to the power of -9 meters. If you want to convert picometers, it's 10 to the power of -12 meters. Okay? So these are given differently. Okay? What is the relation? Okay, no, one more thing to tell. What is frequency? First, from one point, how many waves pass through this one point in one second will be called frequency. The number of waves passing through a point in one second is called frequency. What will be its unit? That is Hertz, or it is also called per second. What is wave number? It is the reciprocal of wavelength. Like its unit was meter, its unit will be per meter. Its unit was angstrom, its unit will be per angstrom. Its unit was nanometer, its unit will be per nanometer. Okay? It is also written. Wave number is equal to 1 / lambda. C, you know that all waves, generally speaking, travel at the speed of light. It is written as C. What is the relation between these three? Yes. C = mu lambda. C = mu lambda. That is, from here it is clear. Mu will be equal to C / lambda. That is, from here you have understood that any wave with a longer wavelength will have a lower frequency. You can also say the opposite. The one with a shorter wavelength will have a higher frequency. Look, the speed of different waves, whether ultraviolet, visible, or infrared, we generally assume their speed to be the speed of light. Then what will be the difference? The difference will be in their frequency. In their wavelength. The one with a longer wavelength has a lower frequency. The one with a shorter wavelength has a higher frequency, sir. What is time period? Just like wave number was the reciprocal of wavelength. Similarly, what will be the time period? That is, the reciprocal of frequency, that is, 1 / mu. Okay? It is written further. Reciprocal of wavelength. All these things explained on the previous page are written here. Yes, this is new for you. What will be amplitude? Suppose the wave is propagating here. The wave is going in this direction. The maximum displacement from this mean position, either in the crest or in the trough, this maximum displacement will be called what? Amplitude, denoted by capital A. I have already told you this. We will not talk about it again. What is particle nature? Only one thing can be in one place. That is called particle nature. What is wave nature? Two or more things can be in one place. All the things we see around us. All of them have particle nature. This pen in my hand, the book, the copy, the wall in front, the cupboard, the books. All of them have which nature? That is particle nature. Like if I place a pen in this hand here. Okay? What? Now, in this place in the entire universe, nothing else can be there except the pen. Nothing else can be there except the pen. Okay? And in wave nature? Like a wave is coming from here. Another wave is coming from there. Now suppose the crest of both overlaps with the crest. Then you know a new wave will be formed. You have studied the superposition principle in class 11th. That is, in which chapter of physics? In waves. Okay? And if the crest falls on the trough, then the resultant wave that comes will be very small. Very small. Okay? So at this point where they combine, both waves are coexisting. Brother, it's simple. We have to study Maxwell's theory of electromagnetic radiation from this. Obviously, this chapter has many things in common that you also study in physics. One of these things is this. What does it say? Wherever the wave is propagating, wherever the wave is going. Okay? In the perpendicular direction, suppose the wave is going in this direction. Then in the perpendicular direction, there will be the electric field vector. There will be the magnetic field vector. The same is done here. If you make an x, y, z. If the wave is going in one direction. Then in the other two directions, one will have the electric field vector, and one will also have the magnetic field vector. Okay? A very important thing that Maxwell said was that any source of radiation, any source of radiation, the light being emitted from it, this light being emitted is being emitted continuously. It keeps getting emitted, keeps getting emitted, keeps getting emitted, keeps getting emitted. It's not that it's emitted, stops, then emitted again. No, it's not like that. It's always getting emitted. So energy is emitted continuously in the form of waves. Okay? It will have perpendicular electric and magnetic fields. That has already been explained. He said these will travel at the speed of light. These waves will travel at the speed of light, whether it is vacuum, solid, liquid, or gas. Okay? That is, they do not depend on the material medium. Although this is not true, but this is what Maxwell said, that they do not depend on the material medium. He also said one more very important thing, which is written here. Yes, it is written. He called energy intensity. First of all, what is intensity? Look here. A unit area. Understood unit area? 1 cm², or 1 m², that is unit area. And in 1 second, the number of rays falling on the unit area in 1 second will be called intensity. What will it be called? Intensity. And this intensity is directly proportional to the square of the amplitude. Is directly proportional to the square of the amplitude. I is directly proportional to the square of the amplitude. I am going to tell you a very important line. Now listen very carefully, on which a question can come and children can make a mistake. It will deliberately come in the exam that according to Maxwell, energy and frequency are proportional to each other. Children will see this, "Yes, yes, e = h nu." Yes, this statement is correct, and they will mark it as correct. That is absolutely wrong. He said there is no relation between energy and frequency. First of all, he called energy intensity. Secondly, he said that this I, intensity, is directly proportional to the square of the amplitude. It does not depend on frequency. Energy depends on what? It depends on the square of the amplitude. That line, E is directly proportional to nu, was not said by Maxwell, it was said by Planck. Okay? So, I will summarize the things that have been read here. First, whatever radiation is emitted from somewhere, what is its nature? Wave nature. Okay? Second, how is it emitted? It is emitted continuously. Third, at what speed does it travel? It travels at the speed of light. Okay? Fourth, there is no relation between energy and frequency. He spoke of energy in terms of intensity, and intensity is directly proportional to the square of the amplitude. Okay? Different types of electromagnetic radiations that can exist. Okay? Among them, the rays that are useful to us, that we can see, are visible rays. I will give you a rough range of the wavelength of visible rays. 3800 to 7600 angstroms. You can also call it 4000 angstroms to 8000 angstroms, son. There is no tension. There is no tension. Okay? You don't need to take so much tension. You can also say 3800 angstroms to 7600 angstroms. Okay? Come, let's talk about different types of electromagnetic radiations. Going from here to here. Cosmic rays, they are written as such. These are not EMR, but okay, it will do. Okay? Cosmic rays, then gamma rays, then X-rays, then ultraviolet, then

Visible, then infrared, then microwave, and then that is radio waves. As you go from here to here, the wavelength is increasing. And you already know, if the wavelength increases, what will happen to the frequency? That is, it will decrease. What will happen to the frequency? That is, it will decrease. Okay? So how to remember this? I have memorized it this way; if you have another method, that will work too. That is, the cancer pill, due to X-rays, UV, right? UV, you know that, that is, it hit Yuvraj Singh, unfortunately, he had cancer, you know. C stands for cosmic rays, G stands for gamma rays. These are X-rays, ultraviolet, visible, infrared, microwave, and radio waves. Okay? He is a very big sports person in India. One of the greatest. God forbid anything happens to him. May Yuvraj Singh live as long as you. So, going from here to here, what is happening to the wavelength? Increasing. And what is happening to the frequency? Decreasing. Okay, it's the same in the visible range. These are what we see in the visible range, right? VIBGYOR. These are what we see. You know that the combination of VIBGYOR is white. In that too, as we go from here to here, lambda increases and frequency decreases. Okay? Look at the question, answer it quickly. What is the answer? That is, 3800 Angstrom to 7600 Angstrom, right? For visible. Let's look at the next question. There is a particular station of All India Radio which is using a frequency of 1368 kHz. The wavelength of the radiation emitted. The wavelength of the electromagnetic radiation emitted by the transmitter is. Okay, lambda is asked. C is given as 3 * 10^8 meters per second. So, C is equal to what? What is it equal to? Mu lambda. So, lambda will be equal to what? That is, c / mu. Here is the value of C. The frequency is 1368 kHz. In Hertz, how much will it be, sir? We will multiply by 1000. When you solve this, 10^5 will remain. Can I write this as? Something like 3000 * 10^2, right? This 10^5 has been separated. If I divide 3000 by 1368, it will be around 2. Something. 2193 * 10^2. 19.3. Sir, do you remember the answer? I took it just two days ago, right? I took a PYQ from a competition, so that's why I remember the answer. Otherwise, I would have had to calculate it. It would have been around 2. Something. I am absolutely sure about that, no doubt about it. But according to that, what were the limitations of the electromagnetic wave theory? Okay? It could not explain the photoelectric effect, nor black body radiation. Sir, why could it not explain? Because they were based on particle nature. Sir, how were they based on particle nature? I will tell you. In the photoelectric effect, what happens? Suppose there is a metal. Okay? You shine a light of suitable frequency on this metal. The electrons inside this metal absorb the energy of that light. Okay? And then they come out. What comes out of the metal? They come out. Now tell me one thing. If the electron has absorbed this energy. Whatever energy this light had, this electron has absorbed it. It will absorb it only when the light has which nature? Particle nature, right? If it had wave nature. Like, suppose you have wave nature, and your mother's slipper also has wave nature. Then what would your mother do? Like, you are here. Your mother would hit you with the slipper, and the slipper would pass right through you. Right? Like, you see when they hit ghosts, the knife goes through their stomach, but nothing happens to the ghost. Why? Because we assume that ghost has what? Wave nature. Okay? I have just taken an example to explain. So obviously, the electrons absorbed the radiations. The electrons absorbed the energy of the radiations. So, it means those radiations must have had what nature? Particle nature. So, when these things were asked, it said, "Brother, I don't know anything about this." Okay? So later it was found that light has what nature? It has particle nature as well as wave nature. Wave nature was discussed by Maxwell. Now it was time for that is, about what? That is, particle nature. And who gave that? Planck gave it. Okay? Almost all the things that Maxwell said, he said the opposite. Right? He said exactly the opposite. He said exactly the opposite of what he said. For example, what did he say? Energy is continuously emitted from the source. He said it is emitted discontinuously. And this is true. If you have a tube light at home, the white tube light, the long one. Exactly like the white tube light here, look very closely. Look very closely. And you will see that the light is flickering. Don't look from afar, look very closely. And you will see that the light is flickering. So, if you look, you will know that yes, the light is flickering. Flickering means energy is being emitted, then stopping, then being emitted, then stopping. This means energy is not emitted continuously, but discontinuously. Okay? And what did he say? When energy is emitted, packets of energy will be emitted. What will they be? Packets of energy. Energy is absorbed or emitted discontinuously in discrete packets. Packets mean they will be separate. Maxwell said they are continuous. He said they are discontinuous. First, you press the button once, one pellet comes out. Then you press the button again, another pellet comes out. They are discontinuous in this way. Okay? And what else did he say? Energy is directly proportional to frequency. These were the things Planck said. Okay? In Planck. Planck said these things. Some constant will come. Okay? It will be h nu. And here n will come. Where n means what? Number of photons. Sir, what are photons? Photons are neutrally charged particles with zero rest mass. Energy is directly. Yes. We will call a packet of energy a quantum or a photon of light. Okay? Whenever you see the number of photons given, listen to me carefully. Either it is not given, or it is not asked. Let me repeat. It is not given in the question. If a numerical came and it was not asked. Then assume n to be one. No sir, it is given. Suppose it is given as 50, then, son, put 50. No sir, it is asked. Then find it, what's the big deal? Okay sir. So, e will be equal to what? That is, mu lambda. So, mu will be equal to c / lambda. Do you know that h is a constant, Planck's constant, whose value is 6.626 * 10^-34 seconds? The value of C is also known to everyone, that is, 3 * 10^8 m/s. So, this hc, h and c, both h and c are fixed in SI units, so their value will be approximately this. 20 * 10^-26. That is, in SI units. It will make the calculation in the exam quite easy for you. Okay, he also said one more thing. The speed of these radiations, which we have kept as the speed of light, is only in vacuum. If you change the medium, meaning if you make it solid, or liquid, or gas, then obviously its speed will change. Okay? It depends on the medium. There is another very wonderful topic on this, on Planck's quantum theory. Suppose there is any substance here. I have shown it with white, this substance. A ray of light came on it, whose frequency was mu1. Okay? Obviously, it will absorb it. Another ray of light fell on it from here, whose frequency is mu2. And it also absorbed it. Okay? Now, the total energy it absorbed, the total energy it absorbed. One is this light it absorbed, and the other is this. It will be h nu. It will be h nu. Now, suppose it emitted the same amount of energy as it absorbed. The same amount of energy was emitted. What will it be equal to? Its emitted frequency is given as mu3. mu3. That is, h mu3. Okay? I can also call this E1. I can call this E2. Its energy is E1, its energy is E2, its energy is E3, which is also called E emitted, no big deal. Suppose the total energy absorbed, and the total energy emitted, right? 100% of the absorbed energy is emitted. So, can I say that energy is additive in nature? Absolutely. Whatever was absorbed, the same was emitted. Can I also say this? If I write frequency instead of this. If I write it in terms of frequency, then it will be this. It will be this, and it will be this. If I take h common, it will cancel out. Can I also say this? Frequency is also additive in nature. Right? Frequency is additive, and energy is additive. But can I say this for wavelength? No sir, you cannot say that. Why not? Its wavelength will be lambda3. Its wavelength will be lambda1. Its wavelength will be lambda2. Look here, put c/mu3. Right? Here it will be c/mu1. Here it will be c/mu2. If I take c common, it will cancel out. That is, 1/mu3 = 1/mu1 + 1/mu2. Okay? So, if you want to find the wavelength being emitted, you will have to do 1/lambda1 + 1/lambda2. So, wavelength is not additive in nature, but energy is additive in nature. Frequency is additive in nature, and I have proven it in front of you. Absolutely. Let's do some questions. Calculate the energy of 1 mole of photons. See, the number is given. n is what? Number of photons. How many? 1 mole. 1 mole means Avogadro's number. Just like a dozen is 12, a mole is Avogadro's number, whose value is 6.022 * 10^23. Okay? You can also approximate it in numericals as 6 * 10^23. Photons of radiation whose frequency is given as 5 * 10^14 Hertz. Do we all know what e will be equal to? Sir, if n is given, I will use it here. Or if n was asked, I would use it here. It is neither asked nor given, so I will put n=1. Equal to n h nu. We can put the approximate value of n here. The value of h is 6.626, but let's put 6.6. Into 10^-34. I have put everything in SI units. This is also in SI units, this is also in SI units. This is just a number. It doesn't have any unit. And the frequency is also in SI units. 5 * 10^14. You can solve it if you want. If you multiply 66 by 5, you get 330. With 330, this decimal will be cut. So, 33 remains. If I multiply 33 by 6, you get 198. Now, do these. These two powers of 10 will make 37 together. If 10^34 is removed from that, then it will be just this. Okay? Sir, the answer is in Joules because everything is put in SI units. This is also put in SI units. This is also put in SI units. So, obviously, this will also come in SI units. What is the SI unit of energy? That is Joule. No sir, if it was asked in kilojoules, then I would divide by 1000. No sir, if it was asked in calories. Son, whenever you convert calories to Joules, you multiply by approximately 4.2. If you want to convert Joules to calories, you divide by 4.2. It is 4.183. But I have said approximately 4.2. Look at the next question. There is a 100-watt bulb. Okay, the power of the bulb is given. You know what power is equal to? That is, energy per unit time. Right? If time is 1 second, then energy is 100 Joules. Okay? Monochromatic light is coming out of it. Monochromatic means it has one wavelength. The wavelength is also given as 400 nanometers. Calculate the number of photons emitted. How many photons will be emitted, that is asked. Energy is given, wavelength is given, n is asked. Is there any relation between them? Yes sir. e = nhc / lambda. So, n will be equal to what? e lambda / hc. The value of e is given as 100. Lambda is in nanometers, son. I am putting everything in SI units. It will be 400 * 10^-9. I told you the value of hc. In SI units, you can keep it approximately this much, which will make the calculation a bit easier for you. So that is 20 * 10^-26. Let's solve this. In the table of 20, on what will it go? Five. What is this? 2000. If I solve these, 10^-17 will remain at the bottom. Which will go up and become 10^17. That is, n is approximately 2 * 10^20. Look at the next question. This is a question from NEET, son. Calculate the energy in Joules. You need to calculate the energy corresponding to light of wavelength 45 nanometers. That is, 45 * 10^-9 meters. Planck's constant is also given. C is also given. Energy is asked. Sir, should I use NHC / lambda again, or HC / lambda? See, neither the number of photons is given, nor is the number of photons asked. If this is the case, then put N=1. So, instead of n, put 1. Instead of hc, I told you, you can approximately put this in SI units, it will save us some time. Divided by lambda. Lambda is here. In the table of 5, this is 4, this is 9. 10^-17. 9 * 4 = 36. It will be 44. 444 * 10^-17. Oh sir, the answer is given in this form. No problem, no problem. How to do it? Uh, let me do this. I will multiply by 10 and divide by 10. The one I multiplied by 10 will make it 4.4. The one I divided by 10 will make it this. Exactly 4.4 * 10^-18. What is called the photoelectric effect? Okay? I told you the definition a little while ago, but still, I will tell you again. Okay? Again, son, the cathode ray tube is taken. Suppose we shine some light from here. Okay, it is said from anywhere. Actually, it would have been better to show it from here. Some light will fall on this metal. Light will fall on this metal, and electrons will come out of this metal. This electrode should have been shown here. The diagram is a bit strange, but no problem. Okay? Light will fall on this metal. The electrons inside this metal will absorb the energy of this light. And they will come out. What will the electrons that come out be called? That is, photoelectrons. Let's understand a bit more properly on the next page. Here is the metal. Light is falling on it, whose energy is h nu. The electrons inside the metal are absorbing this energy. Listen carefully. The energy of the light, h nu, has been absorbed by this electron. Okay? Now, it will spend this energy in two ways. Sir, in two ways? One is to come out of the atom. Right? This is the metal. To come out of the atom of this metal. The energy used to come out is called the work function. Is this somewhat like ionization energy? Yes, it is like ionization energy, but it is not ionization energy. It is like ionization energy, but it is not ionization energy, is it? Well, ionization energy is defined, right? The energy required to remove one electron from a neutral isolated gaseous atom. This is not a gaseous atom. You know, metal is solid. Okay, okay. So, I just told you for explanation. Okay? So, a part of this energy will be used to remove the electron, which is called the work function. Okay? Suppose this was 10 Joules. Okay? Out of that, 4 Joules were used to come out. How much is left, sir? 6 Joules are left, right? You had 10 rupees. You bought a toffee for 4 rupees. How many rupees are left? 6 rupees. And now with the remaining energy, the electron will start moving. That is, all that energy will be converted into kinetic energy. I am doing the same thing here. The total energy was used in what? One, in the work function, to remove it. And the rest in kinetic energy. What is this equal to? h nu. What is the work function equal to? h nu naught. Kinetic energy is known. 1/2 mv^2. Sir, what is this m? Mass of the electron. What is v? Velocity of the electron. What is h? Planck's constant. Mu? Frequency of light. Sir, what is this mu naught? This is called the threshold frequency or critical frequency. Oh sir, what is this? I asked, what is the minimum frequency that the light must have so that electrons can come out, so that the photoelectric effect can occur. Sir, I did not understand this. I will explain. The energy required to remove this electron is the work function. Okay? It is equal to h nu naught. You know the value of h. There will be some value for mu naught, right? Yes sir, there will be. Suppose it came out to be 60 Hertz. How much? 60 Hertz. Now, what does that 60 Hertz mean? It means that if the frequency of this light is 60 Hertz or more, then the electron will come out. Otherwise, it will not come out. Sir, I did not understand. Give a real-life example. I will explain. Suppose you liked a dress. Right? There is a wedding of a friend or relative, and you have to go there, and you liked a dress, and the cost of that dress is 3000 rupees. How much? 3000 rupees. So, what is the minimum amount of money you need from your father? Okay? So that you can buy that dress. Sir, 3000 rupees are needed. You are absolutely right. Okay? So, what is the minimum amount of rupees needed? 3000 rupees are needed. Okay? Now you went to your father. You said, "This and that, there is a wedding, my cousin's son's wedding. I need money for a suit." Okay? So, your father, with a big heart, took out from his pocket and gave you 1000 rupees. And said, "Go Simran, live your life." So, will you be able to buy that dress? The answer is no. Because the minimum amount needed is 3000 rupees. What did your father say? By giving 1000 rupees, right? "Go Simran, live your life." Right? How will Simran live her life? Right? Simran is not studying anyway. Okay? She cannot live her life. I am personally afraid that after Simran's results, Simran's books might commit suicide. I am just joking. You don't need to worry. The books might be useful next year. Let's talk further. Okay? So, what is this minimum frequency that must be there for the photoelectric effect to occur? What will you call it? Threshold frequency or critical frequency. Okay? Take it to the other side. Take h common. This will become. Yes, absolutely, this will become. Instead of mu, c / lambda. And

Instead of c / lambda c, I took out the common. 1 / lambda - 1 / 0 = 1/2 mv². Sir, what is this? Wavelength of light. What is this? This is the threshold wavelength or critical wavelength. Just as sir, you just told that the frequency of light should be equal to or greater than the threshold frequency, only then the photoelectric effect will occur. Can I say this for lambda as well? Absolutely wrong. Absolutely wrong. Sir, how? How is it wrong? Oh, lambda will be less, right? If the frequency is greater than the threshold frequency, then the wavelength of light will be what from the threshold wavelength? Less. Sir, how? Oh, both are inversely proportional to each other. If someone's this is more, then this will be what? Less. Okay, okay, okay. So if this was the minimum frequency that light should have so that the threshold photoelectric effect can occur. So if this was minimum, then what will I call this? The maximum wavelength that light should have so that the photoelectric effect can occur. Right? So that the photoelectric effect can occur. Okay? What was explained on the previous page is written through the image. If the frequency of light is less than the threshold frequency, then obviously it will go inside, but the electron will not come out. But if the frequency of light is equal to or greater than the threshold frequency, then light will go and this electron will come out. Emission will happen. The definition of threshold frequency is also written. Minimum frequency so that electrons can be ejected. Threshold wavelength is the maximum wavelength so that electrons can be ejected. Let's talk about some more things about the photoelectric effect. How many photoelectrons will be ejected in a second? They are proportional to the intensity. Okay? If the intensity is more, then more will be ejected. If it is less, then less will be ejected. Sir, look at this. I have taken a unit area. First, the same metal is here. Work function is 5 joules. Here you are just dropping two rays of light. And their energy is 9 joules each. 9 joules, 9 joules. Tell me, how many electrons will be ejected? Sir, this electron will use 5 joules to come out. The remaining 4 joules will be converted into kinetic energy. Similarly, this electron will also use 5 joules from the light that is coming, it will use 5 joules to come out, and the remaining four joules will be converted into kinetic energy. So how many electrons were ejected? How many electrons were ejected? Emitted. But if you have increased this intensity. Now instead of two, you have made it four. The energy is the same, son. The energy is the same, 9 joules, 9 joules, 9 joules each. So do you know now? Four electrons will come out. Yes. Okay? So the number of photoelectrons will just increase. That's what is written. The number of photoelectrons emitted per second is proportional to the intensity. That's what is written. Okay? The graph is also this. The rate of emission is the same. This is the number of photoelectrons emitted. Okay? Is directly proportional to the intensity. Conditions apply. Sir, what are those conditions? This energy should be greater than the work function. Only then will they come out, right? Otherwise, suppose its energy is less than 5 joules. Then, son, you needed ₹3000 for a dress, and father gave you ₹1000. So, son, will the wedding be celebrated? Right? Then will the wedding be celebrated? Okay, and look, the kinetic energy that will be ejected does not depend on the intensity. Sir, prove it. Here is the proof. Tell me, what was its kinetic energy? 4 joules. Its 4 joules. What is the kinetic energy of all of them? 4 joules. 4 joules. 4 joules. 4 joules. So kinetic energy does not depend on intensity. Earlier, only two rays were falling at unit area. Now four rays are falling at unit area. But there has been no change in kinetic energy. So, did you understand the graph? Yes, sir. Sir, no matter how much you increase the kinetic energy, the kinetic energy will not be affected. No, sir, I want to increase the kinetic energy. Sir, what do I need to do? Then you will have to increase the energy of this light. You will have to increase this. Suppose you made it 15 joules instead of nine. Made it 15 joules. What was the kinetic energy before? Four. Now what will it be? 9 minus 5 is four. Okay? Now what will it be? 15 minus 5 is that is 10 joules. 15 minus 5 is 10 joules. 15 minus 5 is 10 joules. It has become 10 joules. Kinetic energy has increased. So if you want to increase kinetic energy, you have to increase the energy of the light. Sir, how will that increase? Because h is constant. You have to increase this. This is constant. How will it increase? When the frequency increases. Okay? What will increase? Frequency will increase. Sir, I understood this graph too, that kinetic energy will increase only if you increase the frequency. So sir, why didn't the graph start from here? Why didn't it start from here? Why is it starting from here? You know the minimum frequency will be used first in ejecting the electron. Yes, suppose someone's threshold, suppose someone's threshold frequency is 60 hertz. How much is it? 60 hertz. Then, son, until the frequency reaches 60 hertz, the electron will not come out at all. So how will its kinetic energy increase? Oh, the electron will come out, it will move, only then will it have kinetic energy. Here, until it reaches 60 hertz, the electron cannot come out at all. Yes, if you increase it above 60, make it 61, 62, 63, 64, 65. Yes, then kinetic energy will increase. It will come out at 60 joules, kinetic energy is zero. See, it is written zero here. At 61, it will be one. At 62, two. At 63, three. At 64, four. Right? It will increase like this. So if the frequency is greater than the threshold frequency, then kinetic energy will increase. Okay? I have given the proof theoretically and also explained it through the graph. This is a question that came in JEE Main. Look, let's explain the graph. Here is the number of electrons emitted, the same photoelectrons, and here is the frequency. Okay? You know that until the threshold frequency is reached, the electron will not come out at all. Right? It will not come out at all, so there will be no issue. As soon as it becomes equal to the threshold frequency, electrons will be emitted only once, and after that, they will remain constant, unless and until you increase the intensity. Right? If you increase it from two to four, then earlier two electrons were coming out, now four electrons will come out. Right? I am not talking about that. We have already read that. We have already read that. I am talking in terms of I am talking in terms of I am talking in terms of that if you keep increasing the frequency as much as you want, more electrons will not be ejected. Electrons, yes, their kinetic energy will be more. Okay? What is stopping potential? Okay? Look, let's understand it from here. Here it is. Electrons are coming out of this metal. Okay? These are called photoelectrons. This is the anode in front. The anode is generally positively charged. Suppose if I made it negatively charged, then this will also be negatively charged and this will also be negatively charged. Will they repel each other? Yes, they will repel. Will this reduce its kinetic energy? Yes, it will reduce. Okay? If I keep increasing its potential, keep increasing it, keep increasing it. How much potential should I increase it to make its kinetic energy zero? How much potential should I increase it to make its kinetic energy zero? We will call that stopping potential. What will we call it? That is stopping potential. What will be stopping potential? The potential applied to the anode so that the kinetic energy of the emitted electrons becomes zero. That will be called stopping potential. Listen to me carefully and understand. Suppose any charge is at rest. Okay? It can be any charge. It can be an electron or anything else. I am explaining in the sense of an electron. And suppose it is at rest now. If you give it a potential v. Remember, velocity will be written with v. Potential will be written with V. Okay? If you give it a potential v, then it will gain energy. How much energy does it gain? Sir, we have studied that in physics. That is charge multiplied by potential. You can also write it like this. The charge is the charge of the electron, because it was an electron. You can write q, or qv, or ev, it doesn't matter. Just as the charge was at rest. You gave it potential. It gained energy. How much energy did it gain? That is charge * potential. And sir, what will it do with this energy? Sir, it will start moving. That is, all this energy will be converted into kinetic energy. Into kinetic energy. So if this was the stopping potential, then you can write EVS = KE. Where you had written kinetic energy. Where you had written kinetic energy. Where you had written 1/2 mv². You can write EVS there. So EVS = hμ - μ0. Open the bracket and write it too, sir. VS will be equal to? h / here too. Sir, if I make a graph between stopping potential and frequency, then y = mx + c. Stopping potential on the y-axis, frequency on the x-axis. Indeed, sir, stopping potential on the y-axis, frequency on the x-axis. Frequency will be there. Okay? Because the intercept is negative. For this reason, this graph will look something like this. It will go up to here. It will be like this. This is the intercept. This is the intercept. This is the intercept. This is -h0 / e. The other one, from here to here, the value is -hμ0 / e. Sir, I have two-three questions for you. I said, what are the questions? Sir, look here. Suppose this is the graph of sodium. It is indeed sodium. Its threshold frequency is low. You are absolutely right. This is lithium. Lithium's threshold frequency is high. Sir, why is that? You tell me, sir. Lithium has a small size. If its size is small, then the electrons will be closer to the nucleus. The force of attraction will be greater. It will be difficult to remove that electron. Its work function will be higher. Its threshold frequency will be higher. Oh yes, sir. The बात is proven that the smaller the size, the higher the threshold frequency. So lithium's will be higher. Sodium's will be what? Lower. Okay? Sir, similarly, I want to know, the value of -hμ0 / e for sodium is less, and for lithium it is more. Oh, I told you. If this is more, then obviously this value will be more negative. If this is less, then this value is less negative. Okay, okay. Sir, this point is also clear. Sir, suppose I had to make this graph for potassium. For whom? For potassium. Then sir, where would it be made? It would be made to the right of lithium. In the middle, here. It would be made here, son. Here. Okay? Why? Why? Because potassium's size is even larger. That is, the electrons will be even farther from the nucleus. The force of attraction will be less. The work function will be less. The threshold frequency will be less. Okay. Rubidium would be even further to the right. Cesium would be even further to the right. Let's play a question game. Do the question. Threshold frequency is the maximum frequency required for the ejection of electrons from the metal surface. Absolutely wrong. The word minimum should have been here. Right? If this statement were to be correct, then wavelength should have been there instead of frequency. Right? Threshold energy is the minimum frequency. This is wrong. Threshold frequency depends on the metal. Since the first one is wrong, the second one must also be made wrong. By the way, threshold frequency depends only on the metal. It should be that the assertion is wrong, the reason is wrong. But since the assertion is wrong, it has to be made wrong. D will come. D will come. D will come. When photoelectron emission occurs, talking about the photoelectric effect. The energy of the emitted electron, the electron that is coming out, the electron that is coming out. Its energy is greater than the incident photon, same, smaller. What is it? You tell me. Sir, kinetic energy is the total energy minus the work function. So tell me, compared to this energy, sir, it will be less because some of the work function will be used first. So it should be smaller. This is smaller than this, it is clear. Suppose your father wanted to buy a suit for ₹3000, and your father gave you ₹3500. Okay? So out of that, how much is given in total? 3500. Out of that, how much will be used for purchasing your suit? For your food, for your travel, how much will be used? 500 will be used. It won't be like that. It won't be like that. Right? By the way, fathers sometimes do such things. Right? They will give ₹3500, but you will find out that you went by cab for travel. So what will they say? Oh, you spent ₹5000 on travel and food? Damn, you only gave a total of ₹3500. Right? How can I use ₹5000 for travel and food? Right? Whatever is used will be less than ₹3500. Look at the question. Lambda naught and lambda are the threshold wavelength and the wavelength of the incident light. Lambda naught is the threshold wavelength, and lambda is the wavelength of light. You have been asked for the speed of photoelectrons. Sir, we just did it. We took out hc common. What was inside? 1 / lambda - 1 / lambda0 = 1/2 mv². Right? Sir, this is what is asked. This speed is asked. So v² will be equal to? 2 will go and multiply, and m will go and divide. hc * (1 / lambda - 1 / lambda0) = 1/2 mv². So v² = 2hc/m * (1/lambda - 1/lambda0). Or v² = 2hc/m * (lambda0 - lambda) / (lambda * lambda0). Sir, we don't need v², we need v, so its root will come. 2hc / m * (lambda0 - lambda) / (lambda * lambda0). This is option number three. Look at the next question. What is the work function of the metal? You need to find the work function of the metal. If light of wavelength 4000 angstrom. Light of wavelength 4000 angstrom. Generates photoelectrons of velocity. The velocity of the electron is 6 * 10^5 m/s from it. Mass of electron is given as 9 * 10^-31. Velocity is given. Plus constants are given. Charge of electron. You have been asked for the work function. Is there any relation between all these? Absolutely, sir. E is equal to work function plus kinetic energy, which is 1/2 mv². If you need to find this, work function, then it will be equal to E - 1/2 mv². The answer is required in electron volts. Remember, electron volts need to be converted to joules, so we multiply by this. Right? We multiply by the charge of the electron. And if the answer is in joules and you need it in electron volts, then divide by 1.6 * 10^-19. So first, let's calculate it in joules. And at the end, we will divide. Work function will be equal to? E will be equal to? HC / lambda. Can I put the value of hc here? In SI units. Yes. Lambda is given as 4000 angstrom. That is, this much. Mass m is 9 * 10^-31. Velocity is 6 * 10^5 squared. Because it is 1/2 mv². Solve it, son. 200. I'll do this. 10^-16. Multiply by 1000. Divide by 1000. The one divided by 1000 will make it 10^-19. The one multiplied by 1000, 1000 on top, 1000 on bottom. The one divided by 1000 is written here. If I divide 1000 by 200, it will be five. Let's do it here, son. 1/2 * 9 * 10^-31 * 6 squared is 36. This square will be 10^10. This will be 18. This came out to be 5 * 10^-19. Multiply 18 by 9, son. 18 * 9 = 162. And multiply these two. 10^-21. Let's write this in the form of 10^-19 as well. Sir, why? Because then it will be easy to take out the common. Sir, how? Multiply by 100. Divide by 100. The one multiplied by 100, will it make it 10^-19? Yes. And the one divided by 100 will make it 1.62. It will make it 1.62. Take out 10^-19 common. 5 minus 1.68 is 3.38 * 10^-19, sir. It came in joules. In joules. Sir, you have to give the answer in electron volts. No problem. No problem. Whom did I tell? Whom did I tell? We will divide by the entire charge of the electron. 1.6 * 10^-19. If this was 3.2. If it was 3.2 instead of 3.38, then it would be approximately two. It would be approximately two. But sir, this is slightly more than 3.38. So the answer will be slightly more than two. And only one answer is given that is slightly more than two. 2.1. 2.1. Which of the following graphs is not represented below? Which graph is wrong, basically? Kinetic energy versus energy of light. Absolutely correct. Yes, because if the energy is more than the work function, then it will be converted into kinetic energy. This is correct. Number of electrons versus frequency. This is also correct. We just did it. Kinetic energy does not depend on intensity. This is also correct. Kinetic energy will increase when frequency increases. This graph is partially correct. If the graph were like this, from here, meaning, if the frequency is more than the threshold frequency, then it will be converted into kinetic energy. Right? So this one is wrong. This one is wrong. This is a question that came. It's a PYQ. I think it's from JEE Main. Now we will talk about the spectrum. First of all, what is a spectrum? We will talk about the spectrum. Sir, what is a spectrum? First of all, okay. When you pass light through a prism, and in front of it, we have placed a photographic plate, then the light will come in increasing wavelength or decreasing wavelength or increasing frequency or decreasing frequency. What is formed will be called a spectrum. A classic example of this is when we pass white light through a prism. Whenever white light is passed, you know that VIBGYOR will be formed: Violet, Indigo, Blue, Green, Yellow, Orange, and Red. Okay? So this is the spectrum. Spectra are of two types. One is emission spectrum, and the other is absorption spectrum. What is an emission spectrum? The light that you are passing through the prism has come from the sample itself. Sir, what do you mean by "came from the sample"? I'll tell you. Let's go back to the beginning of today's class. In the cathode ray tube. Okay? What did we study in the cathode ray tube? That the electron that will come out of the metal will first do what to the gas? Break it. It breaks it. It separates them. Right? Then again, this electron that was coming out of the metal still has enough energy that it will strike hydrogen. That is, it will give its energy to hydrogen. These electrons of hydrogen, this electron of hydrogen, will absorb this energy and go to a higher shell. Where will it go? To a higher shell. This is called the excited state. I'll repeat. The electron will strike the hydrogen atom again and excite its electron to a higher shell. Okay? To a higher shell. Okay? This is what we call the excited state. The excited state is always unstable. What is it? Unstable. Just as it went up by absorbing energy, it will come down by emitting energy. When it emits energy, light will be produced. We are passing that same light through a prism. We are passing that same light through a prism.

They are passing through. So, whatever light we are passing through the prism, it has itself come out of the sample. What happens in an absorption spectrum? Okay? Suppose you have taken some light. For example, suppose I have taken white light. I passed it through some solution. Suppose I passed it through aqueous NaCl. Okay? What will happen? White light contains everything. Violet, indigo, blue, green, yellow, orange, red. Okay? Some part of this white light, some part will be absorbed? Who will absorb some part of the white light, sir? These particles inside, suppose sodium has absorbed some part. Okay? What will happen, sir? That electron will use that energy to go up. The remaining energy will be passed through the prism. I am repeating. Some part of the white light has been absorbed by it. The remaining part of the white light will pass through the prism. So, whatever is left has not come out of the sample. It was a part of the white light itself. Okay? Like you bought a biscuit for ₹5 and gave ₹20 to the shopkeeper, he will keep ₹5. What will he give back? ₹15. Are those ₹15 yours or the shopkeeper's? They are yours, brother. They are yours, right? You bought something for ₹5. ₹15 came back. It's not the shopkeeper's. ₹15 are yours. Here too, I am saying the same thing. Some part of the white light has been absorbed by it. The remaining part will be passed through the prism. Okay? Next, we will talk about the emission spectrum of the hydrogen atom. How? Hydrogen or a hydrogen-like atom can also be there. You understand hydrogen-like atom, right? It will also have only one electron. Like Helium, not Helium, but Helium positive. Helium has two electrons. Helium positive has one electron. Okay? Similarly, Lithium two positive. Not Lithium, but Lithium two positive. Lithium has three. If it has lost two electrons, only one will be left. Not Beryllium, but Beryllium three positive. Oh, Beryllium has four. If it has lost three, how many will be left? One. Right? So, these are hydrogen-like atoms. Whether it is this or that. They have only one electron per particle. Okay? Now, how that will happen, I have already explained that as soon as you give energy, the electron will absorb it and go to an excited state. The excited state is unstable. When it comes back, it will lose energy. The energy it is losing, emitting, that is what we are passing through the prism. So, whether it is hydrogen or any hydrogen-like atom, the spectrum that will be formed will be what? First, a series of lines, then dark spaces. Then a series of lines, then dark spaces. Space, series of lines, then dark spaces, and so on. Okay? And look at this, look at this. A series of lines will come at the very bottom. Then dark spaces, then a series of lines, then dark spaces, then a series of lines, then dark spaces, series of lines, dark spaces, and so on. Okay? So, everyone asked, how is this happening? First of all, everyone named the lowest series as Lyman series. Then Balmer series, then Paschen, then Brackett, then Pfund, then Humphreys, and so on. Okay? Today, everyone was asked, where did these series of lines at the very bottom come from? So, do you know what it replied? It said, look, the electron that had gone to the excited state. Okay? Maybe in the second shell, third, fourth, fifth, sixth, seventh. Okay? From there, the electron is coming back to the first shell. It might be coming from the second to the first, third to the first, fourth to the first, fifth to the first, sixth to the first, seventh to the first, eighth to the first, ninth, from anywhere. Okay? So, that is called the Lyman series. The next series was named Balmer series. Now, it was asked what is happening? It says that the electron that went up is coming back to the second shell. Where is it coming from? It might be coming from the third, fourth, fifth, sixth, seventh, eighth. Right? And infinity means it had gone out of the atom itself. From there, it is being pulled back by its hair. Hey, where are you going? Your mother is waiting at home. Right? Doesn't it happen? Sometimes we get angry and say we are leaving home. Okay? After half an hour or three-quarters of an hour, we realize that I have no one else besides this home. Right? Then we have to spit out our anger, right? And come back inside the house. That's exactly what this is. Right? And there are some people who are mentally challenged, who truly leave their homes. Right? If parents tell them to get out of the house, they just leave. Okay? That is a sign of mental disability. Okay? Right? So, this is exactly that. It's not mentally challenged. It got out of the atom itself. It was caught by its hair. Okay? Then for such people, advertisements are printed. Right? Advertisements are printed, right? That son, come back home. Right? We won't hit you. Right? Yes, yes, yes. Poor parents are helpless. What can they do? Right? Sir, 190 is confirmed in Physics. Okay, man, out of 720, 190 is like the question, so is the answer. Okay. The third series is Paschen, then Brackett, then Pfund, then Humphreys. Paschen series is when the electron is coming back to the third shell. From where? From four, from five, from six. This means it is coming back to the fourth shell. Yes, from five, from six, and so on. This means it is coming back to five. Okay? N3 needs to be written here. Here is N4. N5. N6 is called Humphreys. Okay? And if it is N infinity, it is called the limiting line. Right? It had gone beyond its limits, beyond its capacity. Now, when the electron comes back, obviously, okay, okay, when the electron comes back, okay, obviously there will be some wavelength, some wave number, some frequency, some energy change. Yes, sir, there will be, sir. How will we calculate that? We will calculate it using the Rydberg formula. From the Rydberg formula, we can calculate the wave number. How? Wave number will be equal to that is equal to Rz² / (1/n1² - 1/n2²). What is R? Rydberg constant, whose value is what? Is it written or not written? Not written. I will write it. Okay? Approximately, if it is not written. 10967 per cm. But if you want to write it in meters, you can also write it like this. Approximately 10 raised to the power 7 per meter. 1.097 x 10 to the power 7. But approximately you can write 10 raised to the power 7. What is Z? The atomic number of whichever spectrum you are making. If it is hydrogen, it will be one. If it is Helium positive, it will be two. If it is Lithium two positive, it will be three. And so on. Sir, what is N1? The shell in which the electron is coming back. You know, Lyman series means in which shell is the electron coming back? First. Balmer means in which is it coming back? Second. Paschen means in which is it coming back? Third. Brackett means in which is it coming back? Four. Pfund means in which is it coming back? Five. And Humphreys means in which is it coming back? Six. Sir, what is n2? Where it is coming from. Where it is coming from. If, for example, it is coming from Paschen to Balmer. Sorry, from Balmer to Lyman. Then n1 is one. What will n2 be? Two. No, sir, if it is coming from Paschen to Lyman. Then n1 is one. What will n2 be? Three. No, sir, if it is coming from Humphreys to Balmer. Then n1 is what? Two. Where is it coming from? From Humphreys. So, what will n2 be? It will be six. Okay? We have explained the meaning of all these things to you. Okay? And there are many other small terms. Sometimes it is said that you do not have to... Oh, this is written further, or should I tell you? I will tell you. Look, we all know this. I will write it here. E = hν and hc/λ and what comes in place of 1/λ, sir? μ bar. Is it clear that when the wave number is high, then the wavelength will also be high and the energy will also be high and the wavelength will be low? Right? When the wave number is high, the frequency will also be high, the energy will also be high, and the wavelength will be low. Clear? See? Is it directly proportional? Yes, sir. So, when ν̄ is maximum, then the frequency will also be maximum, the energy change will also be maximum, and the wavelength will be minimum. Yes, yes, I understood that, sir. Okay? I can also say the opposite. When this is minimum, then this will be maximum. This will also be minimum, and this will also be minimum. Yes. But tell me when that will happen too. Okay? When the electron is caught, right? And it is removed from the atom itself. It is removed from the atom itself. Then what energy will be required? The most. Oh man, if you catch an electron and just take it to a higher shell, energy will be required, but less. If you take it to a higher shell, more will be required. If you take it to an even higher shell, more will be required. Right? To go from here to here, more energy will be required. But if you catch it and remove it from the atom itself, push it out. Okay? Then what energy will be required? The most. What will be required? The most. Okay? So, in such cases, when we are asked for the maximum wave number, maximum frequency, maximum change in energy, or minimum λ, then we have to put the limiting line. Limiting line. Limiting line means putting n2 = infinity. And listen, if I say minimum wave number, minimum frequency, minimum change in energy, and maximum λ, because they are inversely proportional to each other. Okay? Then what will happen? Then it will be the alpha light. What will it be? Alpha light. Alpha line means what will n2 be? That is n1 + 1. That is, if I am talking about Lyman. If I am talking about Lyman. Alpha line. n1 is 1, so what will n2 be? 1 + 1 = 2. That is, the electron came back from here to here. Okay? No, no, sir, tell me for Paschen. Oh, you need to find the alpha line, right? n1 is 3. What will n2 be? That is n1 + 1. That is, 4 + 3. That is, the electron came from here to here. Okay? I think you have understood this. Sir, similarly, beta, alpha line is written. Okay? Similarly, there is also a beta line. Beta line means what will n2 be? n1 + 2. That is, the electron came from where to where? From the shell above. From the shell above. That is, if you want to tell the beta line of Lyman. Then from here to here. That is, n2 will be n1 + 1. That is, 1. Sorry, n1 + 2. That is, 1 + 2 = 3. Similarly, there will be a gamma line. Then in that, what will n2 be? n1 + 3. Similarly, there will be a delta line. In that, what will it be? n2 = n1 + whatever it is, it will be four. Okay? You have also understood the meaning of the limiting line. Okay? If the nth excited state is written. Then what will be the shell number? What will be the shell number? Suppose the second excited state is written. What is written? The ground state, this is the first shell. This is called the ground state. This is the second shell. This is called the first excited state. What is it called? First excited state. Similarly, the next one after the second is the third shell. This is called the second excited state. So, you understand, whatever excited state is given, the shell number will be? One more than that. The shell number will be? One more than that. If it is the first excited state, then the shell number is two. If it is the second excited state, then the shell number is three. That's what is written here. That's what is written. If the nth excited state is written, then the shell number will be? That is n + 1. Right? If it is the second excited state, then it is talking about the third shell. If it is the fourth excited state, then it is talking about the fifth shell. If it is the sixth excited state, then it is talking about the seventh shell. Suppose, whenever electrons are coming from top to bottom. n2, from which shell they are coming. n1, in which shell they are coming. Then what will be the formula for the maximum number of lines? What will be the formula for the maximum number of spectral lines? (n2 - n1) * (n2 - n1 + 1) / 2. n2 means from which shell it is coming. Suppose it is coming from the fifth shell to the second shell. It is coming from the fifth shell to the second shell. So, I will put five here. I will put two here. 5 - 2. Here also 5 - 2 + 1 / 2. What will it be? Three. And what will this be? Four. 3 * 2. What will be the total number of lines? That is six. How many will come? Six. Again, the formula for the maximum number of lines, if the electron is returning to the ground state. Sir, what do you mean by? Ground state. The electron is coming back to the first shell. The electron is coming back to the first shell. That is, where n1 was here, put one in its place. Put it in. If you put n in place of n2. And put 1 in place of n1. Sir, the formula becomes n * (n - 1) / 2. You are absolutely right. That is, suppose the electron is coming from the fifth shell to the first shell. It is coming from the fifth shell to the first shell. So, just put 5 in place of n. The rest is 5 - 1 / 2. That is, 5 * 4 / 2. How many will be there in total? Ten. How many will be there? Ten. Okay? This many lines in the Balmer series. Question: The question is perhaps incomplete. I will do another question instead. Find the total number of lines when an electron returns from Paschen to Balmer. Lyman, Balmer, Paschen, not Pfund, let's do Pfund. To Balmer. Okay? Which one is Pfund? That is five. And which series is Balmer? That is two. That is, what is n2? That is five. And what is n1? Two. So, we will just apply the formula for the maximum number of lines. That is (n2 - n1) * (n2 - n1 + 1) / 2. This will come, brother, three. This will come, brother, 4 / 2. How many lines will come maximum? Six. Look at the question. What is written? Maximum wavelength of a line of the Balmer series of the hydrogen spectrum. Balmer series of the hydrogen spectrum. You have been asked for the maximum wavelength. Tell me, what can be the answer? Did we read something a while ago? If we are talking about the Balmer series, the Balmer series is visible. Lyman is in the ultraviolet. The rest are in infrared or far infrared. For the hydrogen spectrum, so Z will be one. We will take the value of R as 10 raised to the power 7. No problem. Okay? You have been asked for the maximum wavelength. Maximum wavelength means, sir, minimum frequency, minimum wave number, minimum energy change. That is, what should n2 be? Sir, it is the alpha line. Alpha line is n1 + 1. That is, for Balmer, n1 is two. So, what will n2 be? We will solve it now. You have asked for the wavelength. Oh sir, just calculate the wave number and then take the reciprocal later. What's the big deal? Shall I take approximately 10 to the power 7? Z, you know, will be one. n1². What is n1? Two. What is 2 squared? Four. - 1 / 9. Sir, take the LCM. Here it will be 9 - 4. The numerator is 5. The denominator is 36 * 10 raised to the power 7. Sir, we need it in nanometers. First of all, this is in meters, and this is the wave number. Sir, put the wavelength. Oh, let's put the wavelength. So, 10 raised to the power 7 was there, it will become 10 raised to the power -7 on going up. Then you need to put it in nanometers. That is, you need to put 10 raised to the power -9. Only then will you put nanometers. So, no problem. I will multiply by 100. I will divide by 100. The part that was divided by 100 has become this. And the part that was multiplied by 100 will become this. See how much it is becoming. If we solve this, it will be around 700. It will be around 700. It will be around 720. And the statement is absolutely correct. It should have been. If we look at these four, this will be the maximum. Right? Among these four, this will be around 700. Okay? But if we look at these four, this will be the maximum. Sir, it should have been between 3800 Angstroms and 7600 Angstroms, that is, between 380 nanometers and 760 nanometers. Now, between 380 nanometers and 760 nanometers, this is the largest value. Sir, this should have been the answer. There was no need to calculate. The statement is absolutely correct. Which of the following series falls in the visible region? That is Balmer. Right? For hydrogen. This falls in? That is ultraviolet. This is visible. The rest, you know, are in infrared and far infrared. You need to calculate the wave number for the alpha line and the limiting line of the Balmer series. We just did the alpha line, man. Just did it. Because it is Balmer, so n1 will be two. So, what will n2 be? n1 + 1 comes out to be 2 + 1 comes out to be three. Sir, we just did it. For Helium positive, just make Z two. That's the only difference. 1/n1² * n2². I have taken the LCM. Here n2² - n1². Solve it. Approximately 10 to the power 7. Z squared will be 4. This is 4 * 9? 2 squared is 4, 3 squared is 9, 36. What is this three? 3 squared is 9, and 2 squared is 4. If I multiply 5 by 4, it is 20 / 36 * 10 raised to the power 7. Right? The answer will be in meters. No, sir, it is for the limiting line. Let's calculate for the limiting line. Just put infinity in place of n2. If you put infinity in place of n2, then the -1/n2² term will become zero. So, the wave number will directly be Rz² * (1/n1²). Write it like this, sir, it's finished. The value of R is approximately 10 raised to the power 7. Z squared will be 4 because for Helium, Z is 2. For Helium positive, and what will N1 be, sir? N1 is also two, so its square will also be four. Sir, this value is equal to the Rydberg constant. Yes, it is exactly equal. But it was supposed to be written per meter here. Now, before the new model of the atom, the discovery of what happened? Discovery of the neutron. Right? It continued only up to electrons and protons. Rutherford and all that. Okay? Thomson too. Okay? Polonium, which was the source of alpha particles. Alpha particles, you know. Alpha rays, that is the nucleus of Helium. Its bombardment was done on what? On Beryllium. Right? Alpha rays were coming out of this. It is a radioactive particle. Alpha rays were coming out. It was bombarded on Beryllium. And when it was bombarded, it was found that a neutral particle.

Neutron is coming out of these. Okay? Which has almost the same mass as a proton. Although the mass of a neutron is slightly more as compared to a proton. But it is almost the same, but what is it? It is neutral, neutral. Okay? A proton is positively charged, this is neutral. But the mass of both is almost the same. Okay? What was this new thing named? That is neutron was given. Because now three things were found, so a new model of the atom had to be adopted, which was called the Bohr's Atomic Model. What did Bohr's Atomic Model say? That in the center there will be a nucleus, inside it there will be neutrons and protons, and outside there will be circular orbits in which electrons will be revolving. Sir, outside this, look, if there can be an infinite number of orbits like this. Infinite number. How did you know that the electron will revolve in this and not in all these circles? In this, it will revolve. It will not move in this, but it will move in this. It will move in this. In whichever circle the angular momentum, angular momentum, do you know how to calculate it? Mass * angular velocity, which is v * r. Mass * velocity * radius. In whichever the angular momentum is an integral multiple of h / 2π, either 1 h / 2π, or 2h / 2π, or 3h / 2π, or 4h / 2π, or 5h / 2π. Meaning, it will be an integer multiplied by h / 2π. If the angular momentum has that value, then the electron will revolve in it. If it doesn't have that value, it won't. Okay? Here, they have stated some things. This is also based on particle nature. This is also applicable only for single electron atoms, right? For hydrogen and hydrogen-like atoms. The electron will revolve in the nucleus in a fixed circular stationary orbit without losing energy. Because he knew Maxwell, he could also come near it. Just like Maxwell came near him. What was his name? Rutherford. He was told, "The electron is charged." He said, "Yes, it is charged." "Is it accelerated motion?" "Yes, it is accelerated motion." So it will lose energy, it will revolve around the nucleus. He knew that his work could also be ruined. So he said this word first: As long as my electron is revolving in its own orbit, its fixed orbit, its original orbit, whether it is the first, whether it is the second, whether it is the third. It will not lose energy, I mean, its energy will not change, will not change, will not change. Its energy will change only when it changes its shell. Okay? And I have already told you this. Okay? mvr = nh / 2π. If the value of n is one, then it is the first shell. If it is two, it is the second shell. If it is three, it is the third shell. Okay? So when will the energy change? Right? Change in energy = E higher - E lower. Okay? E higher is E n2, E lower means E n1. Suppose the electron is coming from the third to the first. So the value of n2 is three. And the value of n1 is what? It is one. Okay? Second thing, inside the nucleus, are these two attracting each other? Yes. Here, the protons and these electrons, yes. There will be a force of attraction between them. Yes. What will it be equal to? Sir, we have studied Coulomb's Law. f = kq1 q2 / r². Okay? What will it be equal to? It will be equal to the centripetal force. Only then is it not falling on it. Meaning, mv² / r. Both equations were combined: kq1 q2 / r² = mv² / r. And mvr = nh / 2π. So, we first found out the radius. Right? Radius of the nh shell. If it is the first, I will call it R1. If it is the second, I will call it R2. If it is the third, R3. If it is the fourth, R4. If it is the fifth, R5. Now it is based on particle nature. I have already told you, it is applicable for hydrogen and hydrogen-like atoms. This is what is written. KQ1Q2 / R² KQ1Q2 / R². Sir, how is this KQ1Q2 / R² written like this? I will tell you. Tell me. This is the force of attraction, equal to what? Sir? Sir, one is between the nucleus and the electron. q2 is the charge of the electron. Okay? The charge on the nucleus is ze. Sir, where did z come from? Oh, z is the number of protons * charge on one proton. Number of protons is atomic number * charge on one proton. The charge of a proton and an electron is the same. But the sign is just opposite. The sign is opposite. So, multiplying z by e will give ze². Now, using these, we first calculated the radius of the nh shell. What will it be equal to? a₀ * n² / z. Where a₀ means what? That is Bohr's radius. This value is constant and what is it? That is 529 angstroms. It is also called Bohr's radius. If you want to find the radius of any shell, my dear. Any shell. Suppose you want to find the radius of the second shell for lithium two positive. Then n will be two. And if it is lithium two positive, then z will be three. Just put the formula. R of lithium two positive. a₀. I will square n, it becomes four. In place of z, what will come? Three. I have already told you the value of a₀, it will be 0.529 angstroms. Whatever constant is here, the constant. Like here, the constant is a₀. It is the value of the radius of the hydrogen atom. Because it is radius, it is the radius of the hydrogen atom. This is the radius of a hydrogen-like atom. Hydrogen-like atom. As much as hydrogen's radius is * n² / z. Similarly, just as you found the radius, you can also find the velocity of the electron revolving here. What will it be equal to? 2.18 * 10⁶ * z / n meters per second. z is the atomic number, n you already know, it is the shell number. Suppose you want to find the velocity of the electron in the third shell of a helium positive ion. What will be its z? Sir, that is two. So, v2 will be equal to 2.18 * 10⁶ * z / n. z is here, n is here, meters per second. Then again, I said, the value of all these constants is applicable for hydrogen. Meaning, in place of vn, what can I write? v, the velocity of the electron of hydrogen in the first shell * z / n. And do you know what this value is equal to? That is c / 137. It is 137th part of the speed of light. It is 137th part of the speed of light. Just as we found the velocity, just as we found the radius, similarly we can also find the total energy of the electron. Total energy will be equal to? Kinetic energy + potential energy. Sir, how did kinetic energy come? Do we all know that kinetic energy is this? 1/2 mv². Yes, sir, it is. And did we just read that mv² / r = kze² / r²? Absolutely. One r canceled out with one r. Yes. So, in place of mv², what can I write? ze² / r. Is that what is written? Yes, sir, that is what is written. Sir, that is kinetic energy due to the movement of the electron. Sir, where did this potential energy come from? Here is the nucleus. And its electron was like a very close friend. Meaning, it went out of the entire atom. It went to an infinite distance. The nucleus is here, and the electron has gone somewhere far away. Okay? You know, there is no attraction between these two right now. The energy is also zero. Now, to bring this electron back and bring it to its shell by holding its hair, will some work have to be done? Yes. Will energy be lost? Yes. Okay? This energy that was spent, to bring it from here, what will it be called? That is potential energy. What will it be equal to? - kze² / r. Here is the kinetic energy. Here is the potential energy. If we add both, the value will be -1/2 kze² / r. k is constant. e is constant. We wrote the value of r a little while ago: a₀ * n² / z. And, right? So, if we put that here, then the value of these constants, the value of the constant, in electron volts per atom will be -13.6. In joules per atom, right, my dear? Whatever is not a constant, we will keep it aside. In joules per atom, it will be -21 * 10⁻¹⁹. In kilojoules per mole, it will be -131 * z² / n². Do you know how it was converted from this to this? Sir, a little while ago you told us how to convert electron volts to joules, so multiply by 1.6 * 10⁻¹⁹. To convert joules per atom to kilojoules per mole, first, to convert joules to kilojoules, it would have been divided by 1000. To convert one atom to one mole, you would have multiplied by Avogadro's number. Dividing by 1000 and multiplying by Avogadro's number, the value will be -1312 * z² / n². Again, this value given is of what? Hydrogen atom. This is of what? Hydrogen atom. This is the value of hydrogen. Okay? This was in atom to atom, so it is called atom. This is of hydrogen. Similarly, I will say it in terms of moles. Sir, how did this negative sign come for energy? Didn't you just say? This is the nucleus, and here is the electron, which is billions of miles away from it. Right now, the force of attraction is also zero. The energy will also be zero. Now, to bring it here by holding it, will there be a loss of energy? Yes. You know, when there is a loss of energy, energy will go from zero to what? Sir, it will go to negative. That is what I have written. Okay? Second thing, total energy, kinetic energy, and potential energy, is there any relation between them? Absolutely, there is a relation. Look here, total energy is here, and kinetic energy is here. Sir, both are negative of each other. Absolutely right. That is what is written. Total energy is the negative of kinetic energy. Sir, total energy is here. Potential energy is here. Sir, if I multiply this by two, it will become this. So, that is, if you multiply total energy by two, will potential energy be formed? That is what is written. Total energy = potential energy / 2. Potential energy. If you multiply this by two, potential energy will be formed. I have already told you this. Potential energy = twice of total energy. And kinetic energy = negative of total energy. Ionization energy is called. Look, Bohr had already said that energy will change only when it changes its shell. And how will it be calculated? EN2 - EN1. N2 is the shell from which the electron is coming. N1 is the shell in which it is coming. Suppose it is coming from the fifth shell to the second shell. From the fifth shell to the second shell. So, in place of n2, we will write five. In place of n1, we will write two. Okay? I am talking about the emission spectrum. Right? Here, in place of n2, we will write five, and in place of n1, we will write what? That is two. Okay, sir. Okay. Okay. One more thing, if this term comes, ionization energy. What will be ionization energy? From where are you bringing the electron? Sir, it had gone out of the atom. You are bringing it from there. Meaning, in place of n2, we have to put infinity. As soon as you put infinity in place of n2, something divided by infinity becomes zero. So, here it will be E infinity. And here, in place of n1, it will be one. What are we talking about? Ionization energy. What is the definition of ionization energy? The amount of energy required to remove an electron from a neutral isolated gaseous atom, as well as from where? From the first shell. Sir, the first shell is not written in books. Oh, we are talking about hydrogen or hydrogen-like atoms. You know, in hydrogen or hydrogen-like atoms, there will be only one electron. And where will that electron be? Sir, it will be in the first shell. For this reason, I have put what? That is E1. Okay? There is one more term like this. It is called separation energy. Sir, what is the difference between ionization energy and separation energy? My dear, here we are taking the electron from the ground state and sending it out. In separation, what is it? The electron is not in the ground state. But it also has to go out. It also has to go out. The only difference is that it is not in the ground state. It is not in the first shell. Maybe it is in the second shell, third shell, fourth shell. If we take it out from the second shell, then here I will write E2. If we take it out from the third shell, then here I will write E3. If we take it out from the fourth shell, then here I will write E4. The value of E infinity is zero. So, it will be negative of E1. The value of E infinity is zero. So, here it will be negative of EN. Now, the value of n here is variable. Both these things are written there. So, let's play some questions, questions on them. Radius of hydrogen atom in ground state, RH is given as 53 angstroms. You have to find the radius of lithium two positive, meaning Z is 3, in a similar state. Similar state means it is in the ground state, meaning N will remain one. I just told you, what will be the radius of a hydrogen-like atom? As much as hydrogen's radius is * n² / z. Hydrogen's radius is this much, and n squared, meaning 1 squared, and z is three. If I divide 53 by three, if it were 54, then the answer would come. So, the answer will be around 0.18. Around 0.18. Option number one. Second Bohr orbit of hydrogen atom, you have to tell the velocity of the electron. Second second orbit means n will be two. Hydrogen atom means z will be one. What was the formula for velocity? That is, as much as 2.18 * 10⁶ * z / n. z / n. What will be the answer? 1.09 * 10⁶. Yes, sir. Can it be called 10.9 * 10⁵? Will it be this? 1.09 * 10⁶. Multiplied by 10. Divided by 10. The one who multiplied will become this. The one who divided will become this. Do the question. I will be back in just one minute. Start, my dear. You have to tell the energy of the electron in the ground state when n is one. What are we talking about? Helium positive. And it is given as E helium positive is -x joules. You have to tell the energy of the electron in the second shell of beryllium three positive. For beryllium, you know, z will be four. Okay, sir. Let's talk. Can I find the energy of hydrogen from here? Didn't we just say, energy of a hydrogen-like atom = energy of hydrogen * z² / n². You are given this as -x. I have to find this so that I can apply the same similar formula there and find its value. z will be two. So, 2² is 4. n is 1. So, will the energy of the hydrogen atom be this much? -x / 4. I am applying the same formula here. Energy of a hydrogen-like atom = energy of hydrogen * z'² / n². This came out to be -x / 4. z'² that is 16. n² that is 4. Sir, what will be this answer? It will be -x. It will be -x. The answer is option number one. What is the energy in kilojoules per mole? Okay, you have to tell it in kilojoules per mole. When de-excitation is happening. Meaning, the electron is coming from above to below. From where? From n6 to n2. What will be n1? Lower shell. What will be n2? Higher shell. We are talking about helium positive. What will be z? Two. Again, how will the change in energy be calculated? Sir, didn't we just write the formula? E N2 - E N1. Since we have to keep it in kilojoules per mole, we have to use the kilojoules per mole value. Meaning, -1312 Z² / N². Sir, let's take -1312 or something like this. 1312 and z². z is two, so its square is four. Keep that common. Let's keep it, my dear. What will be inside? 1 / n1² - 1 / n 1 / n2² - 1 / n1². n2 is 36. n1 squared. And we will solve this. 36. If I write it like this, 36 * 4, then here it will be 4 - 36. 4 - 36 is what, sir? 4 - 36 will be -32. Minus and minus cancel out. Four goes with four. It goes at eight in the table of four, at nine. The answer should be around 1312. It should be slightly less than 131. Sir, how did you know? It should be slightly less than 1312. Either this will be it, or this will be it. If you say so, I will solve it. It is 1160. If you say so, I will solve it too. 1312 * 8 / 9. That is what is coming. It is coming as 11662, meaning in kilojoules. Okay? Per mole. Can I write it as 1.166 * 10³? Absolutely, sir, you can write it. You are asked for kinetic and potential energy in electron volts. So, we have to find the formula in electron volts. When the electron is present in the third Bohr orbit, meaning n is 3, and it is a hydrogen atom, so z is one. Sir, let's first calculate the total energy. Absolutely, calculate it. What will it be? In electron volts, -13.6 electron volts * z² / n². Something will come out to be -1.51. But sir, you did not ask for total energy. You asked for kinetic energy and potential energy. What was kinetic energy? Sir, it was the negative of the total energy that came. Meaning, what will be the answer? +1.51. And sir, what was potential energy? It was double of the total energy that came. Double of it, meaning -3.02 electron volts. This is 1.51, and that is 3.02, in negative. The answer is option number two. Look at the next question. If the ionization energy of helium positive is given, my dear. Ionization energy of helium positive is given in joules as 19.6 * 10⁻¹⁸ joules per atom. You are asked for the energy of beryllium. Oh, you are asked for the energy of beryllium 3 positive. In what? In the second stationary state, meaning n is 2. And z, you already know, is what? That is four. Again, what will it be equal to? As much as it is for a hydrogen atom. Multiplied by z² / n². Sir, you just have to find this. The question will be solved. Okay? Sir, how will we find that? Do you have its ionization energy given? So, do you know E1 of helium? Are they not negative of each other? We just proved it. We just did it that ionization energy is the negative of E1. Just if you know this, then E1 will be its negative. E1 of what? Of helium positive ion. Obviously, we are talking about helium positive ion. -19.6 * 10⁻¹⁸ joules per atom. Okay? If you know E1 of helium positive ion, then will you know the hydrogen's? Yes, sir. Didn't you just say, as much as hydrogen's is * Z² / N²? z in the case of helium is two. And n, you already know, is what? One. So, what will be hydrogen's? As much as the value came, -19.6 * 10⁻¹⁸ divided by this z squared was four, it will go there and divide. Put the value here.

What will be the energy of Beryllium 3 positive? As much as hydrogen's came, multiplied by z squared, that is 16. N squared, that is 16 z squared. 16 10 squared is 4. Sir, this 16 will cancel out with 16, the answer will be -19.6 * 10 power -18, right? Should be four, right? None of these. Let's talk about the next thing. Sommerfeld's extension of Bohr's model of the atom. What did Sommerfeld do to Bohr's model of the atom? He extended it. Then tell me how he extended it. I'll tell you. Actually, the hydrogen spectrum was created. Okay? That same hydrogen spectrum was observed under an ultra-microscope. Under what was it observed? Under an ultra-microscope. And what was found? What was found? That the single lines that were visible in the hydrogen spectrum. They were not actually single lines. They were clusters of lines. Different small lines. Different lines mean different energies. But what did Bohr say? That all electrons in the same shell within an atom will have the same energy. That is, all electrons in the first shell have the same energy. All electrons in the second shell have the same energy. Oh brother, if the energy is the same, then the wavelength will also be the same. That is, only one line should appear. But in the ultra-microscope, those lines were different. There was a slight difference in energy. So it was taken to Bohr and he was asked, "What is this, man? You said everyone's energy is the same. But everyone's energy is not the same. There is some difference. What is this?" So he said, "I don't know anything." Then Sommerfeld came. Sommerfeld said, "You don't need to worry, Guru Ji. I'll explain." You know, shells have subshells within them. Like there is a very big building. Within that very big building, there are different floors, right? Similarly. Okay? Similarly, there are subshells within a shell. All electrons within each subshell have the same energy. For example, let's say the third shell has three subshells. Okay? So all the electrons within this have the same energy. All electrons within this have the same energy. All electrons within this have the same energy. But the energy of these three will be different. Okay? Then the next question asked to him from Sommerfeld was, how many subshells are there within a shell? Like, how many subshells in the third shell? How many subshells in the fourth shell? How many subshells in the first shell? How many subshells in the second shell? So he said, as many as the shell number, that many subshells there are. That is, there will be one subshell in the first shell. There will be two subshells in the second shell. There will be three subshells in the third shell. There will be four subshells in the fourth shell. Okay? Everyone said, "Very good, man." Okay? Then the next question asked to him was, what will be the shape of those subshells? Because Bohr had said that the orbits, right? The shells, their shape is circular. You are saying there are subshells in between. So what will be their shape? So he said, "Brother, among all the subshells, the first one will be circular." If you want to say circular, 2D, then circular. If you want to say 3D, you can say spherical. Okay? So among all the subshells, the first one will be circular. The rest will be elliptical. For example, let's say it's the fourth shell. How many subshells will be in the fourth shell? Four. Among these four, one, the very first one. Okay? That will be circular. How many are left? Three. They will be elliptical. There will be three subshells in the third shell. One of them will be circular. The remaining two will be elliptical. Okay? So those different lines seen in the ultra-microscope represent the subshells within the shell. The question can be asked like this: In Bohr's theory, who described elliptical orbits? That is, who described them? Sommerfeld. Right? What were the limitations of Bohr's model of the atom? It explained the spectrum of hydrogen, etc. But as soon as multi-electron atoms came, like the spectrum of sodium, or the spectrum of chlorine, it could not explain them. Right? And it could not explain the Zeeman effect. The hydrogen spectrum was created once in the absence of a magnetic field, and once in the presence of a magnetic field. They observed that when it was created in the presence of a magnetic field, when it was created in the presence of a magnetic field, each line split. The line that appeared as one in the absence, in the presence of a magnetic field, it was either one line, or three lines, or five lines, or seven lines. Everyone asked, "What is happening, man? How did these spectral lines split? What does this indicate?" He said, "Brother, I don't know anything about this." Okay? We call that the Zeeman effect. Similarly, the spectrum was created in the presence of an electric field, and the lines still split. That was called the Stark effect. It could not explain this either. Secondly, it could not explain the 3D shape of molecules. Right? It knew nothing about wave nature, about dual nature, because it was based on particle nature. Then later came the discussion, like light, right? We talked about it. Maxwell said that light has wave nature. Okay? Planck said no, it has particle nature. Later it was found that light has dual nature. Sometimes it is a particle, sometimes it is a wave. Obviously, you have read a lot about light in physics. You have seen many experiments that reveal its wave nature, like interference, diffraction, etc. There are many such experiments. Black body radiation, photoelectric effect, etc., from which its particle nature is revealed. Okay? Similarly, it was found that subatomic particles like electrons, protons, neutrons, etc., also have dual nature. Okay? They behave like particles as well as waves. Okay? To talk about that, first, de Broglie talked about it. What did he say? According to Einstein's mass-energy relationship. P will be equal to what? That is, mc squared. According to Planck's quantum theory. E will be equal to what? h nu. If we equate both, then h nu = mc squared. And nu was equal to c divided by lambda. One c will cancel out with one c. Lambda will be equal to h divided by mc. See, c is the speed of light. But generally, you know that particles do not travel at the speed of light. They travel at some other normal speed, which we will denote as v. So lambda = h / mv. Mass multiplied by velocity can also be written as momentum. Okay? Remember this statement. Okay? It's not like that. See, they are microscopic particles, so you know that their mass is small. Okay? Because of this, their momentum will also be small. If the momentum is small, then you know their wavelength will be large. That is, if we talk about electrons, when they move, you will see a wave forming behind them. But if we talk about a car moving, why don't you see a wave forming behind it? Because in daily life, we only see macroscopic particles. Brother, their mass is very large. If the mass is large, then the wavelength will be small. That is, if we talk about macroscopic particles that we see in daily life, it has no significance for them. No, no. Yes, it has significance for microscopic particles because their mass is small, and therefore their wavelength will be very large. It is written in different forms. Okay? One is lambda = h / p or h / mv, which I have written. Another form could be lambda = h / p, h divided by the square root of 2 qv * m. Sir, where did this come from? Where did it come from? See, what? 1/2 mv squared. A little while ago, we talked about it. It is equal to qv in the photoelectric effect. Yes. So from here, v squared will be equal to 2qv / m. And this v will be equal to, if it is in the square root. So, lambda = h / mv. If you put the value of v here and simplify, you will get this value. Okay? Now, for example, if you want to write it for an electron, solve this whole thing. m is constant, q is constant, h is constant. Only v is variable. So the answer will be 12.27 angstroms divided by the square root of v. V is the potential. I have just explained that it is not applicable to macroscopic particles. It is only applicable to microscopic ones. See, an NCERT Exemplar question. If they are moving at the same speed, whose wavelength will be shortest? You know lambda is equal to h / mv. The speed is the same for all. Whose wavelength will be shortest? The one with the largest mass. Now you have to tell the mass. The mass of this is very small. You know the mass of this is very large. 4 amu. Neutron and proton are approximately 1 amu. Approximately the same, I am saying. Not exactly, but approximately the same, I am saying. Okay? So obviously, the one with the largest mass will have the smallest wavelength. It has the least de Broglie wavelength. Then, brother, this is 1 amu. This is 44 amu. Do you know where 44 came from? 64 amu, right? We learned all this in some basic concepts of chemistry. It is asking for the least. So its mass is the largest. If the mass is the largest, then the wavelength will be the least. Next, see. In a hydrogen atom, the de Broglie wavelength of an electron in the second Bohr orbit is. Second Bohr orbit means n will be 2. Okay? So tell me, the wavelength is asked. No problem. Before this, I will tell you one more small thing. Number of waves in an orbit is 2πrn = n lambda. Oh no, sir, where did this come from? Where did it come from? I am telling you. You know this, right? mvr = nh/2π. Sir, Bohr gave this. He proved this. If you do this, bring mv here. Bring 2π here. Then it becomes 2πr = nh / mv. Yes. Is this lambda? Yes. So 2πrn = n lambda. Sir, where did this rn come from? Oh brother, it will be the radius of that shell. If it is the first shell, then it will be r1. If it is the second shell, then it will be r2. If it is the third shell, then it will be r3. What is there to explain about that? From this, it is also understood that in the circumference, how many waves are formed? As many as the shell number. As many as the shell number. That is, look, let's say this is the third shell. Let's say, let's say this is the third shell. Then its circumference, that is 2πr, how many wavelengths will be within it? Three times the lambda. That is, one, two, three, right? One wavelength from here to here, one wavelength from here to here, one wavelength from here to here. It's done. 2πr = n. This is what is used here by Hydron. In Hydron, what? The de Broglie wavelength is to be told. The wavelength in the second Bohr orbit is to be told. No problem. 2πr2 = 2. 2pi = n. That's what I've written. Okay? Do you know the value of r2? Yes, sir. a naught * n squared / z. The value of a naught is given. n squared, that is 2 squared. It will be hydrogen, I think. Yes, it is hydrogen, so z will be 1. In picometers = 2 lambda. Sir, will this 2 cancel out with 2? Now you just multiply it, right? That is your job. I think the answer is not matching. It's not matching. It is matching. It is matching. If I put pi here, if I put pi, it matches. Why is it not matching? So 211.6 pi. Here it is. 21.6 pi. 21. If I multiply by 4, 21.6 pi picometers. Look ahead. Oh yes, correct. There are two particles, A and B, which are in motion. The wavelength of A is lambda A = 5 * 10 to the power of -8. The wavelength of B is asked if the momentum is half. Momentum is half. PB = PA / 2. Brother, if the momentum is half, then the wavelength will be double, because lambda is equal to what? That is, H / P. If this is half, then this will be double. So just multiply by double, multiply by 2. As soon as you multiply by 2, it becomes 10 * 10 to the power of -8, that is, 10 to the power of -7 meters. A stream of electrons from a heated filament was passed through two charged kept plates with a potential difference V. Okay, there are two plates with a potential difference V between them. A stream of electrons is being passed through them. If e and m are the charge and mass of the electron. Okay? We need to find the value of h / lambda. h / lambda. Is there any relation between potential difference and lambda, sir? Sir, just a little while ago, we read it. lambda = h divided by the square root of 2 qvm. You need to find h / lambda, sir. h / lambda will be equal to 2 qvm. And what will q be, sir? That is, the charge. vm. This is the potential. This is the mass. This is the charge. So 2eevm. Here it is. Option number three. This is a question that came in the exam. It's probably from JEE Main. Heisenberg's Uncertainty Principle. What does it say? If there is any macroscopic particle, like this ball. Okay? You can find its exact position and momentum. Like I am standing here. My exact position will also be known, from where the room starts, and my momentum will also be known. But if you talk about a microscopic particle, an electron, proton, neutron, you cannot find their exact position and momentum simultaneously. You cannot find them at the same time. Sir, why can't you? There are many ways to explain it. Okay? For example, let's say this is a nucleus, and electrons are revolving outside. Let's say you want to see these electrons. If you want to see them, you need only two things. What are those two things? One is eyes, and one is light. As soon as you shine light on it, will this electron absorb the energy of this light? It will absorb it, so it will change its position. Right? So, if you focus on the position, the momentum will slip out of your hands. If you focus on the momentum, the position will slip out of your hands. Right? If caution is lost, disaster strikes. So there will definitely be some uncertainty. That is, delta x is the uncertainty in position, and delta P is the uncertainty in momentum, which will be equal to m delta V. Delta V, sir, what is this delta V? That is, uncertainty in velocity. Suppose a particle is moving. Its velocity is 300 meters per second. How much? 300 meters per second. But there is an error of 1% in it. There is an error of 1%. So delta V, you know, will be 1% of 300, which is 3 meters per second. Okay? Suppose a particle is moving on a straight path and can travel a maximum distance of 15 meters. Then tell me, what will be the maximum delta x for it? The maximum possible distance on a straight line is 15 meters, so delta x will be 15 meters. Right? Because it will be found within 15 meters. Okay? This is what was written here. Delta x dot delta p, or the dot product one. Okay? Delta x delta p is greater than or equal to h / 4 pi. Okay? You can also write it in another form if you want. You can also write it in the form of energy and time. Uncertainty in energy, uncertainty in momentum. You can also write it as uncertainty in angular displacement, uncertainty in angular momentum. You can write it like this for angular motion too. There is nothing new. Then we will talk about the significance again. It is applicable. It is significant for whom? For microscopic particles. Macroscopic ones, which we can see with our naked eyes. Like me, all the things you see around us, we are all macroscopic. Our exact position can be known. Our exact momentum can also be known. So it has no special significance in our daily lives. Okay? Question, let's play with questions. It is impossible to determine the exact position and exact momentum of an electron simultaneously. Absolutely correct, man. Right? You can find the exact position and exact momentum. Sir, you cannot, and you know that as soon as I say the assertion is wrong, right? The exact position and momentum of a macroscopic particle can be found, but not of a microscopic one, so you have to say it is wrong. Can the path of an electron in an atom be clearly defined? Now tell me about this statement. Correct it easily and answer this statement. Do it easily. No hurry. Those who are doing it along with me, yes, you are absolutely right. If the path were clearly defined, then what would be the point? Until Bohr, these things were fine, right? But now everything is probability-based. Uncertainty in position and momentum are equal. It's correct now. That one is correct. This one is wrong. That one is correct. Yes, okay. Uncertainty in position and momentum are equal. Okay, delta x = delta p. You are asked to find the uncertainty in velocity, delta V. No problem. We all know delta x delta p is greater than or equal to h / 4 pi. Yes. Because I need to find the uncertainty in velocity, I can write delta V instead of delta x. You can definitely write it. It will be delta V squared. Yes. Which is equal to m squared delta V squared. Sir. Move this m squared to the other side. Very good. Sir, if you want to find delta V, then put it in the square root. Now solve this square root. How much will it be? 4 will come out, and this will also come out. The square root of 4 is 2. Of m squared is m. Brother, here it will be h / pi. 1 / 2m square root of h / pi. This is the option. This is also a question from PYQs, I think from JEE Main. Introduction to Quantum Mechanics. Why was it needed? Because you have learned that until the Bohr model of the atom, particle nature was considered. But later it was found that there is particle nature and wave nature. This means that a new model of the atom will have to be created. We just read a limitation. The path of an electron is not clearly defined. Obviously, due to wave nature. Right? If it had particle nature, it would be fixed. So for this reason, a new model of the atom had to be given. Who gave that new model of the atom? Erwin Schrödinger.

Who was an Austrian physicist. What did he do? He gave an equation which is written in front of you. Schrödinger's wave equation. Here, we can also write delta instead of d. Okay? Psi is the orbital wave function. x, y, z are the coordinates. This is it, right? When the electron will be moving in the x, y, z axes. These are its coordinates. Okay? This represents the total energy. This represents the potential energy. What has been done to the potential energy from the total energy? It has been subtracted. Okay sir? Psi is the orbital wave function. I have just told you. Suppose you had math or not. But at least you know how to solve this. Suppose this is 2, then what will dy/dx be? It will be 2x, and what will y be? That is x². Right? Going from here to there is by differentiation. Coming from there to here is by integration. You know all those things. For example, this is a second-order differential equation. Is its answer this? Similarly. This is also a second-order differential equation. Yes. It will also have an answer. Yes. Psi will tell us. Sir, what will psi tell us? It will tell us which shell the electron is in. Which subshell it is in, and which orbital it is in. You have already studied shell and subshell. You will study orbital in a little while. Okay? But there will be many values of psi. Out of all the values, only a few values will be accepted, right? Yes sir. Which values will they be? It is written here. Appreciable solutions will come for the wave function psi. Right? But among them, the ones we have to accept, the possible solutions we have to consider, must have properties. What properties should they have? Psi must be continuous, finite, and single-valued. Right? It should be a continuous function, it should be finite, and it should be a single-valued function. The probability of finding the electron over all the space from minus infinity to plus infinity must be equal to one. Suppose this is the distance from minus infinity to plus infinity. Then, the electron must be found within this. It is not that the electron will be found outside this. Okay? From the solution of Schrödinger's equation, we will get many values of psi. But the values that are not useful to us, the ones that are useful to us. It is written here, significant values of psi are called eigenfunctions. Okay? The ones that are useful to us, we will call them eigenfunctions. And the energy derived from them will be called eigenvalues. In the new model of the atom, the quantum mechanical model of the atom, what was explained? The energy of an electron in an atom is quantized. That is, it is fixed. Sir, Bohr also said this, absolutely. We cannot determine the exact position and velocity. Heisenberg already said that. The wave function psi will give all the information. I just told you, we will solve psi. Psi itself will tell us which shell the electron is in. Which subshell? Which orbital? Okay? Although it cannot tell about spin. Mathematically speaking, psi is a wave function, and physically speaking, psi represents an amplitude. If you want to get any information about any person in the world, do you need to know these four things about them? Country, state, city, and their home address. If you know these four things about any person, can you extract maximum information about them? Yes sir. Similarly, if we want maximum information about an electron, we need to know those four numbers. What are they called? Quantum numbers. Among these, the first is the principal quantum number, angular quantum number, magnetic quantum number, and spin quantum number. We are going to study these. The very first one is, that is the principal quantum number. What does it tell about the electron? First of all, it tells the shell. Okay? It tells the shell. What if, suppose n is 1? Is it written anywhere? Yes, it is written here. No, it is not written. If, suppose the value of n is 1, then we will say that the electron is in which shell? In the first shell. If the value of n is 2, we will say the electron is in the second shell. If it is 3, in the third shell, and so on. Okay? As soon as you know n, you can calculate its radius. In Bohr's values, rn = a₀ * n² / z. One minute, one minute, wait. You were just saying a little while ago that sir, the radius is not known. I mean, everything will be probable values because Bohr was based on particle nature. This is based on dual nature. Absolutely right. It will give probable values. Most probable values. Okay? It will tell the velocity, it will tell the energy. If you want to know the orbitals in any shell, square n. That is, how many total orbitals will be in the first shell? 1 squared is 1. In the second shell, 2 squared is 4. In the third shell, 3 squared is 9. A maximum of two electrons can be in one orbital. So, what will be the total number of electrons in the shell? That is equal to 2n². I have solved it here as well. If the shell is known, then... Okay, there is a question on this. No, no, one minute, one minute. I will explain this first, then do that question. Look at this. The maximum number of electrons that can be accommodated when the shell number is four. The formula for the maximum number of electrons is 2n². 2 * 4 * 4 = 16 * 2 = 32. Option number three is the correct answer. Okay? Next, look. Angular quantum number, or subsidiary quantum number, or azimuthal quantum number. What does it tell? Just as n told about the shell. This tells about the subshell. Okay? From where are the values of l given? All integers from 0 to n-1. Suppose n is 3, then what will l be? All integers from 0 to 3-1=2. Write all integers: 0, 1, 2. If n is 4, then what will l be? Oh, all integers from 0 to 4-1=3. Write all integers: 0, 1, 2, 3. As many values come, like for n=3, how many values came? 1, 2, 3. Which value? As many values come, three values came. So, there will be three subshells within the third shell. Oh yes, sir. Sommerfeld also explained this. There will be 1, 2, 3, 4 four subshells within the fourth shell. Yes, sir, Sommerfeld also explained this. So, when the value of l is zero, the name of the subshell is s. When it is one, it is p. When it is two, it is d. And when it is three, it is f. Do you know where these words came from? s came from sharp, p from principal, d from diffused, f from fundamental. Do you know where this came from? From when Sommerfeld observed the spectrum under a microscope. What appeared as a single line was actually multiple lines, and these types of lines came from there. Some were sharp. Many were named principal. Diffused, fundamental, they came from there. Okay? Second thing, it also tells the shape of the orbital. If the subshell is s, then its orbital will be spherical. If the subshell is p, then it will be dumbbell-shaped. If it is d, it can be a double dumbbell. Okay? And f does not have a specific shape. Okay? To tell the orbitals within the subshell. Not within the shell. Within the shell, obviously, to tell the orbitals, it is n². How many orbitals are there within a subshell? That is equal to 2l + 1. The value of l, like how many orbitals are there within this subshell? How many orbitals? 2l + 1, which is one. How many orbitals are there within this subshell? 2 * 1 + 1, sir, it will be three. How many orbitals are there within this subshell? 2 * 2 + 1, sir, it will be five. Right? So, to tell the orbitals within any subshell, it will be 2l + 1. And if we want to tell the electrons, since a maximum of two electrons can be in each orbital, I will multiply by two. Orbital angular momentum can also be told as √(l(l+1)) * h / 2π. For example, if it is an s orbital, then if you put l=0, this whole thing will become zero. If you put l=1 for the p subshell, it will be √(1(1+1)) * h / 2π = √2 * h / 2π. If you put l=2, it will be √(2(2+1)) * h / 2π = √6 * h / 2π. If you put l=3, it will be √(3(3+1)) * h / 2π = √12 * h / 2π. Maximum number of electrons in a subshell. Sir, you just told me that to find the orbitals, it is 2l + 1. To find the electrons, multiply it by two. Twice * (2l + 1). Next is the magnetic quantum number. This is what explained the Zeeman effect. That when your subshell is formed, and if you create the spectrum again in the presence of a magnetic field, it splits. Those spectral lines are the orientation, right? It will be written here somewhere. Yes. m determines the specific spatial orientation of the orbital. Okay? What is an orbital? It is the three-dimensional space where the electron spends its maximum time. For example, suppose there is a whole big building. Okay? That will be called a shell. The different floors within it will be called subshells. There are different flats on each floor, which will be called orbitals. Right? So, shell, within the shell, subshell, within the subshell, orbital. Where will you be found? Obviously, sir, in your home. Right? So, suppose the second flat on the third floor of that building, you will be found there maximum. You will be found within that building, but where will you spend the maximum time? You will be found maximum in the second flat of the third floor. Similarly, the electron will be found within the shell. But within the shell, there will be a subshell, and within the subshell, there will be orbitals. The electron will be found maximum time within the orbital. I have already explained this, it explains the magnetic field, it explains. Okay? How are its values written? From -l to +l. For example, suppose the value of l is 0, then what will be the value of m? From -l to +l, meaning from -0 to +0, sir, it is just zero. If l is 1, then what will be the values of m? All values from -1 to +1. Okay, sir. As many values come, that will be the number of orbitals. For example, which subshell was this? For the s subshell, how many values came? One. So, there will be one orbital in the s subshell. For the p subshell, l was 1, so it was the p subshell. For the p subshell, three values came. So, there will be three orbitals in the p subshell. Similarly, if l was 2, the values would be -2, -1, 0, +1, +2. So, it means there will be five orbitals in the d subshell. Similarly, if l was 3, m values would be seven, so there will be seven orbitals in it. Now, there are two electrons in each orbital. How are they differentiated? By spin. Although it is said that the spin quantum number tells about spin. In reality, it is a quantum mechanical term. It has no physical meaning. But to explain something, they say it represents spin. However, it is a quantum mechanical term. It has no classical analog. They just say it. For every orbital, for all the values of l, and for all the values of m, how many values of s will there be? Two values for each orbital. One is +1/2, one is -1/2. One clockwise, one anticlockwise. That's what is written. The first three quantum numbers, n, l, and m, all three are obtained from the solution of Schrödinger's wave equation. Schrödinger could not explain this. We have also written something else here. What was written? Look here. The value of l will always be less than n. Right? See? It is always less than n. Less than n. l can never be equal to n or greater than n. We have already proved it there. Tell me which quantum number is allowed, or not allowed. Allowed is asked. If n is 3, can l be 2? Yes. It can be 0, 1, 2. If l is 2, can m be 1? Yes. Any value from -2 to +2 can be there. Can the spin quantum number be zero? No. The spin quantum number is either +1/2 or -1/2. This is wrong. If n is 2, can l be 0? Yes, it can be 0 and 1. m, yes, it can be from -0 to +0. Spin quantum number -1/2, yes, this can be. If n is 3, then l, -3, and l can never be negative. It can only be 0, 1, 2. This is not possible. If n is 1, can l be 0? Yes, it can be. What will m be? From -0 to +0, meaning it will be zero. It cannot be one. This is also wrong. How many orbitals will be in the third shell? I just said, if you want to find the orbitals, just square it. That is, square 3. What will it be? 9. Option number three. Match list one with list two. Choose the correct answers from the following options. You have to tell the shape, size, orientation of the orbital, and the spin of the electron. First, tell me, who told the size? Orientation of the orbital is told by that. That is, here it is. Orientation of the electron's spin. Spin quantum number. Shape of the orbital, that is, and size, obviously, it will depend on the shell. So, 3, 4, 1, 2. 3, 4, 1, 2. You are saying 3, 4, 1, 2. It will be 3, 4, 1, 2. Option number B. Oh, the size will depend on the shell. Okay? Brother, if it is the first shell, its orbital will be small. If it is the second shell, it is bigger. It will be big. If it is the third, even bigger. Right? So, it will depend on the shell. This came in 2023. Relation between the number of permissible values of the magnetic quantum number for a given value of l. Okay, if the value of l is l, then how many values of m come? Sir, 2l + 1. Which is set equal to nm. Now look at their relation. What will nm be equal to? No, l is calculated. What will l be equal to? nm - 1, and this 2 will go to the other side and divide. nm - 1 / 2. Here it is, option number two. How many electrons can there be? If the quantum numbers are this. Brother, as many orbitals as there are, we can multiply that by two. That many electrons can be there. Shell is this, subshell is this. Okay, orbital. As many values of m are there, that many orbitals are there. How many values of m? Which value? No, how many values are there? There is only one value. -1. No, how many are asked? There is only one value. If there is one orbital, then a maximum of two electrons can be in one orbital. Two electrons can be there. Two, here it is, option number three. The principal quantum number is four. So, tell the total number of orbitals whose l is 3. Total number of orbitals means how many values of m will come. And how many values of m will come? Sir, it is 2l + 1, which is 2 * 3 + 1 = 7. No, you can also calculate and see. Write the values from -l to +l. -3, -2, -1, 0, +1, +2, +3. Which value? No, how many? 1, 2, 3, 4, 5, 6, 7. See, the answer was indeed seven. Answer the following quantum numbers. Possible for how many orbitals? When n is 3, l is 2, and m is +2. Again, if m is +2, how many values are coming? Only one. If one is coming, then you know. Okay? How many orbitals will there be? Sir, only one. If they had asked for electrons, I would have given two. As many values of m, that many orbitals. If the electron's spin quantum number is +1/2 and the magnetic quantum number is -1, then in which can this not be? Cannot be. Can the value -1 of the magnetic quantum number be for a d orbital? Absolutely. What is l? For d, it is 2. Can m have values from -2 to +2? Absolutely. So, beta, sorry, I was saying two. If l is 3, it will be an f orbital. Can it also be for this? Does -1 come between +3 and -3? Yes, it comes. p orbital, l is 1. From -1 to +1, it still comes in it. If it is an s orbital, then l is 0. Then the value of m will only be zero. So, the s orbital is the one in which it cannot be. The value -1 will come here too. It will come here too. It will come here too. It cannot come here. Given the azimuthal quantum number l is 3. You are asked, what will be the maximum number of electrons? Sir, the orbitals were this many. How many electrons will there be? Double this. There are two electrons in one orbital. 7 * 2 = sir, it will be 14. 14, option number two. Total number of electrons asked in all orbitals when the principal quantum number n is 2 and the azimuthal quantum number l is 1. n is 2, l is 1. Find out the values of m. As many values of m there are, that many orbitals will be there, so multiply that by two. How many values of m will come? From -l to +l, meaning there will be three orbitals. 1, 2, 3. So, how many electrons will there be, sir? It will be six. What will be the maximum number of electrons in the subshell? You just told me to multiply 2l + 1 by 2. Multiply 2l + 1 by 2. Here it is, 4l + 2. The quantum numbers are given below. How many sets of quantum numbers are correct? Which ones are correct? Not this. How many numbers to tell? 0, 1, 2, 3, 4. Like this. Can n be 3 and l be 3? No, these two can never be equal. l is always smaller. So, it is wrong. Can n be 3 and l be 2? Can it be? If l is 2, can m be -2? Absolutely. From -2 to +2. This is correct. Can n be 2 and l be 1? Yes, it will be. 0 and 1. If l is 1, can m be 1? Absolutely. -1, 0, +1. This is also correct. Can n be 2 and l be 2? No, these two cannot be the same. So, how many are correct? This one is correct. This one is correct. So, the answer is to write two. Write two. Look, psi, the orbital wave function, physically speaking, only represents amplitude. Okay? What is it equal to? It is equal to the radial wave function and the angular wave function. It is the product of these two. This depends on n and l, and this depends on l and m. Okay? But psi squared, this square, will tell the probability of finding the electron at a point. If the value of psi is high at a point, then we will say that the probability of finding the electron is very high. The electron can be found there. And if psi squared becomes 0 somewhere. Okay? Then we will say that the electron cannot be found there, and we also call it a node. I just said, where psi squared comes, what will it be called? Node. There are two types. One is radial, and one is angular. These depend on distance. These depend on angle. The formula for radial nodes is n - l - 1, and the formula for angular nodes is, that is l. Let me tell you. Always, whenever an orbital is designated, it is done like this. n

l to the power of x. This tells the shell. This tells the subshell. This tells the number of electrons. For example, if it is written, say, 3s². This means that in the s subshell of the third shell, in the s orbital because there is only one orbital within the s subshell, its name is s. There are two electrons inside it. For example, suppose somewhere it is written 2pz¹. This means that in the pz orbital of the p subshell of the second shell, there is one electron. Sir, one more example, absolutely. 4dx² - y² 1. In the dx² - y orbital of the d subshell of the fourth shell, how many electrons are there? That is one. Very good, sir. Now tell me, what will be the formula for radial nodes? n - l - 1. Suppose n is how much? Three. How much is l, sir? For s, the value of l is zero. So n - l - 1, 3 - 0 - 1, sir, it will be two. Here also, 2 and 1, 2 - 1 - 1, it will be zero. 4 and this is two. 4 - 2 - 1, sir, it will be one. How many angular nodes will there be? l is zero, zero. One is one. Two is two. Right? The value of l. How many total nodes will there be? Sir, add both. The number of angular nodes also needs to be told. Radial nodes also need to be told in this. Okay, sir. Angular nodes are equal to l. How much is n? 3. How much is l? 2. That is, it will be two. Okay? How many radial nodes are there, sir? That is n - l - 1. How much will it be? It will be zero. So angular nodes should be written first. And then radial nodes later. Actually, it should have been written as two and zero. But since there is no option, I said zero and two. Inside what? There are three angular nodes and also three total nodes. No problem. Here I will write n. Here I will write l. Here n - 1, total node. Right? This is angular, and what will this tell? Total. How much is n? 6. How much is l? 2. 6 minus 6 minus 1 is five. No, 6n - Ah, it has to be total, right? Yes, total five. One, four, three, two, one, four. n - l. There are three angular nodes and three total nodes. Radial nodes have been asked. n - l - 1. 3 - 1 - 1, it will be one. Angular nodes have been asked. As much as the value of l is. The value of l is two. Here it is. There is an orbital in which the value of n is given, son, 4, and the value of m is given as -3. Okay. Number of radial nodes in this orbital. Number of radial nodes have been asked from you. Do you know? If the value of m is -3. See, actually, the value of l can be any of 0, 1, 2, 3. But you know that the value of m will be -3 only when l is 3. If it were 2, it couldn't be -3. If it were 1, it couldn't be. If it were 0, it couldn't be. So l is 3. Just figure it out, radial nodes. n - l - 1. 4 - 3 - 1. Comes out to be how much? Zero. Son, the graphs of the radial wave function and distance need to be told. This is distance. This is radial wave function, for s orbital and p orbital. I will tell you a few small things. First, pay attention to them. Once you understand them, you won't need to memorize the graphs, you will understand them very well. For s orbital and for p orbital, there is a difference only in the first point. All other points are exactly the same. Right? No need to think about them. Listen carefully, understand. The very first thing, whenever you draw the graph of the radial wave function with distance, it will be a cosine wave. Okay? And this will be a sine wave. Okay, sir. You know how a cosine wave is formed? Sir, it is formed like this, like this. And how is a sine wave formed? Sir, it is formed like this. Very good. Sir, how many phases will you draw? Like this is one phase. This is one phase. This is one phase. If someone asks how many phases are drawn? Three. How many are drawn here? Three. How many are drawn now? 1, 2, 3, 4, five. Right? How many phases will you draw? Whenever you are drawing the graph of 1s, 2p, 3s, 4p, whichever graph you are drawing, how many phases will you draw? I will tell you. The phases will be n - l. Same, same, same, same, n - l. Brother, just give me 2 minutes. See how easy I will make the graphs for you. Third, as the phases increase, the peak of the graph will decrease. That is, the first phase formed will be the largest. The second will be smaller than that, the third smaller than that, the fourth smaller than that, the fifth smaller than that. It will keep happening like this. Sir, here, here also it is the same. One more thing needed to be told. One more thing needs to be told. As the space increases, the peak will decrease. What was that last point? That whenever the last phase is, it will touch R. Yes, the last phase will not touch R. Same, same, same. Like now, look, suppose I have to draw the graph. This is Cr, and this is r, and I have to draw the graph of 3s. First, tell me, which one do I have to draw? Sine wave or cosine wave? Sir, cosine wave. That means the graph starts from here. Second, how many phases do I have to draw? You tell me. n - l. The value of n is 3. The value of l is 0. 3 - 0. Three have to be drawn. Okay, okay. One, two, three have to be drawn. Okay? As the phases progress, the peak will become smaller. That is, the first phase will be large. The second will be smaller than that. The third will be smaller than that. Right? The first one looks how big. The second is smaller than that. The third is even smaller than that. The last phase will not touch R. See? The last phase, 1, 2, 3, the third last phase, will not touch R. Similarly, I will draw a P for you as well. Cr and r. Suppose I am drawing the graph of Cr versus r for 4p. First, tell me, which one do I have to draw? Cosine or sine? Sir, it's P, so sine. Very good. Sir, then how many phases do I have to draw? How much is n? Four. How much is l? 1. 4 - 1. How many, sir? Three have to be drawn. Okay, so we will start from here and draw three phases. The first one the largest, the second smaller than that, the third smaller than that. The first one the largest, the second smaller than that, the third even smaller than that. See? The largest, smaller than that, even smaller than that. Okay? The last one will not touch R. Okay? Now can you tell me which s graph I have drawn? Which s graph have I drawn? 1s, 2s, 3s, 4s, 5s, 6s, 7s. Which one? Similarly, which p graph have I drawn? Which p graph have I drawn? I have drawn a p graph. Okay, I will give a hint. But which p? Absolutely correct. Yes. Right? This is the graph of 1s. Right? The number of phases is one. That is n - l. It is 1. The value of l is 0. So how much will n be? It will be 1. Here also, how many phases are drawn? Two. So n - l is two. The value of l is 1. So how much will n be? It will be three, sir. Very good. Okay? So you can draw any graph. Now, we also have to draw the graph of radial probability density. Sir, what is radial probability density? The probability of finding the electron. The probability of finding the electron in a straight line. This is a straight line. Here you have moved out from the nucleus. In this straight line, r is increasing. Distance is increasing. The probability of finding the electron in this line. Sir, for these graphs also, do we have to draw for s and p both? Yes. There will be a difference in only one thing. Only one thing. You can never go into a trough here. Ever. Why? Because the square of anything cannot be negative. So the graph will always be in the crest and not in the trough. It will remain in the crest. It will remain in the crest. Everything else is the same. Everything is the same. The graph cannot be negative. Finished. Tata, bye-bye. It's just that small a difference. The graph just cannot be negative. All other points are the same. Right? How many phases to draw? As the phases increase, the peak will decrease. The last phase will not touch R. Just one thing has been added. This will be cosine, that will be sine. Everything is the same. The graph just cannot be negative. For example, if I have to tell which p graph I have drawn. Which p graph have I drawn? Because I am drawing a p graph, it is certain that I have to draw a sine wave. That means I will start from here. Look at this. Right? But the graph will not go down this time. Because the square cannot be negative. Right? Are we studying complex numbers that it will become negative? And which s graph have I drawn? Tell me this too. It is s, but which s? I am so sorry. Absolutely correct. Yes. This is 4p. Why? Because how many phases have been drawn? 1, 2, 3. How many phases are there? n - l. That is three. The value of l is 1. So n - 1 = 3. So how much will n be? Four. Here, how many phases are there? One and one, two. n - l is two. The value of l is 0. So how much will n be? It will be two. So which one is it? That is 2s. So you can draw any graph. You don't need to remember any graph. You can draw any. Tell me, a graph is drawn of Cr² and r. What is being talked about here? 1s, 2p, 3s, and 2s. Sir, first of all, this is a cosine wave, right? It is starting from above. So it cannot be 2p. If it is, it will be s. Now tell me, how many phases are drawn? One and one, two phases are drawn. So n - l is two. The value of l is 0. So how much will n be? It will be two. So which one is it? That is 2s. And look. Yes, I will tell you one more thing. It has happened many times that NTA will write Cr as r. So you should not start writing RR in the exam either. RR also means the same. This also means the same. Radial wave function. Many times NTA will do this, it will write r²r instead of Cr². Brother, both mean the same. This is also radial probability density. This is also radial probability density. No arguments, okay? Variation of radial probability density as a function of R. For which one do we have to draw? For 3p. And for 3p. So first of all, it should be a sine wave. This is cosine. This cannot be the answer. And it is 3p, so tell me, brother, how many pieces will there be? n - l. For n=3, for p, l is 1. There will be two phases. So this also cannot be it. Now the answer will come from only these two. Which one will it be, sir? The first phase will be larger. The second phase will be smaller. Here it is. There, the first phase was smaller. The second phase was larger. That is also wrong. Now 4π, π has to come. This i was written by mistake. 4πr² dr² r. Brother, instead of this i², it can also be r². No tension. Sir, first of all, what is this? This is the radial density function. Oh sir, what is this? Like radial probability density was the probability of finding the electron along a straight line. What is this? Take any small distance dr. The probability of finding the electron within this. The probability of finding the electron within this. Within this small shell of thickness dr. The probability of finding the electron within this is called the radial density function. Okay? For this also, we have to draw graphs for all. For s, for p, for d, and for f. First of all, all of these are sine waves. This is not written in any book. This is a sine wave, this is a cosine wave. All are our observations. We haven't seen any book yet. And if someone copies it from somewhere, that's a different matter. But we haven't seen any yet, brother. These are all made from observations so that you don't have to memorize the graphs. First of all, this will be a sine wave. Second, how many phases will there be, brother? n - n. Don't worry about the phases. This point is different. As the phases increase, this time the peak will increase. Okay, make the first one small. The next one larger, the third one larger. Yes, the fourth graph cannot be negative. Sir, that was understood from the square itself. Fifth, the last phase will not touch R. It will not touch R. Like, I am drawing a graph, and again, 4πr² dr² r. Suppose this is the graph of some s orbital. Suppose this is the graph of some s orbital. So tell me, which s orbital is this graph of? The first peak is small, the next one is larger. Which s orbital is this graph of? If it is a graph of an s orbital, then all will be sine waves. This time, whether it is s, p, d, or f. This is the graph of 2s. Absolutely. Because how many phases are drawn? Two. n - l is two. What is the value of l for 0? So how much will it be? 2s. Okay, suppose this is the graph of p. So which p is it? Suppose this is the graph of d. So which d is it? And f. So which f? Sir, if you talk about p. n - l is two. n - 1 is two. So how much will n be? Three. No, sir. Talk about d. n - l is two. The value of l is 2. So how much will n be? Four. No, sir. Talk about f. n - l is two. The value of l is three. How much will n be? Five. Sir, this is the graph of 5f. Right? So you can draw any graph. Shape of orbital. We won't take much time. They are spherical. s orbital. p orbital are dumbbell shaped. In px, the electron density will be along the x-axis. Okay? In y, it will be along the y-axis. In the z-axis, it will be on the z-axis. Right? These are spherically symmetrical. That is, the value of the orbital wave function will be the same in all four quadrants. It is not like that here. Right? One side positive, then negative, positive, then negative, positive, then negative. In the opposite one, d can be of two types. Either the electron density will be in between the axes or on the axes. In between the axes, dxy, dyz, dxz. dxy, so the electron density is between the x and y axes. If it is dyz, then between y and z axes. If it is dxz, then between x and z axes. If it is dx² - y², then the electron density will be on the axes, on x and y. If it is dz², then the electron density will be on the z-axis, and there will be a ring. A ring. The ring is complete in all axes, in x, in y, and in z. Okay? Here, sir, what will be the sine? Of the orbital wave function. Okay? Alternatively, what will it be? It will be opposite. You can also say it like this. You can also say that alternatively the sign will change, or it will be the same in the opposite. You can also say it like this. If this is positive, then this is positive. This is negative, negative. This is positive, then this is positive. This is negative, negative. Sir, can we do this, make these two positive and these negative? Absolutely. Positive, positive, negative, negative. This is positive, this is negative. This is positive, this is negative. Here, if these two are positive, then this ring orbital wave function will be negative. I can also say the opposite. If I make this positive, then these two, and these two will become negative. Okay? This is the sign of the orbital wave function. It has nothing to do with electron density. What will be the nodal plane? What was a node, sir? It was a point where the electron density was zero. What will be a nodal plane? The electron density will be zero in the entire plane. The electron cannot be found in the entire plane. A node is just a point where the electron cannot be found. In a node and a plane, it cannot be found in the entire plane. Sir, on what does this depend? This depends on the angular nodes. On what do angular nodes depend? On L. Like here, here I am writing l. Here, number of nodes. Here, orbital. Here, number of nodal planes. And here, their position. For example, if the orbital is s. In the s subshell, there is only one orbital. Its name is s. For it, what is the value of l? Zero. So how many nodal planes will there be? Zero. There are none. So where will I write the position? Very good, sir. Whether it is px, py, or pz. Sir, for all of them, obviously for the p subshell. What is the value of l? One. So how many nodal planes will there be? One. Sir, where will they be? Okay, tell me, in px, where is the electron density? Sir, the electron density is on the x-axis. Where is it not? Sir, the y and z, the yz plane. It is a nodal plane. Okay, okay, okay. How easy is it, right? If the electron density is on y. Where is it not, sir? On xz. On z, there is electron density. Where is it not, sir? yz and xy. There is no electron. Whether it is dxy, dyz, or dxz. For all three, l is known. There will be two angular nodes. No problem. Here, between which two axes is the electron density, sir? Between x and y. The electron density is between x and y. Where will it not be, sir? If it is xy, then it will not be in the other two. yz and xz. There is electron density in yz. Where will it not be? xy and xz. There is electron density in xz. Where will it not be? xy and yz. Okay, sir. One more is done. dx² - y². Here, the electron density is on the axes. Where is it on the axes, sir? On x and y. If the electron density is on the axes, then in between the axes, at a 45° angle from both x and y, at a 45° angle from the x-axis and the y-axis. And dz². This is the only one. Although its l value is two, there will be no nodal plane. There will only be angular nodes. What will there be? Angular nodes. I will show you too. See? In px, the electron density is on the x-axis. Where is it not? In y and z. In y and z. This gray colored part that you see, this is the nodal plane itself. In the y-axis, where is the electron density? It is on the y-axis. Here is the y-axis. Where is it not? In x and z. Here is x, here is z. This gray colored part that you see, this is the nodal plane. There will be no electron here. There will be no electron here. There will be no electron here. m. Similarly, in pz, where is the electron density? On the z-axis. On the z-axis. Where will it not be? In x and y. This gray colored part that you see, right? We have brought it so that you don't have any problems. I will show you the d ones too. If you see one of the d ones, then all the others will be visible on their own. For example, 3dxy. Where is the electron density? Okay? Sir, it is between x and y. It is between x and y.

Here. This is the Y-axis. It is in the middle. Where is it not, sir? One is between YZ and one is between XZ. Okay? If you can see just one, then you will automatically see the rest. 3dz² is very interesting. Okay? Here it is visible in the shape of a cone. Angular nodes are in the shape of a cone. There will be a similar cone shape below, coming from behind. Okay? A cone will be formed. There are angular nodes, but no nodal planes. There are no nodal planes. Identify the incorrect statements from the following. The shapes of dxy, dyz, and dxz are similar. Yes, they are similar. And the shapes of dx² - y² and dz² are similar, right? There, the electron density is on the axes. They are not similar. This is incorrect, man. The other 5d orbitals will be different in size compared to 4d. Absolutely, 4d ones will be smaller. 5d ones will be larger. The shapes will be similar. Like the shape of 4dx² - y² and 5dx² - y² will be similar. But 4d - x² will be smaller. 5d - x² will be larger. All the five 4d orbitals have shapes similar to 3D. Absolutely, but 4D ones will be larger and 3D ones will be smaller. In an atom, all the 5d orbitals are equal in energy. Absolutely. 3d xy, 3d yz, 3d xz, 3dx² - y², 3dz² all will have the same energy. What does the Aufbau principle say? It says that electrons are filled in the increasing order of energy. Whichever has less energy, we will fill that first. Then more energy, more energy, then more energy. Then it goes on like that. Sir, how will we know if something has more or less energy? Okay? If it is a multi-electron atom, with more than one electron, then the energy will be equal to n + l. What will it be? n + l. Whichever has a lower n + l value has lower energy. Whichever has a higher n + l value has higher energy. No sir, what if both have the same n + l? Like look at this, 2p and 3s. n l 2 1 3 0. Sir, look, this also has n + l = 3, and this also has n + l = 3. If both are the same, then whichever has a smaller n, whichever has a smaller n, will be filled first. Okay, this was about multi-electron atoms. If you have a single-electron atom, hydrogen or a hydrogen-like atom, then the energy will depend on n. That is, 3s, 3p, 3d all have the same n. For hydrogen or hydrogen-like atoms, n is the same. If n is the same, then the energy will also be the same. Okay? Everyone must know how to draw this. Right? If not, then son, write one once. Write two twice. Write three thrice. Write four four times. Then write five four times, then write six thrice. Right? First, write them in increasing order. Then keep it constant at five and write them in decreasing order. For the one written once, put S in front of it. For the one written twice, S and P. For the one written thrice, SPD. For the one written four times, SPDF. Four times, SPDF. Thrice, SPD. Twice, SP. Right? Once S. Twice SP. Thrice SPD. Four times SPDF. Four times SPDF, then SPDS. Write this much. Then after that, how will it move? It will move like this. Right? From 1s to 2s, then 2p, then 3s. Right? There are exceptions in lanthanides and actinides in some places. You have already studied that in inorganic chemistry. I will not talk much about it. For a hydrogen atom, arrange 3s, 3p, and 3d in the increasing order of energy. If it is a hydrogen atom, then you know that energy will depend only on n. n is the same for all three. So the energy will also be the same. If it was not written as a hydrogen atom, but some other multi-electron atom, then we would look at n + l. This would have the lowest. This would be more than that. This would be the highest. Whichever has a higher n + l would have higher energy. This is a question that came in NEET. 4D, 5p, 6s, 5f, and 6p. Arrange them in increasing, sorry, arrange them in the order of decreasing energy. Decreasing energy. Okay, so tell me the correct option. Decreasing energy. So, calculate n + l, man. n + l. 4 + 2 = 6. 5 + 1 = 6. 6 + 0 = 6. 5 + 3 = 8. And 6 + 1 = 7. Sir, 5f will have the highest. Yes, 5f will have the highest. Sir, then 6p will come. Yes, 6p will come. Now, between 5p and 4d, sir, both are coming to six. Whichever has a smaller n, its energy is less. Whichever has a smaller n, its energy is less. What does the Aufbau rule say? A new electron will enter the orbital that has the minimum n + l. Right? First, the one with the least n + l, then the one with more, then more, then more. Whichever has the minimum n + l. Identify electrons by quantum numbers: n=4, l=1; n=4, l=0; n=3, l=2; n=1, l=1. Arrange them in increasing energy. Lowest to highest. Lowest to highest. Whose n + l is the least? Sir, these two. This is also four, and this is also four. So, sir, how will we know? Whichever has a smaller n. That is, the one with four will have less energy, and the one with two will have more. Sir, it will come from here. But let's check further. Its n + l is 5. Its n + l is also 5. But its n is smaller. The one with three will have less, and the one with one will have more. What does the Pauli Exclusion Principle say? It says that the two electrons in an orbital will definitely have different spin quantum numbers. Like look at this. Two electrons in the s orbital of the s subshell of the fifth shell. I have named one as the first electron. Similarly, I have named the other as the second electron. Write their n: 5, 5. Write l: 0, 0. Write m: 0. But the spin quantum number will be different. If this is +1/2, then this is -1/2. If this is -1/2, then this is +1/2. And we will show it like this: one above, one below, right? That one is +1/2 and the other is -1/2. It is not possible to explain the Pauli Exclusion Principle with the help of this atom. For which atom can the Pauli Exclusion Principle not be explained? It can be explained for Boron. 1s² 2s² 2p¹. Yes, it can be explained. Look, it has two electrons. Beryllium has atomic number four. 1s² 2s². Yes, sir, it can be explained here too. Right. Carbon has six. 1s² 2s² 2p². Yes, sir, it can be explained here too. Hydrogen has one. Yes, sir, it cannot be explained here. Right? It only has one electron. If there were two, then it would tell us from Pauli that one spin would be half, and the other would be -1/2. Two electrons that are in the same orbital are distinguished differently by what? Principal magnetic, no sir, the spin quantum number is different. The other three are the same for them. What does Hund's Rule say? It says that until each orbital in a subshell gets one electron each, with the same spin. Until they each get one electron. With the same spin. Okay? Pairing will not start until then. For example, let's say this is the p subshell. You know there are three orbitals inside the p subshell. Right? So, until each gets one electron, with the same spin, pairing will not start. You should not do this. First, everyone will get one electron. Then, pairing will start. Man will be man, right? Boys will understand without being told. Okay? Girls must be wondering what is being said. Come on, let's move on. Let's do the questions. Tell me the correct set of quantum numbers for the unpaired electron of chlorine. You know chlorine has atomic number 17. So, 1s² 2s² 2p⁶. Sir, let's just write it as Neon. We have learned that much. Sir, even in inorganic chemistry, 3s² 3p⁵. 3s, here it is. 3p⁵. There are three orbitals inside the p subshell. First, one electron each came into them with the same spin. Yes. We are talking about this. About this. So, tell me, sir, what is n for this? Three. Very good. What is l? One. Very good. And what is m? Sir, for the p subshell, what will it be? -1, 0, or +1. It will be one of those values. Right? One of -1, 0, or +1. And S will be either +1/2 or -1/2. But the answer came from here, sir. From n=3, l=1, it is one of -1, 0, +1. And the value of S was either +1/2 or -1/2. Which of the following statements given below is the wrong statement? Tell me. The total orbital angular momentum in an s orbital is zero. Absolutely. The total orbital angular momentum is l + 1 h / 2π. The value of l is zero for s, so it will be zero. An orbital is described by three quantum numbers: n, l, m. Absolutely. An electron is described by four quantum numbers because the electron has its own spin, either +1/2 or -1/2. Absolutely correct. The value of m for dz² is zero. Absolutely right. Electronic configuration of the nitrogen atom. Nitrogen is seven. 1s² 2s² 2p³. 1s², yes, okay? 2s², okay? 2p³. One. Sir, look, this is wrong. What did Hund's rule say? First, everyone should have one electron each. With the same spin, the spin should also be the same. Either all three would be drawn upwards, or all three downwards. Here, two are drawn upwards and one downwards. This is wrong, sir. This violates Hund's rule. The orbital diagram should be drawn where the Aufbau rule is violated. Violated means not followed. The Aufbau rule is not followed. The lower orbital is not filled, the one with less energy. The one with higher energy has started to be filled. Here, the lower one is filled. Which one is not followed here, sir? The spin quantum number is not followed here. Uh, sorry, the Pauli Exclusion Principle is not followed. Because the spin quantum numbers of both are the same. So this is not my answer. Yes, this is correct, sir. Look, the lower one is not filled, and the one with higher energy has started to be filled. This is it. Aufbau is being violated. Here too, below. Here, everything is correct. Here too, everything is correct. Okay? This is where the Aufbau is not being violated. Not followed. Whose electronic configuration is this? 1s² 2s² 2p³. 2, 4, 5, 6, seven electrons. It's Nitrogen, sir. Do this yourself. I just did it for the unpaired electron of chlorine. Rubidium is asked. Exceptional configurations of Chromium and Copper, you know that, right? For Chromium, it should be 4s² 3d⁴. It is 4s¹ 3d⁵. For Copper, it should be 4s² 3d⁹. It is 4s¹ 3d¹⁰. Okay? This should be the case. But this will happen. What is the reason? Sir, half-filled and fully filled have higher energy, sorry, lower energy and greater stability. Like this is fully filled, and this is partially filled. This is stable, and this is unstable. But if one electron moves from here to here, then this will also be half-filled, and both will be stable. Similarly, here, this is fully filled, and this is partially filled. This is stable, and this is unstable. But if one electron moves from here to here, then this will also be stable, and this will also become stable. Okay, sir? Half-filled and fully filled have lower energy and greater stability. Sir, why does this happen? There are two reasons. One is symmetry, which is not the main reason. The main reason is that as soon as, look at this, let's say there are four electrons in d here, and five electrons in d here. One, two, three, four, five. One, two, three, four. Those that have similar occupancy. What did I say? Those that have similar occupancy. Like in all these, there is one electron each. So, all of them can exchange their positions. This with this, this with this, this with this. This with this, this with this, and this with this. The total number of exchanges will be six. Position will be exchanged six times, so energy will be lost six times. Energy loss increases stability. Look here, from this, to this, to this, to this, four are done. This with this, this, this, three are done. This with this and this, two are done, and this. Four and three is seven, and two is nine, and one is ten. It will exchange its position ten times. So, energy loss will be ten times. Sir, more energy loss will happen here. Stability will be greater. Which of the following ground state electronic configurations is given below? This is inorganic stuff, right? With this, son, our chapter for today also finishes, which is called That is Atomic Structure. Okay? I am telling you, for the last 6 years, we have been increasing hope. Okay? Ask me personally. I have worked the most in this hope. You will never, never, never be able to convince me that sir, you worked harder in last year's hope compared to this year. Sir, look, that lecture was 8 hours long, and this one is 4 hours long. You will never be able to convince me because I know what I have put myself through. I know. I knew that first biology ran in this hope, then physics ran, then chemistry ran. We are at the very end. Okay? So, the one at the very end has to take care of the entire pack. You, you cannot just think about yourself. You have to see, like, how did hope run, what improvisations should have been made for it, and we did that. Believe it or not. I am giving a slightly vague number. I think I spent at least 200 hours just making the PPTs for all these chapters of physical chemistry that have passed, whether it's Basic Concepts of Chemistry, or Redox, or Thermo, Chemical Equilibrium, Ionic Equilibrium, I said Redox, Solutions, Electrochemistry, Chemical Kinetics, okay, Atomic Structure. At least, at least, and I swear to God, I am not lying. I spent at least 200 hours just making the PPTs. I have never made such PPTs even in any paid batch. Until last year, what used to happen was that in hope, we had to give the same content as was given in the previous batch, so we would bring the PPTs as they were, without doing anything. This time, we have worked a lot on the PPTs. A lot, meaning, meaning, I know this. Only, only I know this. Meaning, whether you believe it or not, that's up to you. You will start playing the comparison game. In last year's hope, it was taught in 8 hours. In this, it was taught in 4 hours. Sir, that is your wish. You can do that. That is your choice. But I have put my best foot forward in this hope. The JEE questions that were relevant, I have definitely covered them here in hope. Okay? Where there is a slight differentiation due to syllabus and all. Okay? We have not included that. Thank you. Thanks to each and every one of you. Because I always believe in finishing what you have started. I really, really, really want to salute you from the bottom of my heart. That you people stuck around from the first class of hope to the last class. I mean, this is not an easy job. When you are down and dusted, still you say, "Not today." You do not give up. This is also a victory. That you have not given up yet. Okay? This is commendable. This will go on for the longest possible run. As long as you are on this earth, you will remember this: that the NEET 2026 exam that had to be given, two-three months before that, man, I used to study 12-12 hours, 14-14 hours. These things will definitely create a difference in your life. Read it and read my lips and record this small thing. You will tell this to your children too. Yes, you heard it right. Right? Sir, we are children ourselves right now. I know you are children yourselves right now. After 20 years, or maybe soon, 20 years is not too long, sir, you said. Oh, let's say 10 years. Then another 10 years after that, because only when the children grow up will you tell them. Okay? You will tell them that, "Brother, the NEET 2026 exam, your brother was very big." And let's come to the main point, which you have been asking me since the class started. Sir, NTA has tweeted, and in it, they have written that the exam can be tough. Sir, we are panicking. I want to ask you a question. I don't want to give an answer. I want to ask you a question. After 20 years, would you want to ask your children this question: "That NTA tweeted something, and I panicked, and my preparation was going very well, but because of that tweet, my mind got disturbed, and I stopped preparing. Then on the day of the exam, because I had not given my best effort for the last 10-12 days, I could not do well. Do you want to tell your children these things?" Tell me, what do you want to tell them? Look, it is their job, they are a conducting agency, and we respect them a lot. Okay? The exam that comes comes the same for all the students. Or, what if Set A comes very difficult, and Set B comes very easy? Then I am with you. Okay? If the exam is easy, it will be easy for everyone. If it is moderate, it will be moderate for everyone. If it is tough, it will be tough for everyone. Okay? If the exam is tough, we get to know at the beginning. I will tell you about a very beloved child of mine from last year, whose name is Om Bhoot. He has an All India Rank of 372. Okay? He is in AIIMS this year, and he has also come home after getting selected. He has come home twice to meet me after selection. Okay? He brings good things. He will come again next time, we will introduce you sometime. So, he told me a story from NEET 2025, which I will never forget in my life. Okay? He said, "Sir, I was doing my exam. The exam was getting late for me, and you know the reason is that the paper was tough. But sir, after an hour and a half, I just lifted my neck and looked up and analyzed myself that my paper was only 30 to 40% done. The entire physics was left, and some portion of chemistry was also left. Okay? But when I looked up, I saw that sir, in the entire class, everyone was sweating, and two or four children were crying during the exam. Okay. He said, "Sir, only then I understood that this situation I am going through, what is happening inside me, is not happening to me alone. It is happening to everyone." You know that graph, you can extrapolate it. He understood. He said that, "Sir, I understood that if children are crying sitting in the class, then when I come out of the class, other children will be crying outside, and there will be a lot of noise. This means the exam was tough. If it was tough, it means I should not panic. I should do as much as I can of the exam." Can you imagine that guy who has just completed 40% of the paper when half the time was over? At halftime, only 40% was done. The entire physics was left, and some portion of chemistry was also left. Okay? That guy has scored like got All India Rank 372. Just imagine, just imagine. Okay? So, the paper will be tough. It will be tough for the whole world. Just if you do not give up in the exam hall, and do as much as you can, then you will score very well. Okay? And if you start crying and moaning even when it is easy, or if you start crying and moaning in the next 10-12 days, then you will leave even the exam that you know. You have to decide what you want to tell your children after 20 years. "I got panicked by a tweet. And I gave my best shot. I worked like an ass. I worked my ass off. I burned the midnight oil. I worked hard like a donkey in the last 10-12 days. When they said it would be like this, I said, 'Try me. Let's see who has the balls.'" Now you have to decide what you want to do, what you don't want to do. Okay? NTA, well, sometimes they make some rules, and sometimes they take them back the next day. It did not happen. Just now, NTA released a notification for the first shifts of JEE Mains that we are allowing calculators. The next day they said, "Oh, oh, no, that was a mistake." Mistakes happen, man. To err is human. Okay? So, you cannot be afraid of a tweet. I don't think you are that mentally weak. Doctors have only read in books, read only in books, that there was a pandemic in 1980 and 1990. Man, a pandemic came. In the pandemic, whose contribution was the most in the whole world? Everyone contributed. But whose contribution was the most? That is medical representatives, doctors, nurses, and all. Okay? No politician, no one contributed more than them. They were not afraid then. They were not afraid then, when millions were dying. When there were corpses all around, when there were only 200 beds in the hospital, and there were 2000 people. Okay? For months, they did not go home, man, thinking, "What if my family gets something if I go home?" Okay? They did not sleep, did not eat properly. They were busy saving people. They were not afraid then. You will be afraid of a tweet. Think, they were not afraid then, so will you be afraid of a tweet? Okay? We will meet you again sometime in a future class, until the exam is over. Okay? And those who have completed this entire hope, I have taken a PYQ session on Competition Wala. You can go there and attempt PYQs for each chapter. It will be very helpful for all of you. Okay? See you. All the best. All the best. My best wishes are all with you. You are going to rock in your exam. If there is one person who has faith in your abilities, only one person that who has faith in your abilities, that is me for sure. I will see you in the result celebration. Bye. Take care.