Transcription
So as we've just discussed, Bohr described electrons as orbiting around the nucleus in specific electron shells or energy levels. And I mentioned briefly that those energy levels can be further subdivided into what is known as electron orbitals. So let's take a moment here to understand those energy levels and look more closely at electron orbitals and how we go about filling those orbitals with electrons. And more importantly, why this is relevant to us in the context of radiology physics.
So let's have a look again at that Rutherford ball model of the atom, and we can see these electron shells or energy levels extending out from the nucleus. And you can see that the number of electrons that those shells can house increases as we extend away from the nucleus. Now, we go about naming these shells by this nomenclature here, where we start at the letter K and we work our way out, L, M, N, O, P. We can also label these with these n equal to one. N is the quantum number or the principal quantum number of that energy level, and we start with one and again work our way out, n equals 2, 3, 4, and so on. And this is what's known as the principal quantum number.
Now, perhaps the most important concept when it comes to energy levels is this concept of binding energy. Binding energy is the energy required to release an electron from the atom itself. Now, binding energy is dependent on two things. One, the electron's proximity to the nucleus. The closer that electron is to the atom's nucleus, the stronger that force of attraction between the positive protons and that negative electron. That stronger force of attraction, the binding energy, the energy that is required to release that electron from the atom, gets stronger as that electron gets closer in proximity to the nucleus. The second dependent factor is the number of protons within the nucleus of that atom. The more protons, the more positive charge, the stronger that force of attraction to the electrons in the various different energy levels. So binding energy gets stronger as we get closer to the nucleus, and it gets stronger as we increase our number of protons within the nucleus. And you'll see when we look at x-ray physics, this binding energy becomes particularly important because in order to create certain types of x-rays, we need to eject an electron from an atom first in order to create what is known as a characteristic x-ray, which we're going to look at in our x-ray physics module. So this concept of binding energy is incredibly important.
Alkyl binding energies are always going to be more than our L shell, and our shell energies will be more than our M shell, respectively. And it's the difference in those binding energies that helps us to create what is known as characteristic x-ray.
So if we go back now to our principal quantum number, the number that we've labeled to build each one of these energy levels, we can use that number to then determine the number of electrons that that specific shell can house. And the way we do that is by using this formula here: two n to the power of two. So if we look at our K shell here, our K shell has a quantum number of one. So the number of electrons that our K shell can house is two times one to the power of two. One to the power of two is one. The number of electrons in our K shell will be two. You can see there are two electrons here. In our L shell, our principal quantum number is two. So our shell can house two times our principal quantum number, which is two to the power of two. This is four. Two times four is eight. There are eight electrons within our shell. Our M shell then can house more electrons. So let's have a look at our M shell. Our principal quantum number here is three. Three to the power of two is nine. Times two equals 18. We can get 18 electrons within our M shell. So you can see the larger atoms that have more energy levels can house more and more electrons in those further out L, M, N, O electron shells. And what is responsible for these numbers, the number of electrons within each shell, is our electron orbitals.
Now, just while we're here and before you move on, if you are here, I assume you're either starting your Radiology Physics journey or you're coming back to revise your Radiology Physics. And I've created a resource in the first line of the description where I've curated a bunch of past paper questions, and I've gone ahead and answered those past paper questions in depth through videos like this. And so if you're interested in that, if you've got a Radiology Physics exam coming up, I'd really appreciate it if you go and check out that course. I've put a lot of time and effort into it.
Now, there are four different types of electron orbitals. We have an S orbital, a P, a D, and an F orbital. Now, what exactly is an electron orbital? Well, an electron orbital, as you can see here, it's a 3D shape, and it's a region of probability or likelihood of an electron occurring in that 3D space within an atom. So electrons don't necessarily go in perfect circles around the nucleus. They actually exist within these various different shapes. Now, as we start at our K shell here, we have only one type of orbital, and that is our S orbital. Moving on to the L shell, we have both an S orbital and a P orbital. Our M shell has an S, a P, and a D. And as we extend further out, we add these orbitals in.
Now, each of these orbitals can house a specific number of electrons, and electrons will always come in pairs within these orbitals. So our S orbital can hold one electron pair, so two electrons in total. Our P orbital can hold three electron pairs, or six electrons in total. Our D orbital can hold five electron pairs, that is ten electrons in total. And our F is seven electron pairs, or 14 electrons in total. So let's have a look. As we said, our K shell has two electrons within its orbital. Our K shell only has an S orbital, and that's where our two comes from. Our L shell has both an S and a P orbital. It's got two plus six, eight electrons. Our M shell also has D orbitals. So we've got 2, 6, 10, 18 electrons, and that's what we calculated with our principal quantum number. So you can see that our classic understanding of how electrons go in these electron shells is slightly more complex when we start to look at electron orbitals.
Now, we can go about determining how to fill those electron orbitals when we're looking at a specific atom. So let me take a moment here to describe this graph to you here. Each one of these rows here determines a different electron shell, our K, L, M, N, as we extend out. The columns represent the types of electron orbitals, and the numbers here are our principal quantum numbers. So we can see our K shell has only got an S orbital. L has got S, P. M has got S, P, D, just as we've looked at in the previous slide.
Now, if we were to take oxygen, for example. Our oxygen has eight protons here. We've seen this before. Our atomic number is eight, eight protons, and mass number is 16. So we've got eight protons and eight neutrons. And assuming that this oxygen was uncharged, we would have eight electrons. So our eight electrons now need to fit into our electron orbitals. And the way we go about filling these electron orbitals is what is known as Hund's rule. We draw a diagonal line through these orbitals like this, and these diagonal lines determine the order in which we fill these orbitals. So you can see as we go down like this, we start at one S orbital, then our 2S, 2P, and 3S, 3P, and 4S, and so on, as we go down.
So let's go about putting these eight electrons into these electron orbitals. We know that our S orbital can house two electrons, our P six, our D ten, and our F fourteen. So we've got eight electrons to play with. So our first two go into this one S orbital. Our second two then go into our 2S orbital. We've now got four electrons left, and our P orbital can house a total of six electrons. So the four electrons can fill into this P orbital. So this is the outermost orbital within our atom, and this is what's known as our valence electrons. A really important concept when it comes to determining how atoms will react to other atoms, how atoms will react to external forces. So here, when we're describing oxygen, we can describe it as a 2p4. A 2p4. Our quantum number of two in the P orbital has four valence electrons. And we can do this with any atom. And it's in fact how we determine our periodic table. Our periodic table on the left-hand side is our principal quantum numbers, one, two, three, or you can think of this as our shells, K, L, M. The numbers across here determine how many electrons are in that valence shell. So if we were to look at oxygen, we know it's a 2p4. We go to our second row, we find our P orbitals, and we go four across. Oxygen will be here on our periodic table. So our valence electrons, the outermost electrons within a specific atom, determines how atoms interact with other atoms, as well as how atoms interact with external forces.
Now, so far, we've looked at atoms as consisting of specific units: protons, neutrons, and electrons. And that is what's known as our classical model of the atom. Now, with the advent of modern physics, or quantum physics, we now know that we can further subdivide those protons, neutrons into smaller packets of quanta, packets of mass and energy. And that brings us into the realms of quantum physics. And there are certain concepts throughout this course that require quantum physics to explain these concepts. So in the next talk, I want to introduce you to the world of quantum physics, and we're just going to dip our toe in there enough to explain these concepts that we will touch on in future talks. So I'll see you all in that talk. Goodbye.