 Hello, I'm Professor Steven Eschivan. I want to tell you a little bit about quantum numbers and Hun's rule in relationship to atomic orbitals. So this is just to reorient you. This is our orbital energy diagram and energy on this axis here and various orbitals. This is the first shell, second shell, and so forth. And I've created, just for the sake of argument here, an excited state electron configuration which would be described this way. In the 1s orbital, there's one electron. There it is. In the 2s orbital, there's also an electron. It's spin down. And in the 2p electron orbital, there's another electron. And I'm using this because I want to talk about the four quantum numbers that are in each that characterize every single electron on a given atom. So let me just march through this. I'm abbreviating Q number there. So that's the quantum number. So one quantum number is called M sub s. It's called the spin quantum number. And we've seen that electrons have spins. We've talked about how they can be spin up or spin down. Turns out the spin up version gets a quantum number of plus one half. M s equals one half. And the spin down version gets a quantum number of minus a half. Let's see. Going on, there's also a shape, quantum number. That's given by the letter L, and that's fairly straightforward, too. The s orbitals, all s orbitals, which are the round guys, have L equals 0. And all p orbitals have an L value of 1 and d orbitals. Have an L value of 2. And it turns out that the first shell has only L equals 0. That means it doesn't have any p orbitals or d orbitals. The second shell gets to have L equals 0 and 1, which means it has s orbitals and p orbitals. And the third shell has L equals 0, 1, and 2, which means it has all three. We can keep on going up there. Another quantum number is called the principal quantum number. It's given the letter n. It affects primarily the size of orbitals and also the energy of those orbitals, more or less. And this is very simple. The first shell has n equals 1, second shell has n equals 2, and it's bigger. And the second shell generally, the orbitals have higher energy. And the third shell has n equals 3. They're even bigger and even higher in energy and so on. The last one is called the orientation quantum number. We're going to call it the orientation quantum number. It's called the letter is M subscript L. Here's the deal. M sub L runs, it can take on values, starting at minus L and going all the way up to plus L. And it tells us the orientation of the orbital if that is relevant. So let me give you an example. An S orbital, remember S orbitals have L equals 0. That means the M sub L quantum number can only run, can only be 0. And that's why there's only one S orbital in each shell. Because that's just what L dictates. M sub L can only be 0. P orbitals, remember, have an L value of 1. So that means M sub L could be minus 1, 0, and 1 as possibilities. And that is why there are three P orbitals in shell, starting shell 2, and then shell 3, and so forth. Because I'm once again referring back to the L quantum number. D orbitals can have, because D orbitals have L equals 2, that means M sub L can go from minus 2, minus 1, 0, and 2. That means there's five. So that's why there are five D orbitals and again, because of these other restrictions, the first set of D orbitals occurs in shell 3. Now let's see if we can do some assignments here. I'm looking at this electron here. It has, it's in the first shell. Okay, that means N is 1. It has the shape quantum number of 0 because it's an S orbital. And M sub L can only be 0, so because of the restriction we talked about before. And I can see that it's spin up, so it N sub S must be plus a half. How about this one? This electron, it's up here. So if you want, you can pause the video and take a, take a stab at it. Okay, I'm saying that this is in the second shell, so it must have an N value of 2. And let's just go on to the rest of my answer there. It's an S orbital, so once again, L is 0. M sub L can only be 0 for S orbitals. And I'm looking at it now, and it's spin down, pointing down, so it's M sub S. It's spin quantum number must be minus a half. How about this one here? And if you want to pause and have a look at it, take a shot at it. All right, I'm saying, here we are still in the second shell, so that means N is 2. It's a P orbital, so now I know that L is 1. Now the M sub L, you know, it's a bit, it depends on how you count it, but I normally count, you know, if I know that M sub L can run from minus 1 to 0 to 1 for P orbital, I could say that's the minus 1, that's the 0, and that's the plus 1. So I'm going to say that the M sub L is 0 for that orbital. And I see that it's spin up, so M sub S is plus and half again. Now, there's a, there's also this thing called, when there is this thing called sub shell degeneracy, what we do is we avoid pairing up and we align spins. Let me explain that. So this is a whole shell. Degeneracy means same energy, and I can see that this S orbital does not have the same energy as those P orbitals, but sub shell means a part of a shell, and yeah, it's pretty obvious that all those three P orbitals have the same energy. So there is definitely sub shell degeneracy going on there, and in this case I need to put two electrons in it. So Hoon's rule says when there is sub shell degeneracy avoid pairing up, that is, don't spin pair, and also align the spins. So in other words, I put them here and here so their spins can be aligned and they're in separate orbitals. So Hoon says this is the better, that is to say the lower energy state, it's probably the ground state for this atom. Hoon would say this is bad, this is a higher energy state, there's nothing illegal about it, it doesn't violate the poly-exclusion principle because they're paired up, but since Hoon really wanted us to split them up into separate orbitals, that is to say avoid pairing and align spins, we would say this must be a higher energy or an excited state. And that's what I want to say.