The purpose of this lesson is to make sure that you understand the connections between the quantum numbers, and to understand what they're telling you about the electrons that have these quantum numbers. So we're going to look at how many electrons in an atom can have the following sets of quantum numbers. For this first one, we know that n is 2, so I'll put a 2 there. And the connection of the possibilities of l when n equals 2, well, l goes from a 0 up to 1 less than what n is. So it'd be 0 and 1. And then let's do all possible m sub ls that have these ls. Well, at 0, this is the only choice, and for 1, we have a negative 1, 0, and 1, because this goes from a negative l up to a positive l by increments of one. So now we can say that any time we have n equals 2, and l equals 1, so these are what we're looking at here. How many electrons? Well, there will be three orbitals with those two numbers, and that would be six electrons. So six electrons and an atom can have an n of 2 and an l of 1. The second one, n equals 4. Well what possible ls do we have? We have 0, 1, 2 and 3. What m sub ls do we have? Well when l is 0, m sub l is 0. When l is 1, m sub l is negative 1, 0 and 1. And we have negative 2, negative 1, 0, 1, and 2. And we have a negative 3, negative 2, negative 1, 0, 1, 2, and 3. So now let's look at what we need. We needed n of 4, which we have, and l of negative 1. Well, how many negative 1s are there? There's this one, this one, and this one. So what I have circled here are three orbitals. These three orbitals will have an l of, n of 4, and m sub l of negative 1. Each of those orbitals can hold two electrons, so that would be six electrons. So six electrons in an atom can have an n of 4, and an m sub l of a negative 1. Okay, let's go to c. For c we have an n of 5. What are my choices for n, for l, it would be 0, 1, 2, 3, and 4. Okay, and my m sub ls, well I'm only going to focus in on this one, because we want an l of 2, so my m sub l's be a negative 2, negative 1, 0, 1, and 2. There's five orbitals there. So five orbitals would have an n of 5 and an l of 2. But we want to keep going a little further. We're going to also say ten electrons because they hold two, but this says that we're only going to be looking at the positive spin, so we can only consider one electron per orbital so this would be five electrons. So there's five electrons in an atom that could have an n equal 5 and l equals 2 and an m sub l of a positive one-half.
