In this learning objective, we are going to be learning to assign locations for our electrons. And we're going to be assigning them to the appropriate shell, subshell, and orbital. We'll be doing these for ground state atoms, meaning that all the electrons are in their lowest possible energy state. So an orbital diagram is going to show these subshells and their orbitals, and they're going to show them being occupied by electrons. I'm going to teach you how to do that. As I said, the ground state means that the electrons are all in their lowest possible energy states. So they're going to be occupying the lowest energy levels. Now, you can do an electrical configuration or a orbital diagram for an excited state, but then there'd be all sorts of correct answers. When you're doing it for the ground state, there will be only one appropriate answer for the orbital diagram of that substance. So let's learn about electrons and their spin and what's called the Pauli exclusion principle. Electrons are going to spin in one direction or the other, clockwise or counterclockwise. All electrons will be spinning in the atom. These electrons will have the same exact amount of spin, but they're in opposite directions. Now the Schrödinger equation, these mathematical equations that define the electrons, define for us what's called the spin quantum number. The spin quantum number is abbreviated m sub s. And m sub s, according to the Schrödinger equations, can be one of two values. It could be a plus one half or it could be a minus one half. Plus one half would be spinning in one direction, minus one half would be spinning in the opposite direction. So let's assign for hydrogen, an orbital diagram that represents those electrons and their spin. Okay? We represent that box to represent the orbital that the electron is occupying. Now, for the ground state, why are we choosing 1s? The smallest n value that we have is an n equal to 1. Okay, so if n is equal to 1, that is what's being represented right here. That's the quantum number 1. And in that first shell, there's only one subshell, it's called the 1s subshell. And in that subshell, there's only one orbital. So that is the one orbital in that first shell. The arrow is representing the electron, okay? So when you do an up arrow, you are representing its spin, and we would represent that spin. And we could associate a value for m sub s. So we want to do the quantum numbers for that electron. We know that we have n, l, m sub l, and now we have a fourth one, m sub s for that electron. The 1 here tells me the n, so that's 1. If it's an s subshell, that is an l of 0. The choices for m sub l is only 0, because m sub l can only go from a negative l up to a positive l. And our spin would be either a plus one half or a minus one half. We will associate this up arrow with a plus one half spin. So where that would be the set of four quantum numbers representing the electron that I have drawn in that box. Okay? And as I said, and you can't see here because I've got it all nicely covered up with words. So I'll do a little erasing there. The up arrow is a spin of a plus one half and the down arrow is a spin of a minus one half. Don't forget that to the name of the subshell and the name of the orbital is the same. So we're in the 1s subshell and it has one orbital. I'm drawing that orbital with a box, and the name of that orbital is 1s. So now we're ready for the Pauli exclusion principle. This is the statement of that principle. No two electrons in an atom can have the same four quantum numbers. What are those quantum numbers? n, l, m sub l, and m sub s. You cannot have any two electrons with the exact same four quantum numbers. Well, the net result of that principle is that you can have no more than two electrons in any orbital. Because the orbital is being defined by the first three numbers. You can have no more than two, because once you have one electron, it's going to be spinning in one direction. And, then to have, not to have the same four, the second one will have to spin in the opposite direction. So that's the net result. No two orbitals can have more than two electrons. I mean, no orbital can have more than two electrons. And those electrons must spin in the opposite direction. So, let's look at helium. Helium has two electrons. If we were to do the orbital diagram of helium, we could put both of those electrons in the same orbital that we had for the hydrogen, okay? But it has to spin in the opposite direction, okay? If we were to assign the quantum numbers for those electrons, actually we'll do that here in a little bit. Okay? So each electron is going to have a set of four quantum numbers. The first three give the location, what shell, subshell, and orbital is the electron located in. And the fourth gives the spin. So if we look once again at the hydrogen atom, I mean, the helium atom, and we look at those two electrons and we assign quantum numbers for it. Okay? The first one would have the quantum numbers 1, 0, 0, plus one-half for the up spin. And the other one would have 1, 0, 0, minus one-half. So they do not have the same four quantum numbers. Three are the same, but the fourth one is different, and that is acceptable. So this is the end of this learning objective. We were just introducing to you the concept of orbital diagrams. And that third, that fourth quantum number m sub s that tells us the spin of the electron. Make sure you understand Pauli's exclusion principle with regard to these quantum numbers.
