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So let's learn about electrons and their spin and

Â what's called the Pauli exclusion principle.

Â Electrons are going to spin in one direction or

Â the other, clockwise or counterclockwise.

Â All electrons will be spinning in the atom.

Â These electrons will have the same exact amount of spin, but

Â they're in opposite directions.

Â Now the SchrÃ¶dinger equation, these mathematical equations that

Â define the electrons, define for us what's called the spin quantum number.

Â The spin quantum number is abbreviated m sub s.

Â And m sub s, according to the SchrÃ¶dinger equations, can be one of two values.

Â It could be a plus one half or it could be a minus one half.

Â 1:38

Plus one half would be spinning in one direction,

Â minus one half would be spinning in the opposite direction.

Â So let's assign for hydrogen,

Â an orbital diagram that represents those electrons and their spin.

Â Okay?

Â We represent that box to represent the orbital that the electron is occupying.

Â Now, for the ground state, why are we choosing 1s?

Â The smallest n value that we have is an n equal to 1.

Â Okay, so if n is equal to 1, that is what's being represented right here.

Â That's the quantum number 1.

Â And in that first shell, there's only one subshell, it's called the 1s subshell.

Â And in that subshell, there's only one orbital.

Â So that is the one orbital in that first shell.

Â The arrow is representing the electron, okay?

Â So when you do an up arrow, you are representing its spin,

Â and we would represent that spin.

Â And we could associate a value for m sub s.

Â So we want to do the quantum numbers for that electron.

Â We know that we have n, l, m sub l, and

Â now we have a fourth one, m sub s for that electron.

Â The 1 here tells me the n, so that's 1.

Â If it's an s subshell, that is an l of 0.

Â The choices for m sub l is only 0,

Â because m sub l can only go from a negative l up to a positive l.

Â And our spin would be either a plus one half or a minus one half.

Â We will associate this up arrow with a plus one half spin.

Â So where that would be the set of four quantum numbers representing

Â the electron that I have drawn in that box.

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Don't forget that to the name of the subshell and

Â the name of the orbital is the same.

Â So we're in the 1s subshell and it has one orbital.

Â I'm drawing that orbital with a box, and the name of that orbital is 1s.

Â So now we're ready for the Pauli exclusion principle.

Â This is the statement of that principle.

Â No two electrons in an atom can have the same four quantum numbers.

Â What are those quantum numbers?

Â n, l, m sub l, and m sub s.

Â You cannot have any two electrons with the exact same four quantum numbers.

Â Well, the net result of that

Â principle is that you can have no more than two electrons in any orbital.

Â Because the orbital is being defined by the first three numbers.

Â You can have no more than two,

Â because once you have one electron, it's going to be spinning in one direction.

Â And, then to have, not to have the same four,

Â the second one will have to spin in the opposite direction.

Â So that's the net result.

Â No two orbitals can have more than two electrons.

Â I mean, no orbital can have more than two electrons.

Â And those electrons must spin in the opposite direction.

Â So, let's look at helium.

Â Helium has two electrons.

Â If we were to do the orbital diagram of helium, we could put both of

Â those electrons in the same orbital that we had for the hydrogen, okay?

Â But it has to spin in the opposite direction, okay?

Â If we were to assign the quantum numbers for

Â those electrons, actually we'll do that here in a little bit.

Â Okay?

Â So each electron is going to have a set of four quantum numbers.

Â The first three give the location, what shell, subshell, and

Â orbital is the electron located in.

Â And the fourth gives the spin.

Â So if we look once again at the hydrogen atom, I mean, the helium atom,

Â and we look at those two electrons and we assign quantum numbers for it.

Â Okay?

Â The first one would have the quantum numbers 1, 0, 0,

Â plus one-half for the up spin.

Â And the other one would have 1, 0, 0, minus one-half.

Â So they do not have the same four quantum numbers.

Â Three are the same, but the fourth one is different, and that is acceptable.

Â