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A second important result is that electrons will fill the lowest energy states available. This would...

A second important result is that electrons will fill the lowest energy states available. This would seem to indicate that every electron in an atom should be in the n=1 state. This is not the case, because of Pauli's exclusion principle. The exclusion principle says that no two electrons can occupy the same state. A state is completely characterized by the four numbers n, l, ml, and ms, where ms is the spin of the electron.

An important question is, How many states are possible for a given set of quantum numbers? For instance, n=1 means that l=0 with ml=0 are the only possible values for those variables. Thus, there are two possible states: (1, 0, 0, 1/2) and (1, 0, 0, −1/2). How many states are possible for n=2?

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Answer #1

Quantum states for n=2

l......ml
0 , 0................................1
1 , -1, 0, +1................................ 3

=2(1+4)

\boldsymbol{=2*2^{2}=8\: allowed\: states}

How many states are possible for a given set of quantum numbers:

\boldsymbol{=2*n^{2}}

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