Which of the following are permissable sets of quantum numbers for an electron i

Question

Which of the following are permissable sets of quantum numbers for an electron in a hydrogen atom? The atom may be in an excited state (ie. the electron need not be in its ground state). Choose all of the correct possibilities.

n = 3, l = 1, ml = 0, ms = +1/2

n = 5, l = -4, ml = +3, ms = +1/2

n = 5, l = 5, ml = +4, ms = -1/2

n = 4, l = 0, ml = 0, ms = +1/2

n = 4, l = 2, ml = -1, ms = +1/2

n = 5, l = 3, ml = +4, ms = +1/2

n = 1, l = 0, ml = 0, ms = +1/2

n = 5, l = 1, ml = -1, ms = +1/2

n = 6, l = 5, ml = +3, ms = +1

n = 4, l = 3, ml = +2, ms = -1/2

Explanation / Answer

Hydrogen - one electron

First Electron

n = 1
= 0
m = 0

starts at zero and goes to n-1, which is zero since we get 1-1 = 0, when using n = 1. When = 0, there is only one possible choice for m, which must be zero.

s = +1/2

s can be +1/2 or -1/2 as it is first electron s = -1/2

This completes the four quantum numbers for the single electron possessed by hydrogen

hence

n = 1 l =0 ml = 0 ms = +1/2

is the only possible quantum number

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