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

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

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

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

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

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

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

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

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

Explanation / Answer

The value of l is from 0, 1,2,......(n-1)

The values of ml are from -l , ...0,.....+l

The values of ms are -(1/2) & +(1/2)

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

n = 1, l = 0, ml = 0, ms = +1/2     (permissable)

n = 6, l = 5, ml = +3, ms = +1     (not permissable) Since the value of ms not equal to +1

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

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

n = 5, l = 5, ml = +4, ms = -1/2    (not permissable) Since the value of ml not equal to n

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

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

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

n = 5, l = 3, ml = +4, ms = +1/2 ( not permissable) since the value of ml is not more than l

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