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

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

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

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

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

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

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

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

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

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

Answer 1

we know that

for a given value of n (principal quantum number) there exist 0 to n-1 values of l (azimutal quantum number) and

for a given value of l there exist 2l+1 values of m (magnetic quantum number) which are from -l to +l including 0.

basing on the above rules the possible orientations are

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

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

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

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

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

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