Quantum Numbers

[605357751]

I have difficulty understanding the rules of quantum numbers, can someone explain why some combinations are allowed and others are not.

State if the following combinations of quantum numbers are allowed or not in a one-electron
atom. For those that are disallowed state briefly why not.
a) n = 4, l = 3, ml = -4, ms = 0
b) n = 3, l = 3, ml = 1, ms = -1/2
c) n = 5, l = 2, ml = -3, ms = +1/2

[AndreiRekesh1I]

IIRC l must be at most one fewer than n in all cases, and the absolute value of ml must be at most equal to l.

[zachary_nhem_4I]

There are some energy levels that don't have certain orbitals. For example, for part b, the f block (l=3) exists within the 6th energy level (n=6), as a result, n = 3, l = 3, ml = 1, ms = -1/2 does not exist.

[Julie Park 1G]

ms (spin quantum number) describes the magnitude and direction that an electrons spins
ms only has two possible values: +1/2 and -1/2

therefore, there is no such thing as ms = 0

[Kennedi2J]

There was also a question: How many electrons can have the following quantum numbers in an atom?
a) n=5, l=3, ml= -1 and the answer was 2 electrons
Can anyone explain why the answer is 2 electrons and not 14 since l corresponds to f orbital and f orbital can hold 14 electrons?