Question

Which of the following quantum number combinations is not allowed in a ground-state atom? (7, 4, -2, -½) (3, 0, 0, +½) (2, 1, 1, -½) (3, 2, 3, +½)

Answer 1

The last combination (3,2,3,+1/2) is not allowed.

The quantum numbers are (n, l, ml, s)

l, the second quantum number, may take values from 0 to n - 1; so:

n = 3 => l may be 0, 1, or 2 => the first and second quantum numbers are a valid combination.

The third quantum number, ml goes from - l to +l, so, given that l is lower than 3, ml cannot be 3. That is why this is not a valid combination.