Question

Which of the following set of quantum numbers (ordered n, ℓ, mℓ, ms) are possible for an electron in an atom? -4, 3, 1, 1/2 4, 2, 3, -1/2 2, 1, -2, 1/2 2, 1, 0, -1 3, 4, 0, 1/2 5, 3, 0, 1/2 5, 3, -3, 1/2 2, 1, 0, 1/2

Answer 1

The answer to your question is determined by using the definitions of the 4 quantum numbers.
n = 1, 2, 3, ..., n
l = 0 to n − 1. This includes all possible values up to n-1.
m_l = all values from -l to +l. Example if l = 2 them m_l = -2, -1, 0, +1, +2
m_s = +1/2 and -1/2

-4, 3, 1, 1/2 - not possible because n cannot be negative.

4, 2, 3, -1/2 - not possible because m_l must be from -2 to +2 by definition.

2, 1, -2, 1/2 - not possible because m_l must be from -1 to +1 by definition.

2, 1, 0, -1 - not possible because m_s can equal only +1/2 and -1/2.

3, 4, 0, 1/2 - not possible beacuse l cannot be greater than n.

5, 3, 0, 1/2 - This is possible according to all of the definitions.

5, 3, -3, 1/2 - This is possible according to all of the definitions.

2, 1, 0, 1/2 - This is possible according to all of the definitions.