# How do I know how to assign quantum numbers to electrons?

Mar 31, 2014

The main rule is, no two electrons in the same atom can have the same values for all four of their quantum numbers.

The four quantum numbers are:

1. The principal quantum number n. n = 1, 2, 3, 4…

2. The angular quantum number l. l = 0, 1, 2 … (n-1). Each combination of n and l corresponds to an energy subshell.

3. The magnetic quantum number m. m = –l, -l +1… 0… l-1, l.

4. The spin quantum number s. s = ±½.

The relationship between the quantum numbers is: 1. They take the lowest available value of n.
2. All orbitals in a subshell must have one electron before they get a second electron. All electrons in singly occupied orbitals have the same spin.
3. No two electrons can have the same values for all four of their quantum numbers.

EXAMPLE:

What are the allowed sets of quantum numbers for Na (Z = 11)?

Solution:

In the order n, l, m, and s, the allowed quantum numbers are

1, 0, 0, ½
1, 0, 0,-½

2, 0, 0, ½
2, 0, 0, -½

2, 1, -1, ½
2, 1, 0, ½
2, 1, 1, ½
2, 1, -1, -½
2, 1, 0, -½
2, 1, 1, -½

3, 0, 0, ½