Question

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

Answer 1

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:

When electrons added to an atom, they follow three rules:

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