# Why are there 2n^2 vacancies

1. May 5, 2010

### motoroller

Having a mental block, I should know the answer but can't remember!

Why are there 2n^2 vacancies for each value of n in an atom?

The factor of two is due to degeneracy in s, and one factor of n comes from angular orbitals, 0<=L<=(n-1), which gives n states (2L+1=n), but where does the second factor of n come from?

2. May 5, 2010

### alxm

Magnetic quantum number: $$-l \leq m_l \leq +l$$