# GRE GR 1777, Problem 012 Solution

Physics GRE GR 1777

1. Quantum Mechanics (Quantum number)

The magnetic quantum number $m_{l}$ can be determined as

$m_l = -l, -(l+1), .., -1, 0, 1, .., +(l-1), +l$

Thus, the number of allowed values of $m_l$ is

$N_{m_{l}} = (2l + 1)$.

Therefore, when $l = 2$, the number of allowed values of $m_l$ is 5.