# How many electrons can have n = 3, l = 2, m_l = 2, m_s = -1/2?

Mar 18, 2016

Only one electron in a given atom can have the set of quantum numbers given in the question.

#### Explanation:

No two electrons in an atom can have the same set of quantum numbers.

The first quantum number is the principle quantum number , which is $n = 3$. This means the electron is in the third energy level (shell).

The second quantum number, the angular momentum , is $l = 2$, and means the electron is in the $\text{d}$ sublevel (subshell).

The third quantum number, the magnetic quantum number , ${m}_{l} = 2$, represents one of the five $\text{3d}$ orbitals.

Lastly, we have the spin quantum number , ${m}_{s} = - \frac{1}{2}$. It indicates the direction of the spin of the electron.

Each electron in an atom has a unique set of quantum numbers.

The given quantum numbers for the electron in the question tell us that there is a high probability that the electron is in one of the $\text{3d}$ orbitals of the atom. 