Question

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

Answer 1

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 `"d"` sublevel (subshell).

The third quantum number, the magnetic quantum number , `m_l=2`, represents one of the five `"3d"` orbitals.

Lastly, we have the spin quantum number , `m_s=-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 `"3d"` orbitals of the atom.

![http://www.meta-synthesis.com/webbook/34_qn/qn_to_pt.html]()

Resources:
http://www.meta-synthesis.com/webbook/34_qn/qn_to_pt.html
http://chemwiki.ucdavis.edu/Core/Physical_Chemistry/Quantum_Mechanics/10%3A_Multi-electron_Atoms/Quantify_Numbers