# Question #2c112

Nov 3, 2017

One.

#### Explanation:

The trick here is to remember that a complete set of quantum numbers can only describe a single electron in a given atom.

In other words, every time you have values for all the four quantum numbers that we use to describe the location and spin of an electron in an atom, you can say that the set can describe a single electron, not more.

In this case, you have

$n = 4 , l = 2 , {m}_{l} = - 2 , {m}_{s} = + \frac{1}{2}$

This set tells you that the electron is located on the fourth energy level, hence why $n = 4$, in the $d$ subshell, hence why $l = 2$, in one of the five $4 d$ orbitals, let's say $4 {d}_{x y}$, hence why ${m}_{l} = - 2$, and has spin-up, hence why ${m}_{s} = + \frac{1}{2}$.

This is the only electron that can have these particular values for the four quantum numbers in the given atom.