## How many electrons can have \(n=3, l=2, m_{l}=2, m_{s}=-\frac{1}{2} ?\)

Answer:

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 ,\(m_{s}=-\frac{1}{2}\) 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 3d orbitals of the atom.