# Question #03b61

Jan 12, 2017

Here's why that is the case.

#### Explanation:

As you know, we can use a total of four quantum numbers, which make up a quantum number set, to describe the location and spin of an electron in an atom. The notation used for a quantum number set is

$\left(n , l , {m}_{l} , {m}_{s}\right)$

The quantum number set given to you cannot describe an electron in an atom because the value of the angular momentum quantum number, $l$, which gives you the subshell in which the electron resides, is too high.

As you can see, the angular momentum quantum number can take values in the range

$l = \left\{0 , 1 , 2 , \ldots , n - 1\right\}$

where $n$, which is the principal quantum number, tells you the energy level on which the electron resides.

$\left(\textcolor{red}{n} , \textcolor{b l u e}{l} , {m}_{l} , {m}_{s}\right) = \left(\textcolor{red}{2} , \textcolor{b l u e}{2} , - 1 , - \frac{1}{2}\right)$
Since $\textcolor{red}{n = 2}$, it follows that $\textcolor{b l u e}{l}$ can only take two possible values
$n = 2 \implies l = \left\{0 , 1\right\}$
Since you have $\textcolor{b l u e}{l = 2}$, the quantum number set given to you is not possible for an electron in an atom.