# An electron has the following quantum number values: n = 3, l = 1, ml = 0. Which of the following notations represents the most likely location of this electron?

Apr 3, 2018

Here's what I got.

#### Explanation:

All you have to do here is to match the values of the three quantum numbers to an energy shell, an energy subshell, and an orbital.

This will give you a pretty good idea of where this electron is located inside an atom.

So, you know that the principal quantum number, $n$, tells you the energy shell in which the electron is located. In this case, you have

$n = 3$

which tells you that the electron is located in the third energy shell.

The angular momentum quantum number, $l$, tells you the energy subshell in which the electron is located. In other words, the angular momentum quantum number tells you the type of orbital that holds the electron.

In this case, you have

$l = 1$

which tells you that the electron is located in the $p$ subshell, i.e. the electron is located in a $p$ orbital.

The magnetic quantum number, ${m}_{l}$, tells you the orientation of the orbital in which the electron is located. In other words, the magnetic quantum number identifies the specific orbital which holds the electron.

An electron located in the $p$ subshell can reside in three $p$ orbitals because the magnetic quantum number can take three possible values.

$l = 1 \implies {m}_{l} = \left\{- 1 , 0 , + 1\right\}$

By convention, we take

${m}_{l} = 0$

to represent the ${p}_{z}$ orbital. This means that the incomplete quantum number set--don't forget that you're missing the value of the spin quantum number, ${m}_{s}$

$n = 3 , l = 1 , {m}_{l} = 0$

can be used to describe an electron located in the third energy shell, in the $3 p$ subshell, in the $3 {p}_{z}$ orbital. Depending on the value of the spin quantum number, this electron can have spin-up, for which ${m}_{s} = + \frac{1}{2}$, or spin-down, for which ${m}_{s} = - \frac{1}{2}$.