# What is a combination of four quantum numbers that could be assigned to an electron occupying a 5p orbital?

Nov 11, 2015

Here's what I got.

#### Explanation:

As you know, you need four quantum numbers to describe the exact location of an electron in a atom and its spin. The principal quantum number, $n$, describes the energy level on which the electron resides. In your case, an electron that can occupy a 5p-orbital will have its principal quantum number equal to $5$

$n = 5 \to$ the electron is located on the fifth energy level

The angular momentum quantum number, $l$, describes the subshell in which the energy can be found. For the fifth energy level, $l$ can take values in the range

$l = 0 , 1 , 2 , 3 , 4$

Now, as its name suggests, a 5p-orbital will be located in a p-subshell, which is characterized by $l = 1$.

$l = 1 \to$ the electron is located in the 5p-subshell

The magnetic quantum number, ${m}_{l}$, tells you the exact orbital in which the electron can be found. A p-subshell can have three orbitals, regardless of energy level.

This means that you have three possibilities here, since the exact orbital is not specified by the problem

${m}_{l} = \left\{- 1 , 0 , 1\right\} \to$ the electron can reside in any of the three 5p-orbitals

Finally, the spin quantum number, ${m}_{s}$, which describes the spin of the electron, can only have two possible values, $+ \frac{1}{2}$ for spin-up and $- \frac{1}{2}$ for spin-down.

This means that an electron residing in a 5p-orbital can have

${m}_{s} = \left\{+ \frac{1}{2} , - \frac{1}{2}\right\} \to$ either spin-up or spin-down

So, one set of quantum numbers that can describe an electron located in a 5p-orbital is

$n = 5 , l = 1 , {m}_{l} = - 1 , {m}_{s} = + \frac{1}{2}$

This electron is located on the fifth energy level, in the 5p-subshell, in the $5 {p}_{x}$ orbital, and has spin-up.

There are a total of six sets of quantum numbers that can be used here.