# How many electrons have #n = 3#, #l = 2#?

##### 1 Answer

#### Explanation:

As you know, quantum numbers are used to describe the location and spin of an electron in an atom.

A total of **four** quantum numbers are used for this purpose, three describing the **location** of the electron and one describing its **spin**.

Now, you are given the values of two quantum numbers, the *principal quantum number*, *angular momentum quantum number*,

The principal quantum number tells you the **energy level** on which the electrons reside. In your case, *third energy level*.

The angular momentum quantum number tells you the **subshell** in which you can find these electrons. The possible values of

#l=0 -># the s-subshell#l=1 -># the p-subshell#l=2 -># the d-subshell

This means that your electrons are located in the **d-subshell**, more specifically, in the **3d-subshell**.

Now, to determine how many electrons can share these two quantum numbers, identify how many *orbitals* you have in the **d-subshell**.

This value is given by the *magnetic quantum number*,

#m_l = { -2; -1; color(white)(-)0; color(white)(-)1; color(white)(-)2}#

So, if the d-subshell can hold a maximum of **five orbitals**, and you know that **each** orbital can hold a maximum of **two electrons**, it follows that a total of

#"no. of electrons" = 2 xx 5 = "10 e"^(-)#

can share the two quantum numbers