# How many orbitals are found in a d subshell?

Dec 29, 2017

$5$.

#### Explanation:

The number of orbitals present in a given subshell is given by the number of values that the magnetic quantum number, ${m}_{l}$, can take.

In turn, the possible values that the magnetic quantum number can take depend on the identity of the angular momentum quantum number, $l$, which denotes the energy subshell in which an electron resides in an atom.

${m}_{l} = \left\{- l , - \left(l - 1\right) , \ldots , - 1 , 0 , + 1 , \ldots , + \left(l - 1\right) , + l\right\}$

Now, the $d$ subshell is described by

$l = 2$

This means that for a $d$ subshell , the magnetic quantum number can take $5$ possible values.

$l = 2 \implies {m}_{l} = \left\{- 2 , - 1 , 0 , + 1 , + 2\right\}$

You can thus say that the $d$ subshells, which can be found in an atom starting with the third energy level, contain five $d$ orbitals.