# How many orbitals are in the 3d subshell?

Nov 6, 2015

Five.

#### Explanation:

The important thing to realize here is that there's nothing special about the 3d-subshell in terms of the number of orbitals it contains.

The d-subshell contains five orbitals regardless of the energy level on which the subshell is located - as long as $n \ge 3$.

Each subshell is characterized by a distinct value of the angular momentum quantum number, $l$. The number of orbitals each subshell can hold is determined by the magnetic quantum number, ${m}_{l}$.

The relationshop between the principal quantum number, $n$, the angular momentum quantum number, $l$, and the magnetic quantum number, ${m}_{l}$, can be described like this

$l = 0 , 1 , 2 , \ldots , n - 1$

and

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

Now, the d-subshell is described by $l = 2$. This mens that any d-subshell you'll ever run into will have a total of five d-orbitals described by

m_l = {-2; -1; 0; 1; 2}

Therefore, the 3d-subshell will contain a total of five 3d-orbitals.

Likewise, the 4d-subshell will contain a total of five 4d-orbitals, the 5d-subshell will contain a total of five 5d-orbitals, and so on.