# What is the total number of f orbitals in an f subshell?

Jan 2, 2016

There are seven $f$ orbitals in an $f$ subshell.

#### Explanation:

The orbitals come from the quantum numbers needed to solve the Schrödinger equation.

The principal quantum number $n$, determines the energy of the orbital. Allowed values are n = 1, 2, 3, 4, …

The azimuthal quantum number $l$, determines the shape of the orbital. Allowed values are integers from $0 \text{ to } n$.

$l = 3$ corresponds to an $f$ orbital.

The magnetic quantum number ${m}_{l}$, determines how many orbitals there are in the subshell. Allowed values are integers from –l " to " +l.

If $l = 3$, the allowed values of ${m}_{l}$ are $\text{-3, -2, -1, 0, 1, 2, 3}$.

So there are seven $f$ orbitals in a subshell.

Four of the $4 f$ orbitals look like eight-leafed clovers, and three look like $p$ orbitals with two doughnuts around their middle.