# What values of l are permitted for an electron with n = 3?

Dec 31, 2016

$l = 0 , 1 , 2$. See below.

#### Explanation:

There are four quantum numbers: the principle quantum number, $n$, the angular momentum quantum number, $l$, the magnetic quantum number, ${m}_{l}$, and the electron spin quantum number, ${m}_{s}$. For this question we are concerned only with the first two.

The principle quantum number, $n$, describes the energy and distance from the nucleus, and represents the shell.

For example, the $3 d$ subshell is in the $n = 3$ shell, the $2 s$ subshell is in the $n = 2$ shell, etc.

The angular momentum quantum number, $l$, describes the shape of the subshell and its orbitals, where $l = 0 , 1 , 2 , 3. . .$ corresponds to $s , p , d ,$ and $f$ subshells (containing $s , p , d , f$ orbitals), respectively. Each shell has up to $n - 1$ types of subshells/orbitals.

Therefore, the $n = 3$ shell has subshells of $l = 0 , 1 , 2$, which means the $n = 3$ shell contains $s$, $p$, and $d$ subshells (each containing their respective orbitals).