# What do quantum numbers describe?

Mar 12, 2018

The energy level, shape of orbital, orientation of the orbital and the spin of an electron, for a given electron.

#### Explanation:

The quantum numbers are represented as: $\left(n , l , {m}_{l} , {m}_{s}\right)$

$n$ represents the energy level of the electron, where $n = 1 , 2 , 3 , 4 , \ldots$. $n$ also indicates the row on the periodic table.

$l$ determines what orbital shape it is, where $l = 0 , 1 , 2 , \ldots \left(n - 1\right)$.
$l = 0 \implies \textrm{s - \mathmr{and} b i t a l}$
$l = 1 \implies \textrm{p - \mathmr{and} b i t a l}$
$l = 2 \implies \textrm{d - \mathmr{and} b i t a l}$
$l = 3 \implies \textrm{f - \mathmr{and} b i t a l}$

${m}_{l}$ determines the orientation of the orbital, where $- l \le {m}_{l} \le l$. This shows that an s-orbital has 1 orientation, a p-orbital has 3 orientations, d-orbital has 5 orientations, and an f-orbital has 7 orientations.

${m}_{s}$ is the spin of the electron which can only be $- \frac{1}{2}$ or $+ \frac{1}{2}$
It tells whether a electron is spin-up or spin-down.

The video below explains how quantum numbers describe the position of an electron. The video also discusses how to determine the quantum numbers for four different electrons (#1, 6, 29).

Video from: Noel Pauller

Hope this helps!