# What are quantum numbers used to describe?

Dec 7, 2014

Quantum numbers are used to describe an atom's electron distributions. Particularly, they represent acceptable solutions to Schrodinger's wave equations for the Hydrogen atom (more here: http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation )

There are $4$ quantum numbers: $n$, $l$, ${m}_{l}$, and ${m}_{s}$.

The quantum number that indicates the orbital is $l$. This quantum number varies from $0$ to $n - 1$ and idicates the s, p ,d or f subshell:

$l$= $0$ -> s subshell;
$l$ = $1$ -> p subshell;
$l$ = $2$ -> d subshell;
and so on.

Think of quantum numbers as forming a map to a certain electron's location, each electron having a distinct set of quantum numbers to describe its position.
For example, $n$=$2$, $l$=$1$, ${m}_{l}$=$0$, and ${m}_{s}$=$+ \frac{1}{2}$ correspond to one electron located on the second energy level, in one of the three $p$-orbitals (the one corresponding to ${m}_{l}$=$0$), that has a positive spin. Therefore, that electron would be located in $2 {p}_{y}$ ( $2 {p}_{x}$ would correspond to ${m}_{l}$ = $- 1$ and $2 {p}_{z}$ to ${m}_{l}$=$+ 1$ ) and have a positive spin.