# Question #32169

Apr 15, 2016

Quantum numbers are unique combinations of information for a particular electron that we can use to explain its behaviour.

#### Explanation:

Quantum numbers are like a unique identity for each electron in an atom. They also explain a lot about why electrons do what they do, like pairing up with others. There are four numbers:

$n$ is the distance of the electron orbital from the nucleus, and can be any positive integer, like $1 , 2 , 3 , 4. . .$. This is the same as the energy level of the electrons, which increases further from the nucleus.

$l$ is the shape of the orbital, and is described by numbers from $0$ to $n - 1$. For example, if $n = 3$, then $l$ can be anywhere in $0 , 1 , 2$. Shapes are often referred to by letters like $s , p , d , f$ rather than by their $l$ value.

${m}_{l}$ is the orientation of the orbital along axes in space like $x , y , z$. Similar shapes can be angled in different ways, which is why you have ${p}_{x} , {p}_{y} , {p}_{z}$ orbitals inside the $p$ subshell. Each orbital projects outwards from the nucleus in a different direction, described by ${m}_{l}$, which ranges from $- l$ to $l$. For example, if $l = 2$, then ${m}_{l}$ could be $- 2 , - 1 , 0 , 1 , 2$.

${m}_{s}$ is the spin of the electrons in an orbital. Spin is a misleading name because it isn't really spinning at all, but it's more of an internal characteristic of the electrons. It can either be $- \frac{1}{2}$ or $+ \frac{1}{2}$.

Fermi exclusion principle states that no two electrons may have the same combination of quantum numbers. Two electrons in an orbital automatically have the same distance, shape and orientation of orbitals, and so they must have opposite spins - this is how electrons form pairs. One spins one way, one spins the other.

Quantum numbers can be used for other applications too, and explain much about behaviour. Put simply, though, they are unique sets of numbers that describe an electron and set it apart from all the others.