# Why are there four quantum numbers?

Jul 6, 2017

Evidently, precisely four are needed to describe the probable location of an electron in an atom. To be sure, nature made it so.

#### Explanation:

$n$: the principal quantum number merely relates the size of the orbital
$l$: the angular quantum number relates the shape of the orbital
${m}_{l}$: the magnetic quantum number relates the spatial orientation of orbital
${m}_{s}$: the spin magnetic quantum number relates the direction of rotation of an electron

For instance, an electron with the quantum numbers:
$3 {p}_{x} , - \frac{1}{2}$

is located in the third shell, the ${p}_{x}$ subshell of said shell, and is spinning down.

What more could we need to know about the electron?