How do you write the four quantum numbers of an element?

Jul 3, 2017

$n$: the principal quantum number relates to the size of the orbital
$l$: the angular quantum number relates the shape of the orbital and ranges from $0$ to $n - 1$
${m}_{l}$: the magnetic quantum number relates the spatial orientation of the orbital and ranges from $\left[- l , l\right]$
${m}_{s}$: the magnetic spin quantum number relates the spin of the electron per orbital

For instance, let's take a look at carbon's electron configuration:
$C : \left[H e\right] 2 {s}^{2} 2 {p}^{2}$

It would contain 2 core electrons, 4 valence electrons, 2 unpaired electrons and three orbitals:
$n$: $1 , 2$
$l$: $0 , 1$
${m}_{l}$: $\left[- 1 , 1\right]$
${m}_{s}$: $\frac{1}{2} , - \frac{1}{2}$ the only two it may possess, ever

In more detail, the $1 s ,$ and $2 s$ orbitals are full of two electrons each, each a sphere in increasing size proportional to $n$. The $2 p$ orbital has two unpaired electrons in accordance with Hund's rule, and three spatial orientations. It'd look something like this