# What is a quantum number set for Arsenic?

Dec 31, 2017

From the Pauli Exclusion Principle, arsenic can have up to $33$ simultaneous sets of quantum numbers, and it's up to you which one you point your finger to... Which of the $33$ electrons?

Well, I don't know, let's say we pick a $4 s$ electron for no reason other than it's there. Then for that electron...

• It must be on the energy level given by $n = 4$.
• $s$ orbitals, spherically shaped, have zero angular momentum, so $l = 0$.
• There can only be one $4 s$ orbital in existence. For $l = 0$, ${m}_{l}$ is limited in range to only the set $\left\{0\right\}$. Each value of ${m}_{l}$ corresponds to one orbital, and so there is only one.
• Every electron can have either spin-up $1 / 2$ or spin-down $1 / 2$ for the value of ${m}_{s}$. Since this orbital is filled already, there is not just one choice.

Thus, one has two options for a $4 s$ electron.

$\left(n , l , {m}_{l} , {m}_{s}\right) = \left(4 , 0 , 0 , + \frac{1}{2}\right)$

$\left(n , l , {m}_{l} , {m}_{s}\right) = \left(4 , 0 , 0 , - \frac{1}{2}\right)$

Maybe you can brainstorm the other $31$ on your own time.