# Atomic number $Z$

If electrons were spin-$\frac {3}{2}$ instead of spin-$\frac {1}{2}$ ,

what would be the atomic number $Z$ for the first noble gas ?

The spin multiplicity will be $2S+1=4$. This means that the first atomic orbital can hold $4$ electrons with four different quantum numbers.
So, the atomic number for the first noble gas is $4$.