Question

In an atom, the total number of electrons having quantum numbers $n=4,\left|m_{l}\right|=1$ and $m_{S}=-1 / 2$ is

Answer 1

$n =4$
$\ell=0,1,2,3 $
$\left| m _{\ell}\right|=1$
$ \Rightarrow \pm 1$
$m _{ s }=-\frac{1}{2}$
For $\ell=0, m _{\ell}=0$
$\ell=1, m _{\ell}=-1,0,+1$
$\ell=2, m _{\ell}=-2,-1,0,+1,+2$
$\ell=3, m _{\ell}=-3,-2,-1,0,+1,+2,+3$
So, six electrons can have $\left| m _{\ell}\right|=1 \,\&\, m _{5}=-\frac{1}{2}$