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

Answer: 6

$n=4$
$\ell =0,1,2,3$
$\left|m_{\ell }\right|=1$
$\Rightarrow \pm 1$
$m_s=-\frac{1}{2}$
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 $\left|m_{\ell }\right|=1\&m_5=-\frac{1}{2}$