Question

How many electrons in an atom may have the following quantum numbers?
(a) $n=4,m_s=-1/2$
(b) $n=3,l=0$

Answer 1

(a) The fourth energy level contains $2n^2=2\times 4^3=32$ electrons. Out of these, one half or 16 electrons have $m_s=+\frac{1}{2}$.
The remaining half, i.e, 16 electrons have $m_s=-\frac{1}{2}$.
(b) 2 electrons are present n 3s orbital.