Question

In an atom, the total number of electrons having quantum number
$n=4,|m_l|=1and{m}_s=-\frac{1}{2}is$ ___

Answer 1

This problem is based on concept of quantum number, follow the following steps to solve this problem.
Write all possible orbitals having combination of same principal, azimuthal, magnetic and spin quantum number.
Then count the all possible electrons having given set of quantum numbers.
For n = 4, the total number of possible orbitals are

According to question $|m_l|=1$, i.e. there are two possible values of $m_l$, i.e. + 1 and - 1 and one orbital can contain maximum two electrons one having $s=+\frac{1}{2}$ and other having $s=-\frac{1}{2}$
So, total number of orbitals having $\{|m_l|=1\}=6$
Total number of electrons having $\{|m_l|=1and{m}_s=-\frac{1}{2}\}=6$