Question
How many electrons in an atom may have the following quantum numbers?
$\text{n}=4,\text{m}_{\text{s}}=-\frac{1}{2}$

Answer

The total number of electrons in $n$ is given by $2 \mathrm{n}^2$
$n=4$, Number of electrons $=2 \times 4^2=32$
Half of 32 electrons will have spin quantum number $\mathrm{m}_{\mathrm{s}}=-\frac{1}{2}$ i.e. 16 electrons

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