The maximum number of electrons that can have principal quantum...

When $n=3, l=0,1,2$ i.e., there are $3 s, 3 p$ and $3 d$ orbitals. If all these orbitals are completely occupied as
$\text{ Total }$18 $\text{ electrons, }$9 $\text{ electrons with }$s=+$\frac{1}{2} \text{ and }$9 $\text{ with }$s=-$\frac{1}{2} .$Alternatively In any $n$th orbit, there can be a maximum of $2 n^2$ electrons. Hence, when $n=3$, number of maximum electrons $=18$. Out of these 18 electrons, 9 can have spin $-\frac{1}{2}$ and remaining nine with spin $=+\frac{1}{2}$.