(a)
The number of orbitals in an orbit (or shell) $= n^{2}$
where, $n =$no. of orbit or shell
Given, $n = 4$
∴ No. of orbitals in the 4th shell =$(4)^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 16$