How many orbitals are there in the n = 4 level of the h-atom?

The H-atom has fourth energy level with n=4.

This energy level can have values of orbital angular momentum l = 0, 1, 2, 3

Now each l can also have magnetic momentum ml from - l to l.

Therefore,

l = 0

ml = 0

l = 1

ml = - 1, 0, 1

l = 2

ml = - 2, - 1, 0, 1, 2

l = 3

ml = - 3, - 2, - 1, 0, 1, 2, 3

Now adding up all the number of ml’s will give us the total number of orbitals:

orbitals = 1 + 3 + 5 + 7

orbitals = 16

Alternatively, we can simply use the formula:

orbitals = n^2 = 4^2 = 16