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