What values of the orbital quantum number, or angular momentum (l) and magnetic (ml) quantum numbers are allowed for a principle quantum number (n) of 3? How many
orbitals are allowed for n = 3?

When n = 3 , l = 0 ≤ ℓ ≤ n − 1 that is 0,1,2

l = 0 , m =0,                                       1(s orbital)

l =1, ml = -1,0,+1                                3 (px,py,pz orbitals)

l = 2 , ml = -2,-1,0,+1,+2                     5 (dxy,dyz,dzx,dx2,dx2-y2)

There is 1 orbital for l = 0, 3 orbitals for l = 1, 5 orbitals for l = 2.

So, 1 + 3 + 5 = 9 orbitals are allowed for n = 3