For the principal quantum number n = 3, we have three possible values for the angular momentum quantum number l: l = 0, 1, and 2. For each value of l, there are 2l + 1 possible values for the magnetic quantum number ml: -l, -l+1, ..., 0, ..., l-1, l. Therefore, the maximum number of electrons that can occupy the n = 3 energy level is:

n = 3, l = 0 (s orbital): 2(0) + 1 = 1 electron

n = 3, l = 1 (p orbital): 2(1) + 1 = 3 electrons

n = 3, l = 2 (d orbital): 2(2) + 1 = 5 electrons

In total, the n = 3 energy level can accommodate a maximum of 1 + 3 + 5 = 9 electrons.