Final answer:
The 4f sublevel has 7 orbitals in the n = 4 shell of an atom.
Step-by-step explanation:
For n = 4, l can have values of 0, 1, 2, and 3. Thus, s, p, d, and f subshells are found in the n = 4 shell of an atom. For l = 0 (the s subshell), ml can only be 0. Thus, there is only one 4s orbital. For l = 1 (p-type orbitals), ml can have values of -1, 0, +1, so we find three 4p orbitals. For l = 2 (d-type orbitals), ml can have values of -2, -1, 0, +1, +2, so we have five 4d orbitals. When l = 3 (f-type orbitals), ml can have values of -3, -2, -1, 0, +1, +2, +3, and we can have seven 4f orbitals. Thus, we find a total of 16 orbitals in the n = 4 shell of an atom.