Final answer:
The term symbol 3F corresponds to J values of 4, 3, and 2 for a total of 21 states distinguished by Mj. The term symbol G is hypothetical as it exceeds the defined terms. The term symbol 2P corresponds to J values of 3/2 and 1/2, totaling 6 states distinguished by Mj.
Step-by-step explanation:
For the term symbol 3F, the term 'F' indicates that the orbital angular momentum quantum number l is 3. The term '3' stands for the multiplicity, which is 2S+1 where S is the spin quantum number. In this case, the multiplicity is 3, so S=1. The possible values of J (total angular momentum quantum number) are given by J = L + S, L + S - 1, ..., |L - S| which yields J=4, 3, 2 for 3F.
Each J state can have 2J+1 projections quantum numbers Mj. Therefore, for J=4 there are 9 states, for J=3 there are 7 states, and for J=2 there are 5 states, giving us a total of 21 states within a 3F term.
For the term symbol G, if we follow the same quantum number descriptions as for the other levels, we'd expect it to refer to l = 4. However, this is a hypothetical term and does not arise naturally in atomic spectra because atomic term symbols are not defined beyond 'f' (l = 3).
For the term symbol 2P, the 'P' indicates that l = 1, and the multiplicity is 2 implying S=1/2. The possible values of J are J=3/2 and J=1/2. For J=3/2, there are 4 Mj states, and for J=1/2, there are 2 Mj states, for a total of 6 states in the 2P level.