What is the corresponding letter and orbital for L=3?

For a quantum number L=3, the corresponding letter representing the angular momentum quantum number is F. This is established by the convention in quantum mechanics, where each value of L corresponds to a specific type of subshell: L=0 (s), L=1 (p), L=2 (d), L=3 (f), and so forth. Therefore, for L=3, the correct designation is F.

The symmetry labels T2g, A2g, and T1g that follow this letter refer to the representations in crystal field theory, specifically for d-orbitals in transition metal complexes. These labels denote different symmetry properties of the orbitals when considering the ligand field around a transition metal ion, usually within octahedral or tetrahedral environments. Although these labels typically arise from d-orbitals, in this context, they accompany the F designation for completeness regarding the symmetry of electronic states.

While the other choices include various orbital designations and symmetry labels, they do not accurately represent the subshell associated with L=3, making them incorrect. The choice that contains F, along with additional symmetry information, appropriately identifies the correct representation for the given angular momentum quantum number.