Final answer:
In the n = 3 shell, an electron can occupy the 3s, 3p, or 3d subshell. The exact subshell depends on the azimuthal quantum number l, which can be 0, 1, or 2, corresponding to the s, p, and d subshells, respectively.
Step-by-step explanation:
If an electron is in the n = 3 shell, the possible subshells it can occupy are the 3s, 3p, and 3d subshells. These are based on the azimuthal quantum number (l), which can be 0, 1, or 2 for the n = 3 shell. Each value of l corresponds to a different subshell designator, where 0 represents an s subshell, 1 represents a p subshell, and 2 represents a d subshell.
For (a) n = 3, l = 1; the electron is in the 3p subshell. For (b) n = 5, l = 3; the subshell is 5f, and for (c) n = 2, l = 0; the subshell is 2s. The Pauli exclusion principle dictates that no two electrons can have the same four quantum numbers within an atom, meaning electrons must fill available subshells in an order that adheres to these rules. The quantum number l is also known as a shell's azimuthal quantum number, and helps determine the shape of an orbital and therefore the subshell in which an electron resides.