Final answer:
For a 3 orbital, the principal quantum number (n) is 3. The allowed angular momentum quantum number (l) values for this orbital are 0, 1, and 2, which correspond to s, p, and d subshells, with the magnetic quantum number (m₁) values depending on the l value.
Step-by-step explanation:
The 3 orbital refers to an atomic orbital with a principal quantum number (n) of 3. For n = 3, the allowed values for the angular momentum quantum number (l) range from 0 to n - 1. Therefore, the allowed values for l would be 0, 1, and 2.
Each of these corresponds to a different type of subshell: l = 0 is an s orbital, l = 1 is a p orbital, and l = 2 is a d orbital. The magnetic quantum number (m₁) for each l value can range from -l to +l including zero. Consequently, for a 3d orbital, where l = 2, the possible m₁ values could be -2, -1, 0, +1, or +2.