Final answer:
The possible values of the magnetic quantum number m₁ for a 3d electron range from -2 to +2.
Step-by-step explanation:
The magnetic quantum number, m₁, specifies the relative spatial orientation of a particular orbital. Generally speaking, m₁ can be equal to -1, −(1 − 1), ..., 0, ..., (1 – 1), 1. The total number of possible orbitals with the same value of l (that is, in the same subshell) is 2l + 1. Thus, there is one s-orbital in an s subshell (l = 0), there are three p-orbitals in a p subshell (l = 1), five d-orbitals in a d subshell (l = 2), seven f-orbitals in an f subshell (l = 3), and so forth.