Which statement about the magnetic quantum number mL is true?

• A. -L-1 to +L+1 inclusive
• B. -L to +L inclusive
• C. 0 to L
• D. -L to L-1

Answer: (B)

The magnetic quantum number mL represents how the orbital angular momentum projects along the z-axis. For a given angular momentum quantum number L, there are 2L+1 possible projections, so mL can take values from -L to +L in steps of 1. This means the allowed values are -L, -L+1, ..., 0, ..., L-1, L. So the statement that mL ranges from -L to +L inclusive is the correct description. For example, with L = 2 (a d orbital), mL can be -2, -1, 0, 1, 2. The other ranges either omit negative values, omit the highest positive value, or extend beyond the allowed endpoints, which is why they’re incorrect.