For a given angular momentum quantum number L, which range correctly describes the magnetic quantum number mL?

• A. 0 to l
• B. -l to +l
• C. -l to l-1
• D. -l to +l-2

Answer: (B)

The magnetic quantum number m_L describes the projection of orbital angular momentum along the z-axis and must take integer steps within a range set by the orbital quantum number l. For a given l, the possible values of m_L are all integers from −l to +l, inclusive. This gives 2l+1 distinct projections, meaning there are 2l+1 possible orientations of the angular momentum about the z-axis. For example, if l = 1, m_L can be −1, 0, or +1; if l = 2, m_L can be −2, −1, 0, +1, or +2. The other ranges omit either negative values or the extreme positive value, which would violate the quantization and symmetry of the angular momentum projection.