Which statement describes the allowed values of the spin quantum number mS?

• A. +1/2
• B. -1/2
• C. 0
• D. ±1/2

Answer: (D)

For an electron, the spin is a spin-1/2 system, so its spin projection along a chosen axis can only take two values: +1/2 or -1/2. This comes from the rule that mS runs from -s to +s in steps of 1, and with s = 1/2 you get exactly -1/2 and +1/2. Therefore the allowed values are the two orientations of the electron’s spin. The value 0 isn’t allowed for a single electron’s spin, though other situations (like orbital angular momentum or a system with total spin zero) can have zero projection in their own context.