The spin quantum number has two possible values, +1/2 and -1/2, which indicate the two fundamental spin states of an electron in an orbital. What are these values?

• A. +1/2 and -1/2
• B. +1 and -1
• C. 0 and 1
• D. +1/2 and 0

Answer: (A)

Spin is a two-state intrinsic property of the electron, and when you measure its spin along any chosen axis, you can only get two results. For an electron, the projection of spin along that axis comes in units of ħ/2, giving ms equal to +1/2 or -1/2. These are the familiar “spin up” and “spin down” states. The reason is that the electron has spin s = 1/2, so its spin projection is quantized with two possible values. While the total spin magnitude is sqrt(3)/2 ħ, the observable projection along the measurement axis is ±ħ/2, i.e., +1/2 or -1/2. This two-state nature also explains why an orbital can hold two electrons with opposite spins, in line with the Pauli exclusion principle.