Final answer:
The two possible values for the electron spin projection quantum number, m₂, are +1/2 and -1/2, corresponding to the two unique spin states of an electron, which are spin up and spin down.
Step-by-step explanation:
The electron spin projection quantum number, often represented as ms, has two possible values for an electron. These values correspond to the two possible spin states of an electron and are due to the quantum mechanical nature of subatomic particles. The two values for the electron spin projection quantum number are +1/2 and -1/2.
Electrons can exhibit a phenomenon that is similar to spinning on an axis, which we describe using quantum numbers. The spin up state corresponds to the quantum number +1/2, while the spin down state corresponds to -1/2. These two states are the only options for the ms quantum number, and they are fundamental to the Pauli exclusion principle, which states that no two electrons can have the same set of quantum numbers within an atom.