spin

Meaning: Spin is the electron's intrinsic angular momentum. It is a built-in property, not a literal rotation. It is the fourth quantum number, ms, and has two allowed values, often called spin up (+½) and spin down (−½). The Pauli exclusion principle says no two electrons in an atom can have the same set of four quantum numbers (n, l, ml, ms). So an orbital holds at most two electrons, and they must have opposite spins. Hund's rule says electrons occupy degenerate orbitals singly, with parallel spins, before they pair.

Equation: ms = +½ or −½, where ms is the spin quantum number (dimensionless).

On the MCAT: You draw orbital diagrams and count unpaired electrons. An atom or ion with one or more unpaired electrons is paramagnetic and is drawn into a magnetic field. One with every electron paired is diamagnetic and is weakly repelled. Fe³⁺ (five unpaired 3d electrons) is paramagnetic, and Zn²⁺ (full 3d subshell) is diamagnetic. Questions also ask you to spot an impossible set of quantum numbers, such as ms = 0 or ms = 1.

Common confusion: Students picture the electron as a tiny spinning ball. Up and down are only labels for the two allowed ms values. Paired electrons have opposite spins, so their magnetic effects cancel. That is why only unpaired electrons give paramagnetism.