What quantum principle forbids two electrons in an atom from having identical quantum states?

The quantum principle that forbids two electrons in an atom from having identical quantum states is the Pauli exclusion principle.

Formulated by Austrian physicist Wolfgang Pauli in 1925, the principle applies to electrons because they are fermions, particles with half-integer spin. In an atom, no two electrons can share the same values for all four quantum numbers: principal energy level, orbital type, orbital orientation, and spin. This rule forces electrons to occupy shells and subshells in an organised structure.

Two electrons can occupy the same orbital, but only if they have opposite spins. This is why helium can have two electrons in its 1s orbital without violating the principle: their spin quantum numbers differ. The rule helps explain the periodic table, chemical bonding, and the stability and volume of ordinary matter.

The Pauli principle is often confused with Hund's rule or the Aufbau principle. Hund's rule describes how electrons fill equal-energy orbitals, while Aufbau describes the order in which orbitals are generally filled. The deeper mathematical basis is the antisymmetry of the wavefunction for identical fermions.