What principle states that no two fermions can have identical sets of quantum numbers?

The principle stating that no two identical fermions can have identical sets of quantum numbers is the Pauli exclusion principle. It explains why electrons in an atom must occupy different quantum states.

Wolfgang Pauli formulated the principle in 1925 while investigating atomic spectra and electron arrangements. An electron is described by four quantum numbers: principal level, orbital shape, orbital orientation, and spin. Two electrons may share an orbital only if their spin quantum numbers differ, so no pair can match in all four values.

The rule applies to all identical fermions, not only electrons. Fermions have half-integer spin and include protons, neutrons, quarks, and electrons. Its deeper foundation is the antisymmetry of the wavefunction under exchange of identical fermions, connected to the spin-statistics theorem. Bosons, such as photons and helium-4 atoms, can share a quantum state. Hund’s rule concerns how electrons fill equal-energy orbitals, while the Aufbau principle describes the order in which orbitals are filled.