What principle states that no two electrons can have the same set of four quantum numbers?

The Pauli exclusion principle states that no two electrons can have the same set of four quantum numbers.

Those four numbers describe an electron’s state: the principal quantum number, azimuthal quantum number, magnetic quantum number, and spin quantum number. In a single orbital, two electrons may share the first three values, but they must have opposite spins. This is why an orbital can hold no more than two electrons.

Wolfgang Pauli formulated the principle in 1925 to explain patterns in atomic spectra and electron arrangements. It is not simply a rule about electrons occupying different physical locations; it reflects the quantum behavior of identical fermions, whose combined wavefunction is antisymmetric when particles are exchanged.

The principle helps explain the structure of the periodic table, chemical bonding, and the stability of ordinary matter. A frequent confusion is with Hund’s rule, which describes how electrons fill equal-energy orbitals, or the Aufbau principle, which describes filling from lower to higher energy. The Pauli rule is broader: it applies to all identical half-integer-spin particles, including protons, neutrons, and quarks.