Pauli exclusion principle

Lore & Background

In the early 20th century, it became evident that atoms with even numbers of electrons are more chemically stable. Lewis postulated that atoms tend to hold an even number of electrons in any given shell. Pauli sought an explanation for these empirical numbers while also trying to explain the Zeeman effect and ferromagnetism. Stoner, which showed that for a given principal quantum number, the number of energy levels of a single electron in an alkali metal spectrum in an external magnetic field equals the number of electrons in the closed shell of noble gases. This led Pauli to realize that the complicated electron numbers could be reduced to one electron per state if four quantum numbers were used, introducing a new two-valued quantum number later identified as electron spin by Samuel Goudsmit and George Uhlenbeck.

Reader's Guide

The Pauli exclusion principle is a cornerstone of quantum mechanics, explaining why matter is stable and why atoms exhibit their characteristic chemical properties. It dictates that fermions—particles with half-integer spin such as electrons, protons, neutrons, and quarks—cannot occupy identical quantum states. For electrons in atoms, this means no two electrons can share the same set of four quantum numbers (n, ℓ, mℓ, ms), forcing them into different orbitals or opposite spins. This principle accounts for the structure of the periodic table, the behavior of electrons in solids, and the stability of ordinary matter. Bosons, with integer spin, are not subject to this rule and can occupy the same state, as seen in lasers and Bose–Einstein condensates. The principle is rigorously justified by the requirement that the total wave function of fermions be antisymmetric under particle exchange, which mathematically forbids identical states. Without this principle, all electrons would collapse into the lowest energy state, making complex chemistry and life impossible.

Did You Know?

• Particles with integer spin (bosons) are not subject to the Pauli exclusion principle; any number of identical bosons can occupy the same quantum state.
• The principle explains why in a poly-electron atom, two electrons in the same orbital must have opposite spins (ms = +1/2 and -1/2).
• The rigorous justification is that the total wave function for fermions must be antisymmetric under exchange of two identical particles, which forces the wave function to zero if they are in the same state.