Pauli Exclusion Principle
The Pauli Exclusion Principle states that no two identical fermions (particles with half-integer spin) can simultaneously occupy the same quantum state within a quantum system. This principle, formulated by Wolfgang Pauli in 1925, explains the structure of the periodic table and the stability of matter — electrons in an atom must each have a unique set of quantum numbers (n, l, m_l, m_s). It underlies the existence of distinct atomic orbitals, the hardness of solids, and the phenomenon of electron degeneracy pressure in white dwarf stars.
Quantum Numbers and Allowed States for Electrons in an Atom
| Quantum Number | Symbol | Allowed Values | Physical Meaning |
|---|---|---|---|
| Principal | n | 1, 2, 3, … | Energy level / shell |
| Azimuthal | l | 0 to n−1 | Orbital shape / subshell |
| Magnetic | m_l | −l to +l | Orbital orientation |
| Spin | m_s | +1/2 or −1/2 | Intrinsic angular momentum |
| Max electrons per orbital | — | 2 | One spin-up, one spin-down |
Interactive Tools
PhET Quantum Bound States
Interactive simulation for exploring quantum states and energy levels.
Open ToolKhan Academy — Pauli Exclusion Principle
Conceptual explanation with examples and practice problems.
Open ToolBrilliant.org — Quantum Numbers
Deep-dive article on quantum numbers and the exclusion principle.
Open Tool
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Related Terms
Quantum Superposition
Quantum superposition is the principle that a quantum system can exist in multiple distinct states simultaneously until a measurement is performed, at which point the wave function collapses to a single definite state. Mathematically, the state of a particle is described by a linear combination (superposition) of basis states, each with a complex amplitude whose squared modulus gives the probability of that outcome. The principle underpins interference phenomena, quantum computing (qubits), and famous thought experiments such as Schrödinger's cat.
Energy Level
An energy level is one of the discrete, quantized values of energy that a bound quantum system (such as an electron in an atom or a molecule) is permitted to have. Unlike classical systems where energy can take any continuous value, quantum mechanics constrains bound particles to specific allowed states, each characterized by a set of quantum numbers. Transitions between energy levels result in the absorption or emission of photons with energies exactly equal to the difference between the two levels, producing the characteristic spectral lines used in atomic spectroscopy.
Ground State
The ground state is the lowest possible energy state of a quantum mechanical system, such as an atom, molecule, or nucleus, in which all quantum numbers take their minimum allowed values consistent with the Pauli Exclusion Principle. A system in the ground state is thermodynamically stable and does not spontaneously emit radiation. The ground state energy of hydrogen is −13.6 eV, and the ground state represents the reference level from which excitation energies of higher states are measured.
Named after Austrian-Swiss physicist Wolfgang Pauli (1900–1958), who proposed the principle in 1925. The word "exclusion" derives from the Latin excludere, meaning "to shut out," reflecting that certain quantum states are forbidden to co-occupy.