Pauli Exclusion Principle

This entry was posted on by (updated on )
Pauli Exclusion Principle
The Pauli exclusion principle states that no two electrons in an atom can have identical quantum numbers.

The Pauli exclusion principle is an important concept in chemistry and in quantum mechanics in physics. The concept takes its name for Austrian physicist Wolfgang Pauli, who formulated the principle in 1925. Here is the definition of the Pauli exclusion principle and a simple explanation of what it means for electrons and other fermions.

The Pauli Exclusion Principle

The Pauli exclusion principle states that no two electrons or other fermions in an atom or molecule have the same electronic quantum numbers (n, l, ml, ms). Since electrons in an orbital share the same first three quantum numbers (the principle quantum number n, the momentum quantum number l, and the magnetic quantum number ml), it’s the electron spin quantum numbers ms that differ between electrons. Spin can take one of two values (½ or -½), so this limits the number of electrons in an orbital and means they have opposite or antiparallel spins:

  • Only 2 electrons can occupy a given electron orbital.
  • These two electrons have opposite or antiparallel spins.

While normally applied to electron behavior, the Pauli exclusion principle actually applies to all fermions. That is, it applies to all particles with half-integer spin, which includes electrons, quarks, neutrinos, particles consisting of three quarks (protons and neutrons), and some atoms (e.g., helium-3). In contrast, bosons are not bound by the Pauli exclusion principle because they are particles with integer spin.

If two or more atoms come together, the outer energy levels of the atoms shift so that the atoms remain different from each other. Further, only two electrons in a solid have the same energy as each other, with others having slightly different valence energy levels. So, the Pauli exclusion principle explains the concept of valence bands.

History

In the early 20th century, scientists realized atoms and molecules containing even numbers of electrons are more stable than those containing an odd number of electrons. Chemists and physicists, including Gilbert N. Lewis, Irving Langmuir, and Niels Bohr, outlined the concept of electron shells that contained an even or symmetrical number of electrons.

Drawing on this research, Austrian physicist Wolfgang Pauli outlined the Pauli exclusion principle. The original 1925 principle applied to electrons, but he expanded it into spin-statistics theorem in 1940 to describe the behavior of all fermions. His work earned him the 1945 Nobel Prize in Physics.

Pauli Exclusion Principle and Electron Configuration

When you write the electron configuration of an atom, you draw upon the Pauli exclusion principle, Madelung’s rule, and Aufbau principle. As an example, consider the electron configuration of beryllium, which is illustrated above using the Pauli exclusion principle. Beryllium has an atomic number of 4, so each atom has 4 protons and a neutral atom has 4 electrons. The first electron shell (1s) holds 2 electrons. The second shell (2s) holds 2 electrons. The electron configuration is 1s22s2. The two electrons in the 1s shell have antiparallel spins. Typically, this is drawn as an “up” arrow and a “down” arrow. Likewise, the two electrons in the 2s shell have antiparallel spins.

In atoms with more electrons, extending into the p, d, f subshells, the principle still applies. The p subshell holds a total of 6 electrons, in three sets of two electrons with antiparallel spins. Electrons have options in these subshells when they aren’t filled, but you never find two “up” or two “down” electrons in the same orbital.

References

  • Dyson, Freeman (1967). “Ground‐State Energy of a Finite System of Charged Particles”. J. Math. Phys. 8 (8): 1538–1545. doi:10.1063/1.1705389
  • Krane, Kenneth S. (1987). Introductory Nuclear Physics. Wiley. ISBN 978-0-471-80553-3.
  • Langmuir, Irving (1919). “The Arrangement of Electrons in Atoms and Molecules”. Journal of the American Chemical Society. 41 (6): 868–934. doi:10.1021/ja02227a002
  • Liboff, Richard L. (2002). Introductory Quantum Mechanics. Addison-Wesley. ISBN 0-8053-8714-5.
  • Massimi, Michela (2005). Pauli’s Exclusion Principle. Cambridge University Press. ISBN 0-521-83911-4.
  • NobelPrize.org (2022). “Exclusion Principle and Quantum Mechanics.” Wolfgang Pauli’s Nobel Lecture, December 13, 1946.