Pauli Formulates the Exclusion Principle Summary

  • Last updated on November 10, 2022

Wolfgang Pauli significantly advanced the understanding of the structure of the atom by establishing the principle that electrons are elementary particles of the “antisocial” type.

Summary of Event

Niels Bohr’s pioneering quantum model of the atom explained the spectral systems of the hydrogen atom. Logically, physicists, including Bohr, directed their efforts toward extending the theoretical success to more complex atoms. From chemical study, it was concluded that every chemical element corresponds to one type of atom, and all the elements display their chemical properties regularly in the periodic table, beginning with the lightest and simplest: the hydrogen atom. Therefore, one task of atomic physicists of the 1910’s and 1920’s was to explain the periodic table of elements—the orderly array and the increasing complexity of the atoms. Another task was to explain the phenomena of atomic spectra. Bohr’s quantum postulates were found inadequate for more complex atoms or for atoms in an external force field such as a magnetic field. Between about 1915 and 1925, European physicists searched intently for new principles and guidelines for the construction of atomic models that would consistently account for chemical phenomena: the periodic table, physical phenomena, and spectral data. [kw]Pauli Formulates the Exclusion Principle (Spring, 1925) [kw]Exclusion Principle, Pauli Formulates the (Spring, 1925) Atoms;structure Exclusion principle Electrons Pauli exclusion principle [g]Germany;Spring, 1925: Pauli Formulates the Exclusion Principle[06380] [c]Science and technology;Spring, 1925: Pauli Formulates the Exclusion Principle[06380] [c]Physics;Spring, 1925: Pauli Formulates the Exclusion Principle[06380] Pauli, Wolfgang Zeeman, Pieter Sommerfeld, Arnold Bohr, Niels Rydberg, Johannes Robert Landé, Alfred Stoner, Edmund C.

Wolfgang Pauli.

(The Nobel Foundation)

That these phenomena would come together to reveal the structure of the atom became increasingly clear for a number of scientists, although it also became clear that the phenomena would be difficult to solve. In this regard, Wolfgang Pauli stated that it was the famous Swedish spectroscopist Johannes Robert Rydberg who noticed that the lengths of the periods in the periodic table—2, 8, 18, 32, and so on—can be expressed simply as “two times n squared” if n takes on all integer values. Atomic physicists were fascinated by these integers and incorporated them into their atomic models.

When Pauli was beginning his serious study of atomic structure, Bohr had already published his explanation of the periodic table with the Aufbauprinzip, which included two important ideas: The state of an electron in an atom is specified by three quantum numbers (the principal, the angular, and the magnetic), and atomic electrons form “shells” that are filled up and closed with specific numbers of electrons. In a sense, the idea of electron shells and their closing anticipated the Pauli exclusion principle. Bohr was applying a basic axiom without much awareness about it. In doing so, among other things, he left a fundamental physical problem unanswered: why all electrons of an atom in its ground state are not bound in the innermost shell. (A physical principle believed to be universally true is that a stable physical system tends to stay in the state of minimum potential energy.) Bohr wrote in his paper, “Going from Neon to Sodium, we must expect that the eleventh electron goes into the third shell.” Pauli, however, was very conscious of the necessity of logic and evidence. He wrote in the margin of Bohr’s paper near the quoted passage: “How do you know this? You only get it from the very spectra you want to explain!” Pauli was on the verge of explaining the difficult spectral phenomena, especially the so-called anomalous Zeeman effect, Zeeman effect which was the magnetic splitting of the spectral lines discovered by Pieter Zeeman.

Alfred Landé had already succeeded in summarizing the spectroscopic data of the anomalous Zeeman effect into simple laws. His true innovation was the introduction of half integers as quantum numbers to explain the doublet spectra of the alkali metals. Although Pauli generalized Landé’s result to account for the so-called Paschen-Back effect Paschen-Back effect[Paschen Back effect] —a special case of the anomalous Zeeman effect discovered by Ernst Back Back, Ernst and Friedrich Paschen Paschen, Friedrich —Pauli was still very puzzled by the “problem of the closing of the electronic shells.”

In order to explain the doublet structure of the alkali spectra, Bohr and others hypothesized that the atomic core had an “angular momentum”—that is, it rotated. Now, after much hard thinking, Pauli realized that he had to eliminate this hypothesis and attribute a new quantum theoretic property to the electron. At that time, he called it a “two-valuedness not describable classically.” This would be the electron’s fourth degree of freedom, requiring a fourth quantum number to specify it. This question of the physical meaning of this “two-valuedness” was answered in 1925 by George Eugene Uhlenbeck Uhlenbeck, George Eugene and Samuel A. Goudsmit, Goudsmit, Samuel A. who realized the idea of the spin of the electron. According to them, the electron has an intrinsic angular momentum that can assume two values that are of the same magnitude but opposite directions.

In October, 1924, an English physicist, Edmund C. Stoner, published “The Distribution of Electrons Among Atomic Levels.” "Distribution of Electrons Among Atomic Levels, The" (Stoner)[Distribution of Electrons] Whenever Pauli talked about the history of the exclusion principle, he would state that it was Stoner’s paper that finally helped him to solve the problem of the closing of the electronic shells. Pauli particularly liked to quote an essential remark made by Stoner: “The number of energy levels of a single electron in the alkali metal spectra for a given value of the principle quantum number in an external magnetic field is the same as the number of electrons in the closed shells of the rare gases which corresponds to this principal quantum number.” In the periodic table, the alkali metals are neighbors of the rare gases. The former are chemically active, whereas the latter are completely inactive. Essentially, Stoner was solving this causal problem: The rare gases have their electron shells closed, whereas each of the alkalis has one electron in an otherwise empty shell; thus this electron is “chemically active.”

Finally showing true loyalty to physical phenomena, Pauli made a trip to Tubingen to use the spectroscopic data assembled there. He was obliged to verify some conclusions of the exclusion principle concerning the anomalous Zeeman effect of more complicated atoms. In the spring of 1925, Pauli published the exclusion principle, which can be formulated as follows: The state of every electron in an atom is specified by four quantum numbers; no two or more electrons in an atom can be at the same time in the same state—in other words, they can never assume simultaneously identical sets of the values of the four quantum numbers.

The formulation of the exclusion principle was made at the same time other fundamental principles of quantum mechanics were being established: Louis de Broglie’s paper was published in 1925, Werner Heisenberg’s in 1925, and Erwin Schrödinger’s in 1926. In pursuing the structure of the atom, like his mentor Arnold Sommerfeld, Pauli adhered to physical phenomena closely. De Broglie, Heisenberg, and Schrödinger were more fascinated by classic quantum correspondence in terms of mathematical formalism. It is an inexplicable historical irony that they became the true founders of quantum mechanics, Quantum mechanics whereas Pauli, then a “true” physicist, did not.


With the foundation of quantum mechanics laid, it was concluded that quantum mechanics implies a statistical (probabilistic or indeterministic) nature for microcosmic configurations and processes. Combining such understanding with the Pauli exclusion principle, Heisenberg, in 1926, pointed out that in comparison with classical physics, quantum mechanics leads to conclusions for particles of the same kind (for example, for electrons, protons, neutrons, or others) that are qualitatively different from conclusions for particles of different kinds (for example, mixed systems of electrons and other particles). In fact, to reflect the fundamental distinction, quantum mechanics needs an independent principle, which can be called the principle of absolute identity. Principle of absolute identity

In both classical and quantum physics, particles of the same kind are supposed to be physically indistinguishable, but classical and quantum physics differ in that the principle of absolute identity does not apply to the former. In classical physics, one can always assume that each of the particles of the same kind is given a (nonphysical) sign—a number or a name—and, from then on, these particles are distinguishable by their signs. Quantum particles of the same kind, however, are absolutely indistinguishable from one another; they cannot even be assigned numbers or any other nonphysical signs. Assigning numbers to particles of the same kind is a meaningful act in “classical” physics because the trajectory of every particle is traceable, at least in principle. Assigning numbers to particles of the same kind is a meaningless act in “quantum” physics because particles are not exactly particles; they do not follow trajectories. The numbers assigned to particles at any moment automatically “drop” at any subsequent moment.

From this principle, it was easily derived that quantum systems of the same kind of particles are either “symmetrical” or “antisymmetrical.” The antisymmetrical particles, called fermions, Fermions obey the Pauli exclusion principle. Like electrons, these particles are “antisocial”; they can never stay in the same quantum state described by the same set of quantum numbers. In contrast, the symmetrical particles, called bosons, Bosons are “sociable.” In fact, these particles tend to gather in the same quantum state. The behavior of a system of the same fermions is decided by the so-called Fermi-Dirac statistics; the behavior of a system of the same bosons is decided by the so-called Bose-Einstein statistics.

After his discovery of the exclusion principle, Pauli was still dissatisfied with its theoretical understanding. In 1940, he succeeded in developing a relativistic quantum theory with which he could prove a necessary connection between spin and statistics: Particles with half-integer spin must be fermions (or fulfill the exclusion principle); those with integer spin must be bosons.

When Paul Adrien Maurice Dirac Dirac, Paul Adrien Maurice pioneered in developing “quantum electrodynamics,” he applied the exclusion principle to predict the existence of the positrons. Later, in 1932, Dirac’s prediction was verified by Carl David Anderson, Anderson, Carl David who found positrons, Positrons the first particles of antimatter. Because the inside of metals is actually an electron gas, and the inside of the atomic nuclei is an assembly of the fermionic nucleons, the Pauli exclusion principle plays an important role in both solid-state physics and nuclear physics. Atoms;structure Exclusion principle Electrons Pauli exclusion principle

Further Reading
  • citation-type="booksimple"

    xlink:type="simple">Boorse, Henry A., and Lloyd Motz, eds. The World of the Atom. Vol. 2. New York: Basic Books, 1966. Collection of clear and informative essays on the nature of atoms. Chapter 59, “The Exclusion Principle,” includes three parts: the editors’ introductory commentary, Edward U. Condon and J. E. Mack’s paper “An Interpretation of Pauli’s Exclusion Principle” (originally published in 1930), and Pauli’s Nobel lecture.
  • citation-type="booksimple"

    xlink:type="simple">Born, Max. “Quantum Mechanics.” In My Life: Recollections of a Nobel Laureate. New York: Charles Scribner’s Sons, 1975. In the founding of quantum mechanics, Pauli’s contribution was great, but not vital. This chapter describes Pauli’s early, somehow misguided attitude toward the physical interpretation and mathematical formalisms of quantum mechanics.
  • citation-type="booksimple"

    xlink:type="simple">Cropper, William H. Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking. New York: Oxford University Press, 2001. Presents portraits of the lives and accomplishments of important physicists and shows how they influenced one another with their work. Chapter 17 is devoted to Wolfgang Pauli. Includes glossary and index.
  • citation-type="booksimple"

    xlink:type="simple">Gamow, George. Biography of Physics. New York: Harper & Row, 1961. Informative, interesting history of mostly modern physics. Discusses the Pauli exclusion principle as well as the so-called second Pauli principle in the context of Dirac’s developing relativistic quantum mechanics.
  • citation-type="booksimple"

    xlink:type="simple">_______. Matter, Earth, and Sky. 2d ed. Englewood Cliffs, N.J.: Prentice-Hall, 1965. Excellent popular science volume explains electron shells and period systems as well as Pauli’s exclusion principle in chapter 13.
  • citation-type="booksimple"

    xlink:type="simple">Gamow, George, and Russell Stannard. The New World of Mr. Tompkins. Cambridge, England: Cambridge University Press, 2001. Revised and updated (by Stannard) edition of Mr. Tompkins in Paperback, a 1965 volume that combined Gamow’s two classic popular science books, Mr. Tompkins in Wonderland (1940) and Mr. Tompkins Explores the Atom (1945). Provides an excellent introduction to many scientific concepts for lay readers, including Pauli’s exclusion principle.
  • citation-type="booksimple"

    xlink:type="simple">Polkinghorne, John. Quantum Theory: A Very Short Introduction. New York: Oxford University Press, 2002. Aims to make quantum theory accessible to the general reader. Among the concepts discussed are uncertainty, probabilistic physics, and the exclusion principle. Includes mathematical appendix and index.

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Categories: History