Wolfgang Pauli's Exclusion Principle

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Wolfgang Pauli's Exclusion Principle

Overview

The Pauli exclusion principle enabled the quantum structure of the atom to be understood. It provided a mechanism to explain the variety and behavior of the chemical elements, and it gave a theoretical basis for the periodic table. It was one of the key pieces of the quantum puzzle and had far-reaching implications, many of which have yet to be fully understood.

Background

Wolfgang Pauli (1900-1958) was a child prodigy, excelling in classical history as well as mathematics and science. At the Döbling Gymnasium (a high school in Vienna) he was taught classical physics just when classical notions were under attack from new quantum ideas. He read widely on general relativity and became something of an authority on the subject, publishing three academic papers within a year of graduating high school.

Pauli went on to study at the University of Munich, under Arnold Sommerfield (1868-1951), who introduced him to the radical new quantum theory. As Pauli recalled years later, "I was spared the shock which every physicist accustomed to the classical way of thinking experienced when he came to know Niels Bohr's basic postulate of quantum theory for the first time." Quantum theory seemed to contradict common sense and was difficult to visualize. However, Pauli found himself devoted to the new field, particularly the partially understood structure of the quantum atom.

Ernest Rutherford's (1871-1937) experiments had determined that the structure of the atom consisted mainly of empty space. Using classical ideas, Rutherford's atom could be described as a small core, with the nucleus (imagine an orange in the middle of a football stadium) surrounded by tiny orbiting electrons (very fast insects somewhere outside the stadium in the parking lot!) Further work by others helped define the structure of the atom, giving positions for the orbits, and so on, using classical ideas such as treating the electrons as planets orbiting a central sun.

However, classical notions of orbits and particles became increasingly unable to explain a multitude of experimental results. Niels Bohr (1885-1962) combined the ideas of Albert Einstein (1879-1955) and Max Planck (1858-1947) and others to offer a new way of defining the atom. Bohr stated that an atom could exist only in a discrete set of stable energy states; that is, atomic energy was "quantized," not continuous. Quantum objects could have only certain energy values and could jump between these values, but the energy levels between these states could not be occupied. For atomic structure this implied that electrons could only exist in certain orbits, and while they might jump between these orbits they could not exist in the "space" between.

Bohr's ideas were expanded upon, and three values were postulated to define the energy state of electrons in an atom. These three numbers roughly correspond to the electron orbit (n), the angular momentum (l), and the magnetic quantum number (m or ml) of the electron. However, these numbers did not explain the atomic structure as completely as physicists would have liked.

In 1922 Bohr gave guest lectures in Göttingen, Germany, in which he dealt with the incomplete ideas of electron structure. Bohr was searching for a general explanation to the experimentally calculated electron orbits, and this quest was to deeply inspire at least one member of his audience, Wolfgang Pauli. "A new phase of my scientific life began when I first met Niels Bohr personally," Pauli noted later.

Pauli went to Copenhagen, Denmark, to work with Bohr, and found himself frustrated by an unexplained experimental result known as the Zeeman effect. In classical physics an electric current moving in a loop acts like a magnet, producing easily calculated magnetic properties. Therefore, it was assumed that electrons in orbit around the nucleus would produce the same classical effect. However, the experimental results did not conform to theoretical predictions. Various experimental refinements were tried, but always the Zeeman effect baffled theorists. Pauli became obsessed with the problem. "A colleague who met me strolling rather aimlessly in the beautiful streets of Copenhagen said to me in a friendly manner, 'you look very unhappy'; whereupon I answered fiercely, 'How can one look happy when he is thinking about the anomalous Zeeman effect?'"

Leaving the puzzle unsolved, Pauli moved to Hamburg, Germany, where he gave his inaugural lecture on the periodic system of elements. The periodic nature of the elements had been recognized by Dmitry Mendeleyev (1834-1907) and published in 1869. Mendeleyev realized that the 63 elements then known had a repeating pattern—they could be grouped into families with similar chemical properties. For example, helium, neon, and argon are all inert gases; that is, they do not react readily with any other elements. He arranged the 63 elements into a table showing their periodic repetition, the periodic table. There were many gaps in Mendeleyev's table, but he was able to predict what type of elements would fit into these gaps. In his own lifetime he saw three new elements added into the spaces he had left, each showing properties he had foretold. However, while the periodic table was a success, there was no underlying explanation for it, which got Pauli thinking.

In 1924 Pauli read a paper discussing quantum numbers, and this gave the final piece to his fractured thoughts. He realized that four quantum numbers, rather than three, were needed to specify the exclusive state of each electron in the atom. This new number (ms) would be unusual, having a two-valuedness not describable in classical terms. With the fourth quantum number Pauli could now make a bold statement, the exclusion principle, that in a multi-electron atom there can never be more than one electron in the same quantum state. That is, a multi-electron atom cannot have the same values for the four quantum numbers.

Impact

Pauli announced his exclusion principle in 1925, but it was given a mixed reception. The fourth quantum number was an abstract concept; it did not seem to refer to any actual property of the electrons. The exclusion principle is a created rule based on the analysis of other peoples' experiments, not a derived property. As Pauli himself noted in 1945, he "was unable to give a logical reason for the exclusion principle or deduce it from more general assumptions." However, it worked, fitting both quantum theory and experimental results. Pauli responded to his critics by writing "my nonsense is conjugate to the nonsense which has been customary so far."

Eventually, the fourth quantum number was found to represent the "spin" of the electron, with a value of 1/2 for clockwise and -1/2 for anticlockwise spin. However, spin is a classical concept, and our common conception of it does not translate exactly into quantum reality. Bohr later showed that electron spin cannot be measure in classical terms. It is a quantum property and so is a little hard to comprehend.

In some ways it is ironic that the development and success of the exclusion principle relied so heavily on the experimental work of other scientists, as the theorist Pauli was actually feared by European experimenters. A legend built up around Pauli that his mere presence in a laboratory could ruin any experiment, often in bizarre and dangerous ways. Otto Stern (1888-1969) went so far as to ban Pauli outright from any of his labs. Pauli himself came to believe in what was dubbed "The Pauli Effect," even justifying it in terms of Jungian philosophy.

The exclusion principle applies not just to atomic structure but also to any system containing electrons. Electrons in a current obey the principle, as do electrons in chemical bonds. Not only electrons, but protons, neutrons, and a whole range of other particles that are collectively called fermions (named after Enrico Fermi [1901-1954]) obey the principle. There are other particles that do not follow the exclusion principle, called bosons (named after Satyenda Bose [1894-1974]).

Pauli's work had major implications for chemistry. Mendeleyev's periodic table could be shown to be a result of the internal structure of the atom, with the families of elements he defined each relating to the same arrangement of electrons within the outer orbit. Because they had the same outer electron arrangement, the elements within a family behaved the same way chemically. This explained why some elements were more reactive than others. The behavior of electrons in chemical bonding could now be defined. The exclusion principle also allows insight into the electrical conductivity of different substances: why, for instance, metals conduct better than semi-conductors, which in turn conduct better than insulators. Everything was explained by the extremely regulated "building" plan of quantum structure as defined by the exclusion principle, which resulted in Pauli being nicknamed the "atomic housing officer."

In 1945 Pauli was awarded the Nobel Prize in physics "for the discovery of the Exclusion Principle, also called the Pauli Principle." The lack of a valid passport and other planning difficulties stopped Pauli from collecting it personally at the awards banquet in Stockholm, Sweden. Instead, a dinner was given for him at Princeton University's Institute for Advanced Study, where to everyone's amazement, Einstein offered a toast in which he designated Pauli as his successor and spiritual son. Pauli was held in high regard in the scientific community, with some physicists going so far as to call him "the living conscience of theoretical physics."

Pauli's exclusion principle was announced in a year that also saw the announcements of Maurice De Broglie's (1875-1960) idea of matter waves and Werner Heisenberg's (1901-1976) matrix-mechanics, from which followed Erwin Schrödinger's (1887-1961) wave mechanics. It was an exciting time for physics, and Pauli's exclusion principle was one of the many important concepts that helped create modern quantum physics.

DAVID TULLOCH