On this page
If you have ever written an electron configuration, you have used Wolfgang Pauli's exclusion principle. It is the reason atoms do not collapse every electron into the lowest shell, and so the reason chemistry has a periodic table at all. Pauli also proposed the neutrino, a particle so hard to detect that it took 26 years to find. This post covers both ideas with worked numbers, and what a student can take from his way of working.
Who was Wolfgang Pauli?
His Nobel biography records that he was born in Vienna on 25 April 1900 and studied at the University of Munich under Arnold Sommerfeld, taking his doctorate in 1921. While still a student he published what the Nobel biography calls a masterly exposition of the theory of relativity. He then worked with Max Born in Göttingen and Niels Bohr in Copenhagen, lectured in Hamburg from 1923 to 1928, and became Professor of Theoretical Physics at the Federal Institute of Technology (ETH) in Zurich. He died in Zurich on 15 December 1958.
He received the 1945 Nobel Prize in Physics "for the discovery of the Exclusion Principle, also called the Pauli Principle".
What problem did the exclusion principle solve?
In his Nobel lecture, Pauli recalls that in Munich the numbers 2, 8, 18, 32, the lengths of the periods in the periodic table, were "zealously discussed", including Rydberg's remark that they have the form 2n². But nobody could say why electrons in an atom did not all sit in the innermost shell.
In 1924 Pauli argued that the electron needed a new quantum property, which he cautiously called a "two-valuedness not describable classically". A paper by Edmund Stoner then gave him a key clue about how many states each shell holds. Pauli's general statement, published in Zeitschrift für Physik in 1925, was that once each electron is labelled by four quantum numbers, each fully specified state can hold only one electron. The Nobel summary puts it simply: no two electrons in an atom can have identical sets of quantum numbers. Soon afterwards, Uhlenbeck and Goudsmit gave the fourth quantum number a physical picture: electron spin.
Worked example: why shells hold 2n² electrons
For a given n, l runs from 0 to n − 1, m runs from −l to +l, and spin has two values.
n = 1: l = 0, m = 0. One orbital, two spins: 2 electrons.
n = 2: l = 0 gives 1 orbital; l = 1 gives m = −1, 0, +1, so 3 orbitals. Total 4 orbitals, 8 electrons.
n = 3: l = 0, 1, 2 give 1 + 3 + 5 = 9 orbitals, so 18 electrons.
In general there are n² orbitals in shell n, hence 2n² electrons. Oxygen, with 8 electrons, fills 1s² 2s² and puts 4 electrons into the three 2p orbitals: two share one orbital with opposite spins and two are unpaired.
A common mistake is to treat the exclusion principle and Hund's rule as the same thing. The exclusion principle says no two electrons can share all four quantum numbers; Hund's rule says how electrons spread across orbitals of equal energy. Our guide to quantum numbers and electron configuration has more practice.
Why did Pauli propose the neutrino?
In beta decay a nucleus emits an electron. If only two bodies came out, the electron would always carry the same energy. Instead experiments showed a continuous spread of electron energies, which seemed to break conservation of energy.
On 4 December 1930 Pauli wrote an open letter to physicists meeting in Tübingen, beginning "Dear Radioactive Ladies and Gentlemen". In the English translation kept by Royal Holloway, University of London, he calls his idea "a desperate remedy": an electrically neutral particle with spin ½, very light, emitted alongside the electron so that the two share the energy. He said he could not come to Tübingen in person because of a ball in Zurich.
You can see the size of the problem with modern masses from NIST. For a free neutron decaying into a proton and an electron, the energy released is (939.565 − 938.272 − 0.511) MeV ≈ 0.782 MeV. In a two-body decay, almost all of that would go to the electron every time. Electrons with less energy are only possible if a third particle carries the rest.
The neutrino was finally detected at a nuclear reactor by Clyde Cowan, Frederick Reines and colleagues, who reported Detection of the free neutrino: a confirmation in Science in July 1956. Reines shared the 1995 Nobel Prize in Physics "for the detection of the neutrino".
If a picture of orbitals filling one by one would help, the Fermi Concept Library covers every concept in physics and chemistry, each with its own lesson.
What can a student take from how he worked?
Look for the rule behind the numbers. The pattern 2, 8, 18 was known; Pauli asked what rule produced it.
Name what you do not understand. "Two-valuedness not describable classically" was an honest label for something he could not yet picture.
Trust conservation laws. Rather than give up energy conservation, he proposed a new particle and waited for experiment.
Write ideas down even when unsure. His neutrino letter was informal and tentative, and it was right.
Pauli's principle sits at the heart of atomic structure; read how Niels Bohr's atom model set up the problem he solved.
Try it: count the orbitals and electrons for n = 4 and check that you get 32.
