Exclusion Principle, Pauli

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Exclusion Principle, Pauli

Historical background

The exclusion principle

Electronic configurations

Rationalizing the periodic law


The Pauli exclusion principle, in physics, states that no two electrons in the same atom can have the same set of quantum numbers; that is, cannot simultaneously occupy the same energy (quantum) state of an atom. The principle was first stated by Austrian-Swiss mathematician and theoretical physicist Wolfgang Pauli (19001958) in 1925. He received the Nobel Prize in physics in 1945 for his work. The fundamental principle is also used in chemistry, where it helps to explain the trends seen in elements of the periodic table.

Historical background

The 1920s were a decade of enormous upheaval in atomic physics. Danish physicist Niels Bohrs (18851962) model of the atom, proposed in 1913, had been a historic breakthrough in scientists attempts to understand the nature of matter. But even from the outset, it was obvious that the Bohr model was inadequate to explain the fine points of atomic structure.

In some ways, the most important contribution made by Bohr was his suggestion that electrons can appear in only specific locations outside the atomic nucleus. These locations were designated as shells and were assigned integral quantum numbers beginning with 1. Electrons in the first shell were assigned the quantum number 1, those in the second orbit, the quantum number 2, those in the third shell, quantum number 3, and so on.

Eventually it became evident to scientists that additional quantum numbers would be needed to fully describe an electron in its orbit around the atomic nucleus. For example, German physicist and mathematician Arnold Sommerfeld (18681951) announced in 1915 that electrons traveled not in circles, but in ellipses around an atomic nucleus. The eccentricity of the elliptical orbit could be expressed, Sommerfeld said, by a second quantum number. By the mid-1920s, two additional quantum numbers, one defining the magnetic characteristics of an electron and one defining its spin, had been adopted.

The exclusion principle

In the early 1920s, Pauli reached an important insight about the nature of an electrons quantum numbers. Suppose, Pauli said, that an atom contains eight electrons. Then it should be impossible, he predicted, for any two of those electrons to have exactly the same set of quantum numbers.

As an example, consider an electron in the first orbit. All first-orbit electrons have a primary quantum number of 1. Then, mathematical rules determine the quantum numbers that are possible for any given primary quantum number. For example, Sommerfelds secondary quantum number can be any integer (whole number) from 0 to one less than the primary quantum number, or, l =0n-1. For an electron in the first shell (n = 1), l can only be 0. The third quantum number can have values that range from +l to -l. In this example, the third quantum number must also be 0. Finally, the fourth quantum number represents the spin of the electron on its own axis and can have values only of +1/2 or -1/2.

What Paulis exclusion principle says about this situation is that there can be no more than two electrons in the first shell. One has quantum numbers of 1, 0, 0, +1/2 and the other, of 1, 0, 0, -1/2.

More variety is available for electrons in the second shell. Electrons in this shell have quantum number 2 (for second shell). Mathematically, then, the secondary quantum number can be either 1 or 0, providing more options for the value of the magnetic quantum number (+1, 0, or -1). If one writes out all possible sets of quantum numbers of the second shell, eight combinations are obtained. They are as follows:

2, 1, +1, +1/2

2, 1, 0, +1/2

2, 1, -1, +1/2

2, 1, +1, -1/2

2, 1, 0, -1/2

2, 1, -1, -1/2

2, 0, 0, +1/2

2, 0, 0, -1/2

Electronic configurations

The Pauli exclusion principle is more than an intellectual game by which quantum number sets can be worked out for individual electrons. Beyond that, the principle allows one to determine the electronic configurationthe way the electrons are arranged within any given atom. It shows that for an electron with 15 electrons, for example, two and only two can occupy the first shell, eight more (and only eight more) can occupy the second, leaving five electrons in a third shell.

The exclusion principle also demonstrates that, as with an onion, there are layers within layers. In the third shell of an atom, for example, there are three subdivisions, known as orbitals. One orbital has the secondary quantum number of 0, one has the secondary quantum number of 1, and one, the secondary quantum number 2.

Rationalizing the periodic law

For more than half a century, chemists had known that the chemical elements display a regular pattern of properties, a discovery originally announced as the periodic law by Russian chemist Dmitri Mendeleev (18341907) in about 1869. The Pauli exclusion principle provided important theoretical support for the periodic law. When a chart is made showing the electronic configuration of all the elements, an interesting pattern results. The elements have one, two, three, four (and so on) electrons in their outermost orbital in a regular and repeating pattern. All elements with one electron in their outermost orbital, for example, occur in column one of Mendeleevs periodic table. They have similar chemical and physical properties, it turns out, because they have similar electronic configurations.



Emsley, John. Natures Building Blocks: An A-Z Guide to the Elements. Oxford, UK: Oxford University Press, 2003.

Massimi, Michela. Paulis Exclusion Principle: The Origin and Validation of a Scientific Principle. Cambridge, UK, and New York: Cambridge University Press, 2005.

Siekierski, Slawomir. Concise Chemistry of the Elements. Chichester, UK: Horwood Publishing, 2002.


Electronic configuration The arrangement of electrons in an atom.

Orbital A group of electrons in an atom that all have the same primary and secondary quantum numbers.

Periodic law A statement that the physical and chemical properties of the chemical elements repeat themselves according to an orderly and periodic pattern.

Shell A group of electrons in an atom that all have the same primary quantum number.

Young, Hugh D. Sears and Zemanskys University Physics. San Francisco, CA: Pearson Addison Wesley, 2004.

David E. Newton