Exclusion Principle

Exclusion Principle, in physics, fundamental principle stating that two electrons cannot simultaneously occupy the same quantum or energy state of an atom. This principle is important in chemistry also because it explains the regularities of the periodic law. The exclusion principle also applies to other elementary particles of half-integral spin. All its implications are probably not yet fully understood. The exclusion principle was developed in 1925 by the Austrian-born theoretical physicist and mathematician Wolfgang Pauli; he received the Nobel Prize in physics in 1945.

According to the quantum mechanical model of the atom, electrons are limited in their states in the neighborhood of a nucleus by four discrete values called quantum numbers. These quantum numbers are used to describe mathematically a three-dimensional model of the atom. The principal quantum number, n, defines the principal energy state, or shell, of an orbiting electron. The angular momentum quantum number, l, describes the magnitude of the angular momentum of the orbiting electron. The lower the value of l, the more highly elliptical the orbit of the electron. The magnetic quantum number, m, describes the magnetic orientation in space of the plane of the orbiting electron. The spin of the electron is designated by the spin magnetic quantum number, m_s’ which may have the value of -y or +y. In the first case, the electron behaves as though it is spinning in one direction; in the latter case, as though it is spinning in the opposite direction. For each quantum number except m_s’ only certain whole-number values are permitted. This rule leads to consequences that are largely in agreement with periodic theory.

For example, when the principal quantum number n is unity, quantum theory permits the orbital number l and the magnetic quantum number m both to be only 0 (zero), and the spin quantum number m to be either +y or -y, that is, the spin can be only left-handed or right-handed. The result is just two possible combinations of quantum numbers: 1-0-0-(+y) and 1-0-0-(-y). According to the exclusion principle, only one electron can have either of these two combinations of quantum numbers. That is, when the principal quantum number n = l, only two electrons can occupy that electron shell.

When n = 2, quantum theory permits l to be 0 or 1, m to be +1, 0, or -1, and m to be either +y or -y. There are eight possible combinations of these quantum numbers. Therefore, in the second electron shell there can be a maximum of eight electrons. It is possible in this way to establish the maximum number of electrons permitted in each electron shell of any atom.

The Pauli exclusion principle applies not only to electrons in atoms but also to free electrons that drift through matter and comprise an electric current when a voltage is applied. Protons and neutrons in the nucleus also appear to be organized so that only two particles of the same kind, but with opposite spins, are permitted in each quantum orbit. Other particles called fermions obey the exclusion principle, but still other particles called bosons do not. Explaining the behavior of these particles remains one of the most important challenges in physics today.