Exclusion Principle

Exclusion Principle, in physics, fundamental principle stating that two elementary particles of half-integral spin, such as electrons cannot simultaneously occupy the same quantum state (energy state) in an atom. It explains the regularities of the periodic law. 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 for Physics in 1945.

According to quantum theory, the possible states of electrons in the atom are specified 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 orbital quantum number, l, describes the magnitude of the angular momentum of the orbiting electron (see Mechanics). The 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, according to the direction of the spin. 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 the periodic law.

For example, when the principal quantum number n is 1, quantum theory permits the orbital number l and the magnetic quantum number m to be 0 only, and the spin quantum number m to be either +y or -y. The result is that there are 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_s 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 periodic law is explained by the degree to which the electron shells of atoms are filled.

The Pauli exclusion principle applies not only to electrons in atoms but also to free electrons that drift through matter as an electric current when a voltage is applied. Protons and neutrons in the nucleus are also organized in quantum states, and only two particles of the same kind, but with opposite spins, are permitted in each state. All fermions (particles with half-integral spin) obey the exclusion principle, but bosons, which have integral spin, do not. See Statistical Mechanics.