Download The Pauli exclusion principle states that no two fermions

The Pauli exclusion principle states that no two fermions can have
identical wavefunctions.
LEARNING OBJECTIVES [ edit ]
State the Pauli exclusion principle and the particles to which it applies.
Illustrate how the Pauli exclusion principle partially explains the electron shell structure of atoms.
KEY POINTS [ edit ]
No two identical fermions (particles with half-integer spin) may occupy the same quantum state
simultaneously.
No two electrons in a single atom can have the same fourquantum numbers.
Particles with integer spin occupy symmetric quantum states, and particles with half-integer spin
occupy antisymmetric states.
TERMS [ edit ]
boson
A particle with totally symmetric quantum states. They have integer spin and include many
elementary particles, and some (gauge bosons) are known to carry the fundamental forces.
fermion
A particle with totally antisymmetric quantum states. They have half-integer spin and include
many elementary particles.
electron
The subatomic particle having a negative charge and orbiting the nucleus; the flow of electrons in
a conductor constitutes electricity.
Give us feedback on this content: FULL TEXT [ edit ]
The Pauli exclusion principle, formulated by Austrian physicist Wolfgang Pauli in 1925, states
that no two fermions of the same kind may simultaneously occupy the same quantum state.
More technically, it states that the total wave function for two identical fermions is
antisymmetric with respect to exchange of the particles. For example, no two electrons in a
single atom can have the same four quantum numbers; if n, ℓ , and mℓ are the same, ms must
be different such that the electrons have opposite spins.
The Pauli exclusion principle governs the behavior of all fermions (particles with half-integer
spin), while bosons (particles with integer spin) are not subject to it. Fermions include
elementary particles such as quarks (the constituent particles of protons and neutrons),
electrons and neutrinos. In addition, protons and neutrons (subatomic particles composed
from three quarks) and some atoms are fermions and are therefore also subject to the Pauli
exclusion principle. Atoms can have different overall spin, which determines whether they
are fermions or bosons—for example, helium-3 has spin 1/2 and is therefore a fermion, in
contrast to helium-4 which has spin 0, making it a boson. As such, the Pauli exclusion
principle underpins many properties of everyday matter from large-scale stability to the
chemical behavior of atoms including their visibility in NMR spectroscopy.
Half-integer spin means the intrinsic angular momentum value of fermions is ℏ =
h
π
2
(reduced Planck's constant) times a half-integer (1/2, 3/2, 5/2, etc.). In the theory of
quantum mechanics, fermions are described by antisymmetric states. In contrast, particles
with integer spin (bosons) have symmetric wave functions; unlike fermions, bosons may
share the same quantum states. Bosons include the photon, the Cooper pairs (responsible for
superconductivity), and the W and Z bosons. Fermions take their name from the Fermi–
Dirac statistical distribution that they obey, and bosons take their name from Bose–Einstein
distribution.
The Exclusion Principle and Physical Phenomena
The Pauli exclusion principle explains a wide variety of physical phenomena. One particularly
important consequence of the principle is the elaborate electron-shell structure of atoms and
the way atoms share electrons. It explains the variety of chemical elements and their
chemical combinations. Anelectrically neutral atom contains bound electrons equal in
number to the protons in the nucleus. Electrons, being fermions, cannot occupy the same
quantum state, so electrons have to "stack" within an atom—they have different spins while at
the same place.
Electrons filling quantum energy levels
When a state has only one electron, it could be either spin­up or spin­down. However, according the the
Pauli Exclusion Principle, when there are two in a state, there must be one of each.
An example is the neutral helium atom, which has two bound electrons, both of which can
occupy the lowest-energy (1s) states by acquiring opposite spin. As spin is part of the
quantum state of the electron, the two electrons are in different quantum states and do not
violate the Pauli exclusion principle. However, there are only two distinct spin values for a
given energy state. This property thus mandates that a lithium atom, which has three bound
electrons, cannot have its third electron reside in the 1s state; it must occupy one of the
higher-energy 2s states instead. Similarly, successively larger elements must have shells of
successively higher energy. Because the chemical properties of an element largely depend on
the number of electrons in the outermost shell, atoms with different numbers of shells but
the same number of electrons in the outermost shell still behave similarly. For this reason,
elements are defined by their groupsand not their periods.