Pauli Exclusion Principle

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rooney

Pauli's exclusion principle gives an exclusive identity to an electron. Its like every electron in an electronic system (i.e. atom) has an exclusive existence. Something like , in general view, no two people in this world have same face (even twins are not EXACTLY same). Every person has different characteristics (finger prints, face shape etc...), same way, every electron in an atom is UNIQUE (having its own face, fingerprints, height......i.e. the 4 quantum numbers).

I have just tried to convey the "feeling" on which pauli's exclusion principle is based. It might not be a very "scientific" answer.

edison

Paulis exclusion principle hold only for FERMIONS that is paricles with half spin. For bosons there is no such exclusion principle and thus any number of particles can occupy the given state for BOSONS.

But for fermi particles, no two particles can occupy the same state with all the set of four quantum numbers (n, l, m and s) identicle.

edison

Pauli Exclusion Principle

No two electrons in an atom can have identical quantum numbers. This is an example of a general principle which applies not only to electrons but also to other particles of half-integer spin (fermions). It does not apply to particles of integer spin (bosons).

The nature of the Pauli exclusion principle can be illustrated by supposing that electrons 1 and 2 are in states a and b respectively. The wavefunction for the two electron system would be

but this wavefunction is unacceptable because the electrons are identical and indistinguishable. To account for this we must use a linear combination of the two possibilities since the determination of which electron is in which state is not possible to determine.

The wavefunction for the state in which both states "a" and "b" are occupied by the electrons can be written

The Pauli exclusion principle is part of one of our most basic observations of nature: particles of half-integer spin must have antisymmetric wavefunctions, and particles of integer spin must have symmetric wavefunctions. The minus sign in the above relationship forces the wavefunction to vanish identically if both states are "a" or "b", implying that it is impossible for both electrons to occupy the same state.

edison

Fermions

Fermions are particles which have half-integer spin and therefore are constrained by the Pauli exclusion principle. Particles with integer spin are called bosons. Fermions incude electrons, protons, neutrons. The wavefunction which describes a collection of fermions must be antisymmetric with respect to the exchange of identical particles, while the wavefunction for a collection of bosons is symmetric.

The fact that electrons are fermions is foundational to the buildup of the periodic table of the elements since there can be only one electron for each state in an atom (only one electron for each possible set of quantum numbers). The fermion nature of electrons also governs the behavior of electrons in a metal where at low temperatures all the low energy states are filled up to a level called the Fermi energy. This filling of states is described by Fermi-Dirac statistics.

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Pauli Exclusion Principle