# Plots of the Fermi-Dirac Distribution

Plots of the Fermi-Dirac Distribution

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Fermi-Dirac statistics deals with identical and indistinguishable particles with half-integral spins. Electrons, protons, neutrons, and so on are particles (called fermions) that follow Fermi-Dirac statistics. Fermions obey the Pauli exclusion principle, which states that two fermions cannot occupy the same quantum state at the same time. The Fermi-Dirac distribution function gives the probability that a given energy level is occupied by a fermion for a system in thermal equilibrium.

The Fermi-Dirac distribution function of elements is given by , where is the Fermi energy of the element, is the Boltzmann constant, and is the probability that a quantum state with energy is occupied by an electron. This Demonstration shows the variation of the Fermi-Dirac distribution function of representative metals with energy at different temperatures.

f(ϵ)=1/(exp[(ϵ-)/(T)]+1)

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