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Plots of the Fermi-Dirac Distribution

​
elements
lithium
temperature (°K)
0.01
General
:Exp[-5.5615×
7
10
] is too small to represent as a normalized machine number; precision may be lost.
General
:Exp[-5.5615×
6
10
] is too small to represent as a normalized machine number; precision may be lost.
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
f(ϵ)=1/(exp[(ϵ-
ϵ
F
)/(
k
B
T)]+1)
, where
ϵ
F
is the Fermi energy of the element,
k
B
is the Boltzmann constant, and
f(ϵ)
is the probability that a quantum state with energy
ϵ
is occupied by an electron. This Demonstration shows the variation of the Fermi-Dirac distribution function of representative metals with energy at different temperatures.
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