Fermi-Dirac statistics

In statistical mechanics, Fermi-Dirac statistics determines the statistical distribution of fermions over

Related Topics:
Statistical mechanics - Fermi - Dirac - Statistics - Fermion

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the energy states for a system in thermal equilibrium. In other words, it is a probability of a given energy level to be occupied by a fermion. Fermions are particles which are indistinguishable and obey the Pauli exclusion principle, i.e., no more than one particle may occupy the same quantum state at the same time. Statistical thermodynamics is used to describe the behaviour of large numbers of particles. A collection of non-interacting fermions is called a Fermi gas.

Related Topics:
Indistinguishable - Pauli exclusion principle - Fermi gas

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Fermi-Dirac (or F-D) statistics are closely related to Maxwell-Boltzmann statistics and Bose-Einstein statistics. While F-D statistics holds for fermions, B-E statistics plays the same role for bosons – the other type of particle found in nature. M-B statistics describes the velocity distribution of particles in a classical gas and represents the classical (high-temperature) limit of both F-D and B-E statistics. M-B statistics are particularly useful for studying gases, and B-E statistics are particularly useful when dealing with photons and other bosons. F-D statistics are most often used for the study of electrons in solids. As such, they form the basis of semiconductor device theory and electronics. The invention of quantum mechanics, when applied through F-D statistics, has made advances such as the transistor possible. For this reason, F-D statistics are well-known not only to physicists, but also to electrical engineers.

Related Topics:
Maxwell-Boltzmann statistics - Bose-Einstein statistics - Fermions - Bosons - Gas - Photon - Electron - Solid - Semiconductor device - Electronics - Quantum mechanics - Transistor - Electrical engineers

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F-D statistics was introduced in 1926 by Enrico Fermi and Paul Dirac and applied in 1927 by Arnold Sommerfeld to electrons in metals.

Related Topics:
Enrico Fermi - Paul Dirac - Arnold Sommerfeld

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The expected number of particles in an energy state i  for F-D statistics is

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:

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n_i = rac{g_i}{e^{left(epsilon_i-mu ight) / k T} + 1}

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where:

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:ni  is the number of particles in state i

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:gi  is the degeneracy of state i

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:εi  is the energy of state i

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:μ  is the chemical potential. Sometimes the Fermi energy EF is used instead, as a low-temperature approximation.

Related Topics:
Chemical potential - Fermi energy

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:k is Boltzmann's constant

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:T is absolute temperature

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:exp is the exponential function

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