IEVref: | 521-01-19 | ID: | |

Language: | en | Status: Standard | |

Term: | Fermi-Dirac-Sommerfeld velocity distribution law | ||

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Definition: | algebraic equation giving the number dN of particles of a quantized system in equilibrium, the velocity components of which are included in the intervals (u, u + du), (v, v + dv), (w, w + dw) :respectively: $\text{d}\text{\hspace{0.17em}}N=2N\cdot \frac{{m}^{3}}{{h}^{3}}\cdot \frac{\text{d}\text{\hspace{0.17em}}u\cdot \text{d}v\cdot \text{d}\text{\hspace{0.17em}}w}{1+\text{exp}{\displaystyle \left(\frac{E-{E}_{\text{M}}}{kT}\right)}}$
where $E=\frac{m}{2}\left({u}^{2}+{v}^{2}+{w}^{2}\right)$
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Publication date: | 2002-05 | ||

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Internal notes: | 2017-06-02: Cleanup - Remove Attached Image 521-01-191.gif 2017-06-02: Cleanup - Remove Attached Image 521-01-192.gif | ||

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respectively:

$\text{d}\text{\hspace{0.17em}}N=2N\cdot \frac{{m}^{3}}{{h}^{3}}\cdot \frac{\text{d}\text{\hspace{0.17em}}u\cdot \text{d}v\cdot \text{d}\text{\hspace{0.17em}}w}{1+\text{exp}{\displaystyle \left(\frac{E-{E}_{\text{M}}}{kT}\right)}}$

where

*N* is the total number of particles

*m* is the mass of the particle

*T* is the thermodynamic temperature

*k* is the Boltzmann constant

*h* is the Planck constant

*E* is the kinetic energy of a particle,

$E=\frac{m}{2}\left({u}^{2}+{v}^{2}+{w}^{2}\right)$

*E*_{M} is the inner work function

d*N*/*N* represents the probability that a particle has its components within the intervals considered.