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Area Semiconductor devices and integrated circuits / Introduction to atomic physics

IEV ref521-01-05

en
Maxwell-Boltzmann velocity-distribution law
algebraic equation giving the number dN of particles of a non-quantized system, the components of velocity of which are comprised in the intervals (u, u + du), (v, v + dv), (w, w + dw) respectively:

dN=Aexp[ m( u 2 + v 2 + w 2 ) 2kT ]dudvdw MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaaiaabsgacaWGobGaeyypa0JaamyqaiabgwSixlaabwgacaqG4bGaaeiCamaadmaabaWaaSaaaeaacqGHsislcaWGTbWaaeWaaeaacaWG1bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaamODamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaadEhadaahaaWcbeqaaiaaikdaaaaakiaawIcacaGLPaaaaeaacaaIYaGaam4AaiaadsfaaaaacaGLBbGaayzxaaGaaeizaiaaykW7caWG1bGaeyyXICTaaeizaiaaykW7caWG2bGaeyyXICTaaeizaiaaykW7caWG3baaaa@5C4B@

where

A=N [ m ( 2πkT ) ] 3/2 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaaiaadgeacqGH9aqpcaWGobWaamWaaeaadaWcaaqaaiaad2gaaeaadaqadaqaaiaaikdacqaHapaCcqGHflY1caWGRbGaamivaaGaayjkaiaawMcaaaaaaiaawUfacaGLDbaadaahaaWcbeqaamaalyaabaGaaG4maaqaaiaaikdaaaaaaaaa@44B1@

N is the total number of particles
m is the mass of a particle
T is the thermodynamic temperature
k is the Boltzmann constant

Note – dN/N represents the probability that a particle has its components of velocity within the intervals considered.


fr
loi de distribution des vitesses de Maxwell-Boltzmann, f
relation algébrique donnant le nombre dN de particules d'un système non quantifié dont les composantes de vitesse sont comprises respectivement dans les intervalles (u, u + du), (v, v + dv), (w, w + dw) :

dN=Aexp[ m( u 2 + v 2 + w 2 ) 2kT ]dudvdw MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaaiaabsgacaWGobGaeyypa0JaamyqaiabgwSixlaabwgacaqG4bGaaeiCamaadmaabaWaaSaaaeaacqGHsislcaWGTbWaaeWaaeaacaWG1bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaamODamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaadEhadaahaaWcbeqaaiaaikdaaaaakiaawIcacaGLPaaaaeaacaaIYaGaam4AaiaadsfaaaaacaGLBbGaayzxaaGaaeizaiaaykW7caWG1bGaeyyXICTaaeizaiaaykW7caWG2bGaeyyXICTaaeizaiaaykW7caWG3baaaa@5C4B@

A=N [ m ( 2πkT ) ] 3/2 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaaiaadgeacqGH9aqpcaWGobWaamWaaeaadaWcaaqaaiaad2gaaeaadaqadaqaaiaaikdacqaHapaCcqGHflY1caWGRbGaamivaaGaayjkaiaawMcaaaaaaiaawUfacaGLDbaadaahaaWcbeqaamaalyaabaGaaG4maaqaaiaaikdaaaaaaaaa@44B1@

N désigne le nombre total de particules
m la masse d'une particule
T la température thermodynamique
k la constante de Boltzmann

Note – dN/N représente la probabilité pour qu'une particule ait ses composantes de vitesse comprises dans les intervalles considérés.


ar
قانون توزيع السرعات لماكسويل -بولتزمان

de
Maxwell-Boltzmann-Geschwindigkeitsverteilung, f

es
ley de distribución de las velocidades de Maxwell-Boltzmann

fi
Maxwellin-Boltzmannin nopeusjakauma

it
legge di distribuzione delle velocità di Maxwell-Boltzmann

ko
맥스웰 볼츠만 속도 분포의 법칙

ja
マックスウェル–ボルツマン速度分布則

pl
prawo rozkładu prędkości Maxwella-Boltzmanna

pt
lei de distribuição das velocidades de Maxwell-Boltzmann

sr
Максвел–Болцманов закон расподеле брзина, м јд

sv
Maxwell-Boltzmanns hastighetsfördelning

zh
麦克斯韦-玻尔兹曼速度分布律

Publication date: 2002-05
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