One way to decide whether Maxwell-Boltzmann statistics arevalid is to compare th

Question

One way to decide whether Maxwell-Boltzmann statistics arevalid is to compare the de Broglie wavelength of a typicalparticle with the average interparticle spacing d. If <<d then Maxwell-Botzmann statistics aregenerally acceptable. (c) Use the result of part (b) to determine whetherMax-Boltz stats are valid for Ar gas at room temperature (293 K)and for the conduction electrons in pure silver (Ag) at T = 293K. One way to decide whether Maxwell-Boltzmann statistics arevalid is to compare the de Broglie wavelength lambda of a typicalparticle with the average interparticle spacing d. If lambda

Explanation / Answer

from the debroglies relation = h/mv = h/p if E is kinetic energy of particle then E = 1/2mv2= p2/2m p = 2mE then = h/2mE when charged particle carrying a charge q is accleratedby a potential difference v volts then its kinetic energy E =qv = h/2mqv when material particle is in thermal equlibrium at atempertatre T then E = 3/2kT where K is boltz man constent so de Broglie's relation =h/2m(3/2kT) = h/3mkT.

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