One way to decide whether Maxwell-Boltzmann statistics are valid is to compare the de Br...

One way to decide whether Maxwell-Boltzmann statistics are valid is to compare the de Broglie wavelength λ of a typical particle with the average interparticle spacing d. If λ<< d then Maxwell-Boltzmann statistics are generally acceptable. (a) Using de Broglie’s relation λ = h/p, show that

(b) Use the fact that N/V = 1/d³ to show that the inequality λ << d can be expressed as

(c) Use the result of (b) to determine whether Maxwell- Boltzmann statistics are valid for Ar gas at room temperature

(293 K) and for the conduction electrons in pure silver at T = 293 K.