GREPhysics.NET: GR0177 #77

GR0177 #77

Problem

GREPhysics.NET Official Solution

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Statistical Mechanics $\Rightarrow$ }Maxwell-Boltzmann Distributions

The Maxwell-Boltzmann distribution is $N\propto g e^{-\epsilon/(kT)}$ , where g is the degeneracy.

Given $\epsilon_a = 0.1+\epsilon_b$ , one finds the ratio of distributions (thus ratio of numbers) to be $e^{-(0.1+\epsilon_b)/kT}/e^{-\epsilon_b/kT}= e^{-0.1/kT}$ .

The problem gives $kT = 0.025$ eV, and thus the above ratio becomes $e^{-.1/.025}=e^{-4}$ , as in choice (E).

Alternate Solutions

Ning Bao
2008-02-01 07:39:44

Quick elimination: higher states are less likely->D or E.

Ratio of given energy to kT mist be important: as Energy of A increases, likelihood in state A decreases ->E.

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Ning Bao
2008-02-01 07:39:44

Quick elimination: higher states are less likely->D or E.

Ratio of given energy to kT mist be important: as Energy of A increases, likelihood in state A decreases ->E.

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