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GR0177 #77
Problem
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Statistical Mechanics}Maxwell-Boltzmann Distributions

The Maxwell-Boltzmann distribution is , where g is the degeneracy.

Given , one finds the ratio of distributions (thus ratio of numbers) to be .

The problem gives eV, and thus the above ratio becomes , as in choice (E).  Alternate Solutions
 Ning Bao2008-02-01 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.Reply to this comment gbenga2014-10-18 22:35:18 semi-fast soln: rn rnThis power is negative so A,B, & C are eliminated. The denominator is small so D is unlikely. Remaining is E Reply to this comment gbenga2014-10-18 22:32:03 semi-fast soln: This power is negative so A,B, & C are eliminated. The denominator is small so D is unlikely. Remaining is EReply to this comment QuantumCat2014-09-01 10:39:10 A quick way to solve this problem (knowing that the occupation number depends on the energy) is to say that state B is at zero energy so that the exponential for state B just becomes 1, which is infinitely easier to deal with. Reply to this comment Ning Bao2008-02-01 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.Reply to this comment      LaTeX syntax supported through dollar sign wrappers $, ex.,$\alpha^2_0$produces . type this... to get...$\int_0^\infty\partial\Rightarrow\ddot{x},\dot{x}\sqrt{z}\langle my \rangle\left( abacadabra \right)_{me}\vec{E}\frac{a}{b}\$