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Chapter 9: Q10CQ (page 403)

There are more permutations of particle labels when two particles have energy0 and two have energy1 than when three particles have energy 0and one has energy . 2(The total energiesarethe same.) From this observation alone argue that the Boltzmann distribution should be lower than the Bose-Einstein at the lower energy level.

Short Answer

Expert verified

The Boltzmann suppresses the possibility of discovering a particle with the lowest energy. And it鈥檚 encouraged for Bose- Einstein, demonstrating the Boltzmann probability is smaller.

Step by step solution

01

Boltzmann Statistics:

In the classical limit, Boltzmann statistics describes the energy distribution of an ensemble of identifiable particles. Bose - Einstein statistics, on the other hand, describes the energy distribution associated with a group of identical particles. A Boltzmann distribution can approximate the Bose-Einstein distribution in the case where temperature is effectively high or particle concentration is low.

02

Einstein Distribution:

Because there are more permutations for four particles occupying 0and ,1 where both states are doubly-filled, this suggests that at very low energies, these particles tend to cluster towards the same state.

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