Solution to 2008 Problem 78

The probability of finding a particle in a state with energy E is
\begin{align*}\frac{e^{-E/kT}}{\sum_i e^{-E_i/kT}}\end{align*}
where the summation is over all states i. If there are only two states, and we would like probability that the particle is found in state i=2, then this equation gives
\begin{align*}\boxed{\frac{e^{-E_2/kT}}{e^{-E_1/kT} + e^{-E_2/kT}}}\end{align*}
Therefore, answer (B) is correct.

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