Discussion
In a two-state system, one with energy 0 and other with energy \(\varepsilon \gt 0\). The system will have both the levels equally occupied when :
Answer: B
The two levels are equally occupied when T is infinite.
In thermal equilibrium the ratio of occupations is given by the Boltzmann factor:
\[ \frac{N_{\varepsilon}}{N_{0}} = e^{-\varepsilon/k_{B}T} \]
For any \(\varepsilon \gt 0\) this ratio is less than 1 at every finite temperature, and it reaches 1 only in the limit \(T \rightarrow \infty\). At T = 0 all particles are in the lower level, and at very low temperature nearly all are. At a very high but finite temperature the populations approach equality without reaching it, which is why 'very high' is not exact.
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