Discussion
For a system with non-degenerate zero energy state and doubly degenerate upper state (with energy E), the partition function is :
Answer: D
The partition function is 1 + 2e−E/kT.
The molecular partition function sums the Boltzmann factor over all levels, each weighted by its degeneracy g:
\[ \begin{aligned} q &= \sum_{i} g_{i}\,e^{-E_{i}/kT} \\ &= 1\cdot e^{0} + 2\,e^{-E/kT} = 1 + 2e^{-E/kT} \end{aligned} \]
The ground level at zero energy is non-degenerate and contributes exactly 1. The doubly degenerate upper level contributes 2e−E/kT.
2e−E/kT leaves out the ground state, 2 + e−E/kT puts the degeneracy on the wrong level, and 3e−E/kT treats all three states as if they had energy E.
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