The degeneracy of the lowest level of a Br atom is 4. The first excited electronic level lies the equivalent of 3685 cm^-1 higher in energy and has a degeneracy of 2. Calculate the electronic partition function at a temperature of 2500 K. A) 4.24 B) 1.00 C) 4.00 D) 6.00

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Quizplus · Accepted Answer

The electronic partition function, $q_e$, can be calculated using the formula $q_e = \sum g_i e^{-\epsilon_i/kT}$, where $g_i$ is the degeneracy of level $i$, $\epsilon_i$ is the energy of level $i$, $k$ is the Boltzmann constant (in appropriate units to match the energy units, here we use $k = 0.695 cm^{-1}K^{-1}$), and $T$ is the temperature. For the ground state, $g_0 = 4$ and $\epsilon_0 = 0$. For the first excited state, $g_1 = 2$ and $\epsilon_1 = 3685 cm^{-1}$. At $T = 2500 K$, the partition function is calculated as follows:$$q_e = g_0 e^{-\epsilon_0/kT} + g_1 e^{-\epsilon_1/kT} = 4 e^{0} + 2 e^{-3685/(0.695 \times 2500)} \approx 4 + 2 e^{-2.12} \approx 4 + 2(0.12) = 4.24.$$

The Degeneracy of the Lowest Level of a Br Atom