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Approximate the vibrational partition function
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Assignment ID: FG132521713
The energy of the vibrational modes of a molecule are the same as those of a (quantum) harmonic oscillator with frequency ω. There is a gas of nitrogen molecules in thermodynamic equilibrium for which ? / = 3340.
a) What fraction of the molecules are in the ground state, the 1st excited state, and the 2nd excited state of their vibrational modes at a temperature of 800 K? Use the exact partition function for this part.
b) At what temperature will 4% of the molecules be in the 1st excited vibrational state? You may approximate the vibrational partition function with the largest two terms in it.
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