chem5314_hwk6_soln

chem5314_hwk6_soln - Chem 5314 homework #6 solutions...

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Chem 5314 homework #6 solutions Problem 1 A molecule has an excited state 500 cm - 1 above its ground state. Only consider these two states. The excited state is doubly degenerate and the ground state is non-degenerate. For what temperature range does the population of molecules in the excited state exceed that of the ground state? solution: We can, without loss of generality, set E 0 = 0 and E 1 Δ E = 500 cm - 1 . Then q = 1 + 2 e - β Δ E . We are asked for the temperature range for which P (1) /P (0) 1. This corresponds to 2 e - β Δ E 1 or - β Δ E ≥ - ln 2. Multiplying by - 1 on both sides (which reverses the inequality) and rearranging gives Δ E k B T ln 2 or T Δ E/ ( k B ln 2). Putting in the numbers (convert units and multiple by hc to turn wavenumbers into energy) gives T 1039 K. Problem 2 The vibrational frequency of I 2 is 208 cm - 1 . At what temperature will the population in the first excited state be half of the ground state? solution:
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chem5314_hwk6_soln - Chem 5314 homework #6 solutions...

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