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# chem5314_hwk6 - the third fourth and ﬁfth excited states...

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Chem 5314 homework #6 – not for credit 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? 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? Problem 3 a) For I 2 , the harmonic oscillator approximation (force constant k=170 N/m) assumes that the vibrational energy levels are equally spaced. At 300 K, calculate the ratio of molecules in the ﬁrst excited state compared to the ground state. Also calculation the proportion of molecules in the second excited state relative to the ground state. Repeat for
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Unformatted text preview: the third, fourth, and ﬁfth excited states as well. b) Show that you do not need q , the partition function, to calculate these quantities. Show that, if you are only interested in relative populations (eg. how many more molecules are in one state compared to another state), you can always calculate this without knowing the value of q . c) I 2 is experimentally found to have vibrational energy levels at the following wavenum-bers above the ground state: 213.30 cm-1 , 425.39 cm-1 , 636.27 cm-1 , 845.93 cm-1 , 1054.38 cm-1 ,.. Repeat the relative population analysis you did in part (a) for the actual molecule I 2 using the experimental data. d) Compare the answers of (a) and (c) and comment. 1...
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