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HW2 - Chemistry 252 Homework 2 Due Wed February 4 1 The...

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Chemistry 252 Homework 2. Due Wed. February 4 1. The vibrations of a diatomic molecule are well modeled by harmonic oscillator. As you know the energy states of a harmonic oscillator are given by E n = h ω n + 1 2 . From spectroscopy we know that h ω = 214.5 cm -1 for I 2 molecule. By using appropriate Boltzmann factors calculate the ratio of the numbers of molecules in the 1 st excited vibrational state (n=1) to that in the ground vibrational state (n=0) in iodine gas at room temperature (T = 300 K). An energy unit conversion table behind the front cover of the book may help. 2. Solve the same problem for hydrogen gas. h ω = 4401cm -1 for H 2 . 3. Rotational energy states of a linear molecule are: E J = BJ J + 1 ( ) , where J = 0,1,2… is the angular momentum. It is important that there are total of 2 J +1 states for every J, e.g. there are 3 states of J =1. What is the number of hydrogen molecules that are in J =1, J =2, and J =3 states compared to that of J =0 at 300 K.
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