Chemistry 252 Homework 2. Due Wed. February 41.The vibrations of a diatomic molecule are well modeled by harmonic oscillator.As you know the energy states of a harmonic oscillator are given byEn=hωn+12. From spectroscopy we know that hω=214.5 cm-1for I2molecule. By using appropriate Boltzmann factors calculate the ratio of thenumbers of molecules in the 1stexcited vibrational state (n=1) to that in theground vibrational state (n=0) in iodine gas at room temperature (T = 300 K). Anenergy unit conversion table behind the front cover of the book may help.2.Solve the same problem for hydrogen gas. hω=4401cm-1for H2.3.Rotational energy states of a linear molecule are:EJ=BJ J+1(), where J =0,1,2… is the angular momentum. It is importantthat there are total of 2J+1states for every J,e.g.there are 3 states of J=1. What is the number of hydrogenmolecules that are in J=1, J=2, and J=3 states compared to that of J=0 at 300 K.
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