hw_5 - HOH bond angle is 104.45 degrees Hints using the O...

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Physics 780.04 Winter Quarter 2007 Dr. Herbst HOMEWORK ASSIGNMENT # 5 DUE: FRIDAY 23 FEBRUARY 1. In rotational Raman spectroscopy, a laser is shone into a sample and different frequencies emerge. The differences between the laser frequency and the output frequencies are equal to rotational energy differences in the sample molecule (divided by h) . For example, if the molecule undergoes the transition J = 2 <-0, the difference in frequency is 6B. Calculate the ratio of the two lowest difference frequencies for C 2 , O 2 , and CO in their ground electronic states assuming the Raman selection rule for the molecule to be Δ J=2. What do the different ratios tell us? 2. Bernath, page 362, problem 3a,b,c 3. a) Determine the rotational constants (A, B, C in GHz) and the asymmetry parameter for the planar molecule water (H-O-H), in which the OH bond distance is 0.958 Å and the
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Unformatted text preview: HOH bond angle is 104.45 degrees. Hints: using the O atom as the origin, determine the center of mass and then compute the moment of inertia tensor using x, y, z axes of your choice. You should find all products of inertia to be zero so that the three moments you calculate are the principal moments. b) Draw a diagram of the water molecule and label the a, b, and c axes. Also show the direction of the dipole moment of the molecule. What type/s of transitions do you expect (e.g. a-type)? c) Use Table 6.2 (Bernath, page 196) to calculate the frequencies of the allowed Δ J = 1 transitions for J’ = 2 and J” = 1. 4. Radioastronomers are able to detect molecules containing unusual isotopes. At what frequency should an astronomer search for the J = 1 ->0 transition of 13 CO? You can estimate B from the 12 CO value of 57.6 GHz....
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