CHM 3411

Problem Set 10

Recommended Discussion questions: 13.1-6. Recommended Excercises (Ch. 13, all b): 2-6, 8, 14, 16, 17, 23. Due Monday, April 13.

I. Rotational spectroscopy (microwave and rotational Raman)

1. Atkins Exercises 13.12b, 13.13b, 13.15b.

2. The following two rotational transitions are observed in the microwave spectrum of ¹²C¹⁶O in the region 500 Hz to 700 GHz. (1 GHz = 10⁹ Hz = 10 s^-1. Herz (Hz) is a unit of frequency (n) and is used as an alternative “energy unit” to wavenumber (, cm^-1) for measuring rotational transitions. To convert between the two, multiply or divide by c, the speed of light.)

transition relative intensity

579.01 0Hz 1.00

694.81 0Hz’ 1.19

No other transitions are seen in the above frequency range. Assume that r_e is independent of isotopic composition (a reasonable assumption). The following information will be useful:

¹²C 12.0000 amu ¹⁶O 15.9949 amu ¹⁴C 14.0033 amu

a. What is the value of B, the rotational constant, for ¹²C¹⁶0? Give your answer both in units of GHz and cm^-1.

b. From the value of B, calculate the equilibrium bond length, r_e.

c. Assign the rotational transitions above (that is, give the initial and final values of J for each transition).

d. From the relative line intensities, estimate the temperature at which the spectrum was taken.

e. Calculate the frequencies (in GHz) of the corresponding rotational transitions for ¹⁴C¹⁶O.

II. Vibrational-rotation spectroscopy (Infrared and vibrational Raman)

3. Atkins Exercises 13.22b, 13.23b

4. Atkins Problem 13.12

Extra Credit (worth one problem set): Atkins Problem 13.6

5. Atkins, Problem 13.6.