14.68.Determine the number of Raman-active vibrations for
the following molecules. You may have to determine their
symmetry first.
(a)CH 4 (b)CH 3 Cl (c)CH 2 Cl 2 (d)CHCl 3 (e)CCl 4
Compare your results with the answers to exercise 14.54,
above.
14.69.The mutual exclusion rulestates that for certain mole-
cules, vibrations that are IR-active are not Raman-active, and
vice versa. Molecules must have a certain symmetry element
in order for the mutual exclusion rule to apply. Examine the
character tables in Appendix 3 and determine what that sym-
metry element is.
14.70.Is xenon tetrafluoride, XeF 4 , tetrahedral or square pla-
nar? IR and Raman spectra each show three vibrations. Use the
GOT and analyses like those in Examples 14.19 and 14.22 to
propose a structure for this molecule.
14.71.Several equations can be derived from equations 14.41
and 14.42 and used to determine, graphically or numerically,
the various molecular parameters for a molecule from rovibra-
tional spectral data: Two of them are
B 1 2 DJ(J^2 J 1)B 0 2 DJ(J^2 J 1)where R(J) is the line in the Rbranch that originates from the
Jrotational level and P(J) is the line in the Pbranch that orig-
inates from the Jrotational level. Use the following data to
R(J1) P(J^ 1)
4(J ^12 )R(J) P(J)
4(J ^12 )determine B 0 , B 1 , and DJfor HCl. All numbers are in units
of cm^1.R(0) 2906.047
P(1) 2864.825 R(1) 2925.814
P(2) 2843.370 R(2) 2944.859
P(3) 2821.433 R(3) 2963.180
P(4) 2798.773 R(4) 2980.777
P(5) 2775.631 R(5) 2997.893
P(6) 2751.765 R(6) 3014.286
P(7) 2727.658 R(7) 3029.95514.72.Use equation 14.17 to determine the energies of ro-
tation for ammonia, NH 3 , as the rotational quantum number
Jranges from 1 to 10. (IaIb4.413
10 ^47 kg m^2 , Ic
2.806
10 ^47 kg m^2 ) Then, construct an energy level dia-
gram for all of the rotational levels, and label them with Jand
Kquantum numbers. What are the degeneracies of the levels?
14.73.What are the energy changes for the allowed rota-
tional transitions from the energy level diagram constructed in
exercise 14.72?
14.74.Construct and compare the energy level diagrams for
the rotations of a diatomic molecule assuming it acts as a rigid
rotor (equation 14.21) and a rigid rotor with centrifugal dis-
tortion corrections (equation 14.26). Use HBr as a model sys-
tem, where B8.473 cm^1 and DJ3.72
10 ^4 cm^1.
Compare rotational levels up to J20.
14.75.Construct and compare energy level diagrams for vi-
brations of an ideal harmonic oscillator and an anharmonic os-
cillator. Use HCl as a model oscillator, and compare levels up
to v25. Use e2989.74 cm^1 and exe52.05 cm^1.518 Exercises for Chapter 14
Symbolic Math Exercises