23.8 Other Types of Spectroscopy 999
the splittings between lines. Assume that the harmonic
oscillator–rigid rotor energy level formula applies.
c.Describe the Stokes band of the rotational Raman
spectra of the two substances, including the Raman
shifts of the first four lines.
d.Describe the fundamental Stokes band of the
vibrational Raman spectra of the two substances,
including the Raman shifts of the first two lines in the
OandSbranches.23.60Consider the ozone molecule:
a.Draw the electron dot structure as you would in
freshman chemistry. Is resonance necessary? If it is,
include the principal resonance structures. Assign
formal charges.
b.What is the shape of the molecule?
c.Is the molecule polar?
d.What vibrational normal modes would you expect to
occur? List them in order of increasing frequency.
e.What normal modes will produce infrared absorption
bands?23.61a.Calculate the reciprocal wavelength of the band center
of the fundamental vibrational band of the CO
molecule, using the expression for the corrected
energy levels in Eq. (22.2-50) and information from
Table A.22 of Appendix A. Compare your value with
the value from the uncorrected energy level
expression.
b.Calculate the reciprocal wavelength of the band center
of the first overtone band of the CO molecule, using
the expression for the corrected energy levels and
information from Table A.22 of Appendix A. Compare
this reciprocal wavelength with double the reciprocal
wavelength from part a. Compare your value with the
value from the uncorrected energy level expression.
c.Calculate the reciprocal wavelength of the first line of
the microwave spectrum of the CO molecule using the
corrected energy level expression. Compare your
value with the value from the uncorrected energy level
expression.
d.Calculate the reciprocal wavelength of the second line
of the microwave spectrum of the CO molecule using
the corrected energy level expression. Compare your
value with the value from the uncorrected energy level
expression.
23.62Describe qualitatively the following spectra:
a.The microwave spectrum of CH 4.
b.The infrared spectrum of CO 2.
c.The emission spectrum of atomic hydrogen.
23.63There is a vibrational normal mode of benzene in which
all of the carbons rise above the plane of the molecule as
all of the hydrogens move below the plane of the
molecule. Will this normal mode be seen in the infrared
spectrum of benzene? Will it be seen in the Raman
spectrum of benzene? Explain your answer.
23.64a.Write a computer program to calculate the reciprocal
wavelength of the spectral lines in the fundamental
band of the vibration–rotation spectrum of a diatomic
molecule, using the corrected energy level expression
of Eq. (23.2-50). Use the program to calculate the
reciprocal wavelengths of the band center, of the first
15 lines in thePbranch, and of the first 15 lines in the
Rbranch of the HCl fundamental band, using
information from Table A.22 of Appendix A.
b.Use the program to repeat the calculation of part a for
the first overtone band of HCl.
c.Modify your program to calculate the reciprocal
wavelengths of the lines in the microwave spectrum of
a diatomic molecule. Use the program to calculate the
reciprocal wavelengths of the first 15 lines of the
microwave spectrum of HCl.
23.65Write a computer program to calculate the relative
intensities of the spectral lines in the fundamental band
of the vibration–rotation spectrum of a diatomic
molecule, assuming that the absorbance is displayed in
the spectrum. Set the maximum absorbance of the first
line of thePbranch equal to 1. Assume the Boltzmann
probability distribution and assume that the transition
dipole moments for all transitions are equal. Use your
program to calculate the relative intensities for the
first 15 lines in each branch of the HCl spectrum
at 298 K.23.66Using information from Table A.22 of Appendix A,
consider the HF molecule.
a.Find the value of the moment of inertia.
b.Find the value of the force constant.
c.Draw a simulated microwave spectrum, assuming that
the temperature is 298 K and using reciprocal
centimeters as the independent variable. Use the
uncorrected energy levels. Assume that the transition