Problem Set #8
Note:Relevant Chapters in Mortimer are Chapters 19 and 20.
Please note that where is expressed in cm-1; and where is expressed in Hz.
Rotating Diatomic Molecules
1. For a diatomic molecule in a electronic state, we observe a microwave transition from J = 1 to J = 2 in the presence of an electric field. How many lines will appear in the spectrum?
2. Which of the following diatomic molecules have a rotational microwave spectrum: IF, , KCl, .
3. Calculate the bond length of using and the reduced mass is .
Vibrating Diatomic Molecules
4. Which of the following vibrational transitions will be observed for a diatomic molecule (treated as a harmonic oscillator): v = 1 to v = 3; v = 2 to v = 3; v = 5 to v = 4.
5. Calculate the frequency of the J = 3 to J = 4 transition in the pure rotational absorption spectrum of . The equilibrium bond length is 115 pm. Assume no centrifugal distortion. The mass of a nitrogen atom is 14.003 amu; the mass of an oxygen atom is 15.995 amu; and the conversion factor is .
Rotation of Polyatomic Molecules
6. Identify the molecules that will exhibit a pure rotational absorption microwave spectrum:
7. What information about the molecular geometry for can be determined from knowing that a pure rotational absorption spectrum is observed for this molecule?
8. The moment of inertia about an axis perpendicular to the principal axis for is . There are different types of rigid rotors: linear, spherical top, prolate symmetric top, oblate symmetric top, asymmetric top. Which type of rotor is ? Calculate the separation (expressed in ) of the pure rotational spectrum lines for . Hint: The moment of inertia about the principal axis is given by , where the mass of a hydrogen atom = mH = ; the N-H bond length = R = ; and the bond angle is 106.78° . The moment of inertia about the principal axis is .
9. The molecule is a prolate symmetrical top with and . Calculate the energy corresponding to J = 2 and K = ± 1.
Vibration of Polyatomic Molecules
10. Consider the vibrational mode that corresponds to the uniform expansion of the benzene ring. Is it infrared active?
11. Explain the difference between Stokes and anti-Stokes lines in Raman Spectroscopy.