Problem Set 6: Quantum Mechanics: Spectroscopy
1. Which of the following molecules will exhibit pure rotational (microwave)
absorption spectra: CH4, HCl, CH3Cl, and H2 ?
2. Which of the following molecules will exhibit vibrational (infrared) absorption
spectra: N2, HCl, and CH4 ?
3. The rotational transition from J = 2 to J = 3 for the H1Cl35 molecule occurs at a
wavenumber of 63.56 cm-1. From this information, and the atomic weights for H1
and Cl35, use the rigid rotor approximation to estimate the bond length of the
H1Cl35 molecule.
4. The molecules H1I127 and H1F19 show pure vibrational absorption transitions at
the following wavenumbers: 2309 cm-1 for H1I127, and 4141 cm-1 for H1F19. From
these data, estimate the force constants for the H-I and H-F bonds.
5. Using your results from Problem (4) above: next, consider the molecules D2F19
and D2I127, where “D2” represents deuterium. Assume that the force constants for
the bonds in D2I127 and D2F19 are the same as those for H1I127 and H1F19. Calculate
the wavenumbers for the pure vibrational transitions in D2I127 and D2F19.
6. The H1Cl35 molecule is observed to have the following vibrational transitions: (i)
from n = 0 to n = 1 at 2885.9 cm-1, and: (ii) from n = 0 to n = 2 at 5668.0 cm-1.
Based on these data, and the Morse potential model for an anharmonic oscillator,
estimate: (i) the wavenumber corresponding to the transition from n = 0 to n = 3,
and (ii) the dissociation energy for the H1Cl35 molecule.
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