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Question 1

Calculate the moment of inertia for a tetrafluoromethane, CF₄, molecule. The C-F bond length in tetrafluoromethane is 1.315 Å.

a) 1.455 × 10^-⁴⁵ kg m²

b) 5.456 × 10^-⁴⁶ kg m²

c) 1.637 × 10^-⁴⁵ kg m²

d) 3.286 × 10^-⁴⁵ kg m²

Question 2

The A rotational constant of a phosphorus pentafluoride, PF₅, molecule is 3.566 Hz. Calculate the lengths of the equatorial P-F bonds.

a) 2.731 Å

b) 1.577 Å

c) 1.109 Å

d) 1.325 Å

Question 3

What is the degeneracy of the rotational energy level with J = 4 for a heteronuclear diatomic molecule?

a) 1

b) 2

c) 4

d) 9

Question 4

For the linear molecule nitrous oxide, N₂O, predict which rotational energy level will be most populated for a temperature of 300 K. The rotational constant of nitrous oxide is 0.419 cm^-¹.

a) 0

b) 1

c) 15

d) 12

Question 5

Lines in the rotational microwave spectrum of carbon monoxide, CO, were observed at the following frequencies. Calculate the centrifugal distortion constant for carbon monoxide.
Q.10 data

a) 756 kHz

b) 189 kHz

c) 578 kHz

d) 1158 kHz

Question 6

Calculate, as a wavenumber, the Doppler width of a transition in the vibration-rotation spectrum of carbon dioxide that occurs at a wavelength of 9.1μm for a temperature of 300 K.

a) 0.205 m^-¹

b) 0.002 cm^-¹

c) 0.170 cm^-¹

d) 0.059 cm^-¹

Question 7

Transitions in the rotational spectrum of electronically excited gas-phase aluminium hydride, AlH, have a width of 0.85 cm^-¹ because of lifetime broadening. Estimate the lifetime of the excited state.

a) 0.16 ps

b) 4.5 ps

c) 5.3 ps

d) 6.2 ps

Question 8

The rotational structure in the Raman spectrum of carbon dioxide, CO₂, is offset from the wavenumber of the incident radiation by 2.3622 cm^-¹, 5.5118 cm^-¹, 8.6614 cm^-¹, ... . Determine the rotational constant of carbon dioxide.

a) 0.3937 cm^-¹

b) 1.1811 cm^-¹

c) 0.5906 cm^-¹

d) 2.3622 cm^-¹

Question 9

Calculate the force constant for a Br-Br bond, given that the harmonic vibrational wavenumber of the ⁷⁹Br⁸¹Br isotopomer of the bromine molecule is 323.2 cm^-1.

a) 246 N m^-¹

b) 984 N m^-¹

c) 323 N m^-¹

d) 107 N m^-¹

Question 10

How many normal modes of vibrational are possible for a benzene molecule?

a) 6

b) 30

c) 12

d) 31

Oxford University Press, Online Resource Centre, Chapter 19.

Chapter 19

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