Deck 11: Molecular Spectroscopy

Question 1

Boron trifluoride, BF₃, has a three-fold symmetric planar equilibrium geometry with a B-F bond length of 1.30 Å. Calculate the moment of inertia for rotation about the three-fold axis of symmetry perpendicular to the molecular plane.

A) 9.63  10^-19 kg m²
B) 5.33  10^-46 kg m²
C) 1.60  10^-45 kg m²
D) 8.00  10^-46 kg m²

Answer 1

C

Question 2

The bond length in a nitric oxide molecule, NO, is 1.15 Å. Calculate the rotational constant.

A) 322 GHz
B) 126 GHz
C) 0.591 GHz
D) 51.2 GHz

Answer 2

D

Question 3

Calculate the angular momentum of a molecule with a rotational quantum number J = 3.

A) √12 ℏ
B) 3ℏ
C) 9ℏ
D) 12ℏ

Answer 3

A

Question 4

What is the degeneracy of the rotational level with quantum number J = 6 in a linear molecule?

A) 13
B) 0
C) 1
D) 6

Question 5

The rotational constant of a hydrogen fluoride, HF, molecule is 3.12  10¹¹ s^-1. Predict which transition in the rotational absorption spectrum will be most intense at a temperature of 400 K.

A) from J = 0 to J = 1
B) from J = 1 to J = 2
C) from J = 2 to J = 3
D) from J = 3 to J = 4

Question 6

For which of the following molecules are pure rotational spectroscopic transitions observed?
Benzene, C₆H₆, Sulfur hexafluoride, SF₆, Carbon disulfide, CS₂, Nitrous oxide, N₂O.

A) Benzene, C₆H₆
B) Sulfur hexafluoride, SF₆
C) Carbon disulfide, CS₂
D) Nitrous oxide, N₂O

Question 7

The harmonic vibrational wavenumber of the ³²S¹⁶O isotopomer of sulfur monoxide is 1123.7 cm^-1. Calculate the force constant for the sulfur monoxide bond.

A) 79.4 mN m^-1
B) 794 N m^-1
C) 7.94 N m^-1
D) 7.94 N m^-1

Question 8

For chlorine monofluoride, ClF, the harmonic vibrational wavenumber is 793.2 cm^-1 and the anharmonicity is 0.0125. Calculate the wavenumber of the first vibrational overtone in the infrared absorption spectrum of chlorine monofluoride.

A) 793.2 cm^-1
B) 1526.9 cm^-1
C) 773.4 cm^-1
D) 1586.4 cm^-1

Question 9

Calculate the number of vibrational normal modes in methanol, CH₃OH.

A) 6
B) 9
C) 12
D) 13

Question 10

Spectroscopic vibration-rotation transitions in the P- and R-branches of the high-resolution infrared spectrum of hydrogen iodide, HI, are observed to be separated by a wavenumber of 6.37 cm^-1. Calculate the length of the bond of a hydrogen iodide molecule.

A) 1.03 Å
B) 10.3 Å
C) 0.728 Å
D) 7.83 Å

Question 11

A -* transition in hexa-1,3,5-triene, C₆H₈, corresponds to a separation between energy levels of 4.84 eV. Predict the wavelength of the corresponding maximum absorbance in the UV-visible spectrum of hexatriene.

A) 256 nm
B) 165 nm
C) 217 nm
D) 290 nm

Question 12

The absorbance of a solution of path length 10.0 cm that contained two cyanine dyes, A and B, was found to be 24.1 ? 10³ at a wavelength of 550 nm and 21.9 ? 10³ at a wavelength of 650 nm. Use the following data for the molar absorption coefficients of the dyes at these wavelengths to determine the concentration of dye A in the solution.
$\quad\quad\quad\quad\quad\quad\varepsilon /\left(10^{5} \mathrm{dm}^{3} \mathrm{~mol}^{-1} \mathrm{~cm}^{-1}\right)$
$\begin{array}{lcc} &\quad\quad 550 \mathrm{~nm} & \quad\quad650 \mathrm{~nm} \\\text { Dye A } & 1.48 & 0.24 \\\text { Dye B } & 0.56 & 2.29\end{array}$

A) 0.008 mol dm^-3
B) 0.020 mol dm^-3
C) 0.015 mol dm^-3
D) 0.025 mol dm^-3

Question 13

When monochromatic radiation of energy 21.22 eV from a helium lamp is used to irradiate a sample of nitrogen, N₂, gas in a photoelectron spectrometer, electrons are ejected with a maximum kinetic energy of 1.41  10⁶ m s^-1. Calculate the molar ionization energy of N₂.

A) 4.13  10³ kJ mol^-1
B) 2.60  10³ kJ mol^-1
C) 15.5 kJ mol^-1
D) 1.50  10³ kJ mol^-1

Question 14

In the photoelectron spectrum of carbon disulfide, CS₂, ionization from the highest occupied, 1_g, molecular orbital results in little vibrational structure. In contrast, ionization from the next lowest occupied 1_u molecular orbital results in a long vibrational progression in the ₁ symmetric stretching mode of the CS₂⁺ ion. Which of the following descriptions of the bonding in neutral CS₂ best explains these observations?

A) Both the 1_g and 1_u molecular orbitals of CS₂ are non-bonding in character.
B) The 1_g molecular orbital of CS₂ is antibonding in character and the 1_u orbital is non-bonding in character.
C) The 1_g molecular orbital of CS₂ is nonbonding in character and the 1_u orbital is bonding in character.
D) Both the 1_g and 1_u molecular orbitals of CS₂ are antibonding in character.

Question 15

When radiation of wavelength 495 nm from a monochromatic flash lamp of power 0.500 kW is used to irradiate a low-pressure sample of iodine vapour, I₂, the rate of production of iodine atoms is 3.24  10¹⁹ s^-1. Assuming that all of the photons emitted by the lamp are absorbed by the iodine vapour, calculate the quantum yield for dissociation of iodine molecules.

A) 0.026
B) 0.070
C) 0.052
D) 0.013

Question 16

For a particular substituted stilbene dendrimer the quantum yield for fluorescence following electronic excitation is 0.14, with the observed lifetime of the excited state 4.6 ns. Calculate the rate constant for fluorescence.

A) 33  10³ s^-1
B) 30  10⁶ s^-1
C) 1.6  10⁹ s^-1
D) 6.4  10^-10 s^-1

Question 17

The lifetime of an excited electronic state is 2.9 ns in the absence of a quencher and 1.7 ns if a quencher is present. What is the quantum yield for quenching?

A) 0.83
B) 0.71
C) 0.59
D) 0.41

Question 18

The observed lifetime of an excited electronic state of a porphyrin-like metal complex was determined to be 0.35 ns, with rate constants for fluorescence and intersystem crossing of 0.6  10⁹ s^-1 and 1.8  10⁹ s^-1 respectively. Determine the rate constant for non-radiative internal conversion.

A) 0.5  10⁹ s
B) 3.0  10⁹ s^-1
C) 2  10^-9 s^-1
D) 1.2  10⁹ s^-1

Question 19

In an experiment to investigate the decay of photoexcited tryptophan, the observed lifetime of the excited state was measured for various concentrations of oxygen, O₂, which acted as a quencher. By constructing a Stern-Volmer plot of the following data, determine the rate constant for fluorescence quenching.
$\begin{array}{llllll}{\left[\mathrm{O}_{2}\right] / \mathrm{mol} \mathrm{dm}^{-3}} & 0.02 & 0.04 & 0.06 & 0.08 & 0.10 \\\tau_{\text {pbs }}\left(\mathrm{O}_{2}\right) / \mathrm{ns} & 1.64 & 1.18 & 0.91 & 0.74 & 0.63\end{array}$

A) 12.3 ? 10^-9 mol^-1 dm³ s^-1
B) 2.7 ? 10^-9 mol^-1 dm³ s^-1
C) 15.9 ? 10^-9 mol^-1 dm³ s^-1
D) 10.7 ? 10^-9 mol^-1 dm³ s^-1

Question 20

In an experiment to investigate the folding of tethered labelled peptides using fluorescence resonant energy transfer, the quantum yield for fluorescence of a rhodamine dye donor was found to decrease, on average, by a factor of 0.21 in the presence of a Texas red dye acceptor. Use the Förster theory of resonant energy transfer to determine the separation of the donor-acceptor pair, given that the Förster distance parameter for the rhodamine-Texas red pair is R₀ = 4.4 nm.

A) 4.4 nm
B) 3.5 nm
C) 21.0 nm
D) 0.86 nm