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

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.

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

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

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

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.

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

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.

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. 

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

Transitions in the high-resolution infrared spectrum of ¹²C¹⁶O are observed at wavenumbers of 2131.4, 2135.3, 2139.2, 2146.2, 2150.7, 2154.1 cm^–1. Determine the rotational constant.

The absorbance of a solution of two laser dyes, cresyl violet and oxazine, was found to be 7.30 ´ 10^–7 at a wavelength of 350 nm and 7.06 ´ 10^–6 at a wavelength of 550 nm for a path length of 1.0 cm.  Use the following data for the molar absorption coefficients of the dyes at these wavelengths to determine the concentration of cresyl violet in the solution.

The longest wavelength absorption in the UV visible spectrum of acetone, CH₃COCH₃, occurs at 335 nm.  Predict the energy required to excite an electron from a lone pair orbital on the oxygen atom to an antibonding orbital centred on the carbonyl group.

The first ionization energy of nitric oxide, NO, is 9.27 eV.  Calculate the velocity of the photoelectrons ejected when a sample of nitric oxide gas using radiation of energy 21.22 eV from a helium lamp source.

The first band in the photoelectron spectrum of hydrogen, H₂, occurs close to 15.4 eV and consists of a progression of peaks separated by 285 eV corresponding to transitions to excited vibrational states of the H₂⁺ ion.  Calculate the wavenumber of the vibration of the lowest electronic state of the H₂⁺ ion.

The second band in the photoelectron spectrum of oxygen, O₂, at 17 eV corresponds to ionization to the excited A²P_u state of the O₂⁺ ion.  The band consists of a long vibrational progression of peaks separated by approximately 900 cm^­–1.  The vibrational wavenumber of the ground X³S_g electronic state of a neutral oxygen molecule is 1580 cm^–1.   Which of the following statements is consistent with the observed photoelectron spectrum?

When a solution of iodine, I₂, molecules in tetrachlorometane solution is irradiated with radiation of wavelength 436 nm from a 50 W lamp source, the rate of production of iodine atoms by photodissociation when total absorption occurs is 1.45 × 10²⁰ s^–1.  Calculate the quantum yield for photodissociation.

The quantum yield for the quenching of an excited fluorescing state was measured to be 0.34 with a lifetime of 4.1 ns.  Calculate the lifetime of the state in the absence of a quencher.

The decay of photoexcited propanone in the presence of dicyanoethene in solution was investigated by measuring the fluorescence lifetime of the excited state for different concentrations of quencher.  By constructing a Stern–Volmer plot of the following data, determine the rate constant for quenching.

Chlorophyll molecules act as both donors and acceptors in fluorescence resonance energy transfer.  The fluorescence lifetime of chlorophyll molecules in a dilute solution of an organic solvent wa found to be 1.2 ns.  When chlorophyll molecules were instead embedded in a biopolymer, the fluorescence lifetime was measured to be 820 ps.  Given that R₀ = 5.6 nm for chlorophyll molecules, estimate the separation between the donor–acceptor pairs in the polymer.