Radiation from a mercury lamp source is of energy 2.845 eV.  Calculate the wavelength of the radiation.

Electrons are produced through the photoelectric effect when electromagnetic radiation of wavelength 434 nm is used to irradiate caesium metal.  Given that the work function of caesium is 2.10 eV, determine the kinetic energy of the photons ejected.

Determine the de Broglie wavelength of an electron with a kinetic energy of 1.00 eV.

An electron in a carbon nanofibre is effectively confined within a region of length 100 nm.  What is the minimum uncertainty in the speed of the electron?

Calculate the quantum-mechanical zero-point energy of an electron confined within a one-dimensional box of length 1.0 nm.

The electrons within the p system of conjugated hydrocarbons may be treated as particles confined within a one-dimensional box.  The lowest energy transition in the spectrum of buta-1,3-diene, C₄H₆, corresponds to excitation of an electron from the highest occupied energy level to the lowest unoccupied level and is observed in the ultraviolet region of the spectrum at a wavelength of 210 nm.  Estimate the effective length of buta-1,3-diene.

An electron is confined to a circular ring of diameter 1.1 Å.  Calculate the energy of the first excited rotational level.

The force constant of the bond in a hydrogen chloride, HCl, molecule is 516 N m^–1.  Calculate the vibrational potential energy of an HCl molecule with a bond that is extended from its equilibrium length by 0.11 Å.

The vibrational frequency of an ¹H⁸⁰Br molecule is 79.5 THz. By treating the vibration as the oscillation of the hydrogen atom with the heavier bromine atom stationary, predict the vibrational frequency of the ²D⁸⁰Br isotopomer.

How many nodes are expected for the vibrational wavefunction with quantum number v = 4?