Exam 20: Quantum Physics of Molecules and Solids

The rotation spectrum of the HCl molecule has been observed in the far infrared, around 50 * 10-6 m.The spacing between successive lines in the spectrum corresponds to radiation of wavelength equal to 5 microns (1 $\mu$ m = 10-6 m).Determine the frequency of the photon associated with this transition.

In the hydrogen molecule, H2, the separation between the protons is 10-10 m.If the molecule is in its first rotational energy state, what is the angular velocity of the molecule about its centre of mass?

A molecule makes a transition from the J = 1 to the J = 0 rotational energy state.The wavelength of the emitted photon is 2.6* 10-3 m.What is the moment of inertia of the molecule (in kg .m2)?

The diagram below shows the distance between the nuclei, pA and pB, and the electrons, e1 and e2, in a hydrogen molecule.We would expect the electrostatic potential energy of this molecule to be:

The fundamental frequency of CO is 6.42 *1013 Hz.If the atomic masses are 12 u and 16 u (1 u = 1.66 *10-27 kg), find the force constant (in N/m) for the diatomic molecule.

The rotation spectrum of the HCl molecule suggests a photon in the far infrared (around 5.0 *10-6 m) can excite the first rotational level.From this data, the moment of inertia of the HCl molecule (in kg . m2) is:

The rotational kinetic energy of a diatomic molecule can take the form:

In the Lennard-Jones model of the hydrogen molecule, the potential is given by .In this model, the minimum internuclear separation, r0, is:

The energy released when an atom takes an electron is called:

When a molecule jumps from a rotational energy level characterised by the rotational quantum number J to one characterised by J + 1, the change in energy, EJ + 1 - EJ, is:

The difference between donor and acceptor atoms in a doped semiconductor is that:

The energy gap for germanium is 0.670 eV at room temperature.What wavelength must a photon have (in nm) to excite the electron to the conduction band?

The dissociation energy of the hydrogen molecule is approximately 5 eV.What is the temperature of a monatomic molecule whose kinetic energy is equal to 5.000 eV?

Because HF, hydrogen fluoride, is a covalent gaseous molecule at room temperature, we might reasonably expect that at room temperature HCl, hydrogen chloride, is:

When a molecule jumps from a rotational energy level characterised by the rotational quantum number J to one characterised by J- 1, the difference in energy of levels J and J -1, EJ - EJ - 1, is:

In comparing vibrational and rotational levels in molecules, we find that the energy separation between adjacent energy levels is:

The moment of inertia of a CO molecule is 1.46 *10-46 kg . m2.What is the wavelength of the photon emitted if a rotational transition occurs from the J = 3 to the J = 2 state?

To find the number of electrons per unit volume with energy between E and E + dE in a metal we must multiply the number of allowed states per unit volume with energy E by:

The Fermi energy of a metal at a temperature T is 7.0 eV.What is the average energy (in eV) of a conduction electron at that temperature?

The energy gap for a semiconductor is 1.25 eV.Of the frequencies given below, what is the minimum frequency photon than can move an electron from the valence band to the conduction band?