Exam 20: Quantum Physics of Molecules and Solids

The smallest object one can distinguish using the electron microscope is on the order of one nanometer (1 nm = 10-9 m).How many atoms of gold are contained in a cube whose edge is 1 nm long? The atomic mass of gold is 197 and its density is 19.3 g/cm3.

When calculating the rotational kinetic energy of a diatomic molecule, with atoms of mass m1 and m2,the moment of inertia about an axis passing through the molecule's centre of mass, with r the atomic separation, is:

How many degrees of freedom does a diatomic molecule have?

The Fermi temperature of copper is 80 000 K.The corresponding Fermi energy (in eV) is:

The force constant of HCl is 480 N/m.If the atomic masses are 1 u and 35 u (1 u = 1.66 *10-27 kg), find the fundamental frequency (in Hz).

A diatomic molecule consists of two point masses, m1 and m2, separated by a distance r.If x is the distance from m1 to the centre of mass, find the moment of inertia in terms of x about an axis parallel to the molecular axis through the centre of mass.

A diatomic molecule consists of two point masses, m1 and m2, separated by a distance r.Find the moment of inertia through the centre of mass about an axis perpendicular to the molecular axis.

If an electric field is applied to a metal:

The energy of a molecule can normally be divided into the following categories:

Solid argon has a density of 1650 kg/m3.The atomic weight of argon is 40.0.Assuming each atom occupies a cubical volume, what is the distance between the argon atoms?

Assume a diatomic molecule can be considered to be two point masses separated by a distance r.The centre of mass of the system is located a distance x from m1, equal to:

The frequency of a microwave absorbed by a molecule when changing from the J = 3 to J = 4 rotation energy state is 4.61 * 1011 Hz.The moment of inertia of the molecule (in kg . m2) is:

The Fermi temperature is:

A diatomic molecule consists of two point masses, m1 and m2, separated by a distance r.If x is the distance from m1 to the centre of mass, find the moment of inertia in terms of x about an axis perpendicular to the molecular axis through the centre of mass.

What is the energy of the first rotational state of the hydrogen (H2) molecule? The separation between the protons is 10-10 m and the mass of each proton is 1.67 *10-27 kg.(h = 6.626 * 10-34 J . s and 1 eV = 1.6 *10-19 J.)

Assume the angular momentum of a diatomic molecule is quantised according to the relation .What are the allowed rotational kinetic energies?

An energy band in a solid consists of:

The fundamental frequency of HF is 8.72 * 1013 Hz.The energy associated with a transition from the 10th to the 9th vibrational quantum number (in eV) is:

The wave functions of some molecules are a combination of wave functions with different values of the orbital quantum number .The wave function of PF5 combines s, p and d states in an sp3d hybrid orbital.We would expect such an overlap of wave functions in individual molecules to represent:

An oxygen molecule has a moment of inertia of 5 * 10-46 kg . m2.Calculate the bond length (in nm).Recall that the atomic mass of oxygen is 16 u (1 u = 1.66 * 10-27 kg).