PHY.K03 Solid State Physics Exercise Exam
02.05.2023

1. Rotational and vibrational spectra

The interatomic distance of a 1H35Cl molecule is $r_e = 1.2745$ Å.

(a) Calculate the reduced mass of this molecule. The atomic mass constant is, $u = 1.66 \times 10^{-27}$ kg.

(b) What is the rotational energy for $J = 5$ using the rigid rotator approximation?

(c) Calculate the frequency, the wavelength, and the wavenumber of the rotational transition $J = 4 \rightarrow J = 5$.

$$\hbar = 6.58 \times 10^{-16} \text{ eVs,}\qquad c = 299792458 \text{ m/s,}\qquad e = 1.6 \times 10^{-19}\text{ C}$$

2. Bond potential

The potential energy of a diatomic molecule as a function of the interatomic distance $r$ is,

$$U(r)=\frac{-A}{r^6} + \frac{B}{r^{12}}$$

The equilibrium interatomic distance was experimentally determined to be 3 Å and the binding energy was experimentally determined to be 18 meV.

(a) Sketch the bond potential and indicate the two experimentally determined quantities in the drawing.

(b) Show that the equilibrium interatomic distance is $r_e=\left(\frac{2B}{A}\right)^{1/6}$.

(c) What kind of bond is this?

3. Bravais lattice

Silver forms an fcc crystal structure. The distance to the nearest neighbor atoms is 2.87 Å.

(a) How many nearest neighbor atoms does a silver atom have in this crystal structure?

(b) What is the length of a side of the conventional unit cell?

(c) Draw the arrangement of the atoms in the Ag(110) plane. The Miller indices are indexed using the conventional unit cell. Label the directions in your drawing with Miller indices.