Irodov Solutions → Atomic and Nuclear Physics → Molecules and Crystals 
6.169. Find the angular momentum of an oxygen molecule whose rotational energy is E = 2.16 meV and the distance between the nuclei is d = 121 pm.
6.190. Calculate the zeropoint energy per one gram of copper whose Debye temperature is Θ = 330 K.
6.196. Evaluate the maximum values of energy and momentum of a phonon (acoustic quantum) in copper whose Debye temperature is equal to 330 K.
6.197. Employing Eq. (6.4g), find at T = 0:
6.198. What fraction (in per cent) of free electrons in a metal at T = 0 has a kinetic energy exceeding half the maximum energy?
6.199. Find the number of free electrons per one sodium atom at T = 0 if the Fermi level is equal to E_{F} = 3.07 eV and the density of sodium is 0.97 g/cm^{3}.
6.200. Up to what temperature has one to heat classical electronic gas to make the mean energy of its electrons equal to that of free electrons in copper at T = 0? Only one free electron is supposed to correspond to each copper atom.
6.201. Calculate the interval (in eV units) between neighbouring levels of free electrons in a metal at T = 0 near the Fermi level, if the concentration of free electrons is n = 2.0*10^{22} cm^{3} and the volume of the metal is V = 1.0 cm^{3}.
6.205. The increase in temperature of a cathode in electronic tube by ΔT = 1.0 K from the value T = 2000 K results in the increase of saturation current by η = 1.4%. Find the work function of electron for the material of the cathode.
6.206. Find the refractive index of metallic sodium for electrons with kinetic energy T = 135 eV. Only one free electron is assumed to correspond to each sodium atom.
6.207. Find the minimum energy of electronhole pair formation in an impurityfree semiconductor whose electric conductance increases η = 5.0 times when the temperature increases from T_{1} = 300 K to T_{2} = 400 K.
6.208. At very low temperatures the photoelectric threshold short wavelength in an impurityfree germanium is equal to λ_{th} = 1.7 μm. Find the temperature coefficient of resistance of this germanium sample at room temperature.
6.209. Fig. 6.11 illustrates logarithmic electric conductance as a function of reciprocal temperature (T in kK units) for some ntype semiconductor. Using this plot, find the width of the forbidden band of the semiconductor and the activation energy of donor levels.
6.210. The resistivity of an impurityfree semiconductor at room temperature is ρ = 50 Ω*cm. It becomes equal to ρ_{1} = 40 Ω*cm when the semiconductor is illuminated with light, and t = 8 ms after switching off the light source the resistivity becomes equal to ρ_{2} = 45 Ω*cm. Find the mean lifetime of conduction electrons and holes.
6.212. In Hall effect measurements in a magnetic field with induction B = 5.0 kG the transverse electric field strength in an impurityfree germanium turned out to be η = 10 times less than the longitudinal electric field strength. Find the difference in the mobilities of conduction electrons and holes in the given semiconductor.
6.213. The Hall effect turned out to be not observable in a semiconductor whose conduction electron mobility was η = 2.0 times that of the hole mobility. Find the ratio of hole and conduction electron concentrations in that semiconductor.
