# 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. Free solution >> 6.190. Calculate the zero-point energy per one gram of copper whose Debye temperature is Θ = 330 K. Free solution >> 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. Free solution >> 6.197. Employing Eq. (6.4g), find at T = 0: (a) the maximum kinetic energy of free electrons in a metal if their concentration is equal to n; (b) the mean kinetic energy of free electrons if their maximum kinetic energy Tmax is known. Free solution >> 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? Free solution >> 6.199. Find the number of free electrons per one sodium atom at T = 0 if the Fermi level is equal to EF = 3.07 eV and the density of sodium is 0.97 g/cm3. Free solution >> 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. Free solution >> 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*1022 cm-3 and the volume of the metal is V = 1.0 cm3. Free solution >> 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. Free solution >> 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. Free solution >> 6.207. Find the minimum energy of electron-hole pair formation in an impurity-free semiconductor whose electric conductance increases η = 5.0 times when the temperature increases from T1 = 300 K to T2 = 400 K. Free solution >> 6.208. At very low temperatures the photoelectric threshold short wavelength in an impurity-free germanium is equal to λth = 1.7 μm. Find the temperature coefficient of resistance of this germanium sample at room temperature. Free solution >> 6.209. Fig. 6.11 illustrates logarithmic electric conductance as a function of reciprocal temperature (T in kK units) for some n-type semiconductor. Using this plot, find the width of the forbidden band of the semiconductor and the activation energy of donor levels. Free solution >> 6.210. The resistivity of an impurity-free semiconductor at room temperature is ρ = 50 Ω*cm. It becomes equal to ρ1 = 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 ρ2 = 45 Ω*cm. Find the mean lifetime of conduction electrons and holes. Free solution >> 6.212. In Hall effect measurements in a magnetic field with induction B = 5.0 kG the transverse electric field strength in an impurity-free 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. Free solution >> 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. Free solution >>