296 5 Solid State Physics5.19 The resistivity of a certain material is 1. 72 × 10 −^8 Ωm whilst the Hall coeffi-
cient is− 0. 55 × 10 −^10 m^3 C
− 1. Deduce:
(a) The electrical conductivity (σ)
(b) Mobility (μ)
(c) The inter-collision time (τ)
(d) Electron density (n)5.20 In a Hall effect experiment on zinc, a potential of 4. 5 μV is developed across
a foil of thickness 0.02 mm when a current of 1.5 A is passed in a direction
perpendicular to a magnetic field of 2. 0 T. Calculate:(a) The Hall coefficient for zinc
(b) The electron density5.21 The density of states function for electrons in a metal is given by:
Z(E)dE= 13. 6 × 1027 E^1 /^2 dE
Calculate the Fermi level at a temperature few degrees above absolute zero
for copper which has 8. 5 × 1028 electrons per cubic metre.
5.22 Using the results of Problem 5.21, calculate the velocity of electrons at the
Fermi level in copper.
5.23 For silver (A = 108), the resistivity is 1. 5 × 10 −^8 Ωmat0◦C density is
10. 5 × 103 kg/m^3 and Fermi energyEF= 5 .5 eV. Assuming that each atom
contributes one electron for conduction, find the ratio of the mean free pathλ
to the interatomic spacing d.
5.24 Calculate the average amplitude of the vibrations of aluminum atoms at 500 K,
given that the force constantK=20 N/m.
5.25 The Fermi energy in gold is 5.54 eV (a) calculate the average energy of the free
electrons in gold at 0◦K. (b) Find the corresponding speed of free electrons (c)
What temperature is necessary for the average kinetic energy of gas molecules
to posses this value?
5.26 The density of copper is 8.94 g/cm^3 and its atomic weight is 63.5 per mole,
the effective mass of electron being 1.01. Calculate the Fermi energy in copper
assuming that each atom gives one electron.
5.27 Find the probability of occupancy of a state of energy (a) 0.05 eV above
the Fermi energy (b) 0.05 eV below the Fermi energy (c) equal to the Fermi
energy. Assume a temperature of 300 K.
5.28 What is the probability at 400 K that a state at the bottom of the conduction
band is occupied in silicon. Given thatEg= 1 .1eV5.29 The Debye temperatureθfor iron is known to be 360 K. Calculateνm,the
maximum frequency.