Electrical conductivity
1 A certain conductor has a free electron concentration of 5.9 x 1028 m-3. What current density
in the conductor will correspond to a drift velocity of 1/1.6 mm s-1.
2 Calculate the free electron concentration, mobility, drift velocity of electrons in an Al wire of
length 5m, resistance of 60 milli ohms that carries a current of 15A. Al has 3 free electrons At
wt of Al=26.98 and density 2.7 x 103 kg m-3.
3 Find the relaxation time of conduction electrons in a metal having 6.5 x 1028 electrons per m-
3 if the resistivity of the metal is 1.43x 10-8 ohm m
4 There are 1020 electrons per m-3 in a material having a resistivity of 0.1 ohm -m. Find the
charge mobility and the electric field needed to produce a drift velocity of 1ms-1.
5 Show that the mobility of an electron in a metal is related to temperature according to the
relation =
e
3
mkT where λ is the mean free path of an electron.
6 An electron makes approximately 1012 collisions/s at a temperature 300K. How many collisions
is likely to make in 5 seconds if the temperature is raised by 100K?
7 The resistivity of silver is about 10-8 Ωm. What potential difference must be applied across a 2
m long silver wire to have a current density of 108 A/m2. If there are 1028 conduction electrons
per unit volume what is the drift velocity of those electrons?
8 A battery is connected across a conductor and it is found that the drift velocity is 4 x 10 -4m/s.
The battery is disconnected it is found that after a duration, t, the acquired velocity drops off
to 1.48 x 10-4m/s. What will be the acquired velocity after a time 2t?
9 eE
Show that the product of the drift velocity and thermal velocity can be written as
m
where λ is the mean free path of an electron.
10 The valence number of Gold is 1. Its density, atomic weight and resistivity are 19300 kg/m3,
197 and 2.21 x 10-8Ωm. Calculate, the number density and the mobility of electrons.
11 Show that the probability of occupation of a level ΔE above EF is the same as the probability of
non occupation of a level ΔE below EF.
12 Show that the probability of non occupation of a level ΔE above EF is the same as the probability
of occupation of a level ΔE below EF.
13 Show that the sum of the probabilities of occupation of a level ΔE below EF and a level ΔE above
EF is 1.
14 Show that the average kinetic energy of electrons at zero Kelvin is 0.6EF where EF is the Fermi
energy.
15 It is given that Ag is monoatomic and its density is 10500Kg/m3. If the atomic weight of Ag is
108 calculate its Fermi energy (in eV)
16 Show that the density of states at the Fermi level is given by 𝑔(𝐸𝐹 ) = 3𝑛 , where n is the
2𝐸 𝐹
number density of “free” electrons
17 The probability of occupation of an energy level 0.02eV above the Fermi level is 0.25. What will
be the probability of occupation of a level 0.05eV below the Fermi level?
18 The probability of occupation of an energy level 0.02eV above the Fermi level is 0.25. What will
be the probability of occupation of a level 0.05eV below the Fermi level?
19 Calculate the probability of occupation of the following energy levels at 300K: (i) E = EF +0.5kT
and (ii) E = EF – kT
20 At what temperature will the probability of a level 0.01eV above the Fermi level be 0.1? What
will be the change in the probability if the temperature is (i) doubled and (ii) halved
21 Calculate the mean free path of electrons in the following metals whose Fermi energies are
given: (a) sodium, EF = 3.1eV, (b) cadmium, EF = 7.5eV and (c) aluminium, EF = 11.6eV. Assume
that in all these metals the mean collision time is 10fs.
