are the merits of classical free electron theory?
is used to verify Ohm’slaw.
is used to explain electrical and thermal conductivities of metals.
is used to derive Wiedemann –Franz law.
is used to explain the optical properties of metal.
are the drawbacks of classical free electron theory?
Classical theory states that all free
electrons will absorb the supplied energy; on the contrary, quantum theory
states that only a few electrons will absorb the supplied energy.
Electrical conductivity of
semiconductors and insulators (non –metal) could not be explained by this
The phenomena such as photo –electric
effect, Compton effect and black body radiation could not be explained on the
basis of this theory because these phenomena are based on quantum theory.
mean free path.
The average distance
traveled by a free electron between any two successive collisions in the
presence of an applied field is known as mean free path. It is the
product of drift velocity of the electron (vd) and collision time (τ)
4. Define relaxation time of an
The average time taken
by a free electron to reach its equilibrium position from its disturbed
position due to application of an external electrical field is called relaxation
5. Define drift
velocity of electron. How is it different from the thermal velocity of an
The average velocity
acquired by a free electron in a particular direction after a steady state is
reached on the application of an electrical field is called drift velocity.
It is denoted as vd..
The thermal velocity is
random in nature and its value is very high (105 m/s), but the drift
velocity is unidirectional and its value is very small (50 cm/s).
6. Define mobility of electrons.
magnitude of the drift velocity per unit electric field is defined as the mobility
Where vd→ drift velocity of electrons E→
7. Define electrical conductivity.
It is the amount of
electrical charge (q) conducted per unit time (t) across unit area (A) of the
solid per unit applied electrical field (E).
8. State Wiedemann –Franz law.
It states that the
ratio of thermal conductivity (K) to electrical conductivity (σ)ofa metal is
directly proportional to absolute temperature (T) and this ratio is constant
for all metals at a given temperature.
K/ σ∞T i.e., K/ σ= LT
Where L is a constant and it is known as Lorentz
9. What is Lorentz number?
between thermal conductivity
(K) of a
metal to the
(σ)ofa metal and absolute temperature (T) of the metal is a constant. It is
called Lorentz number and it is given by
L = K/σT
Define Fermi distribution function.
The probability F (E)
of an electron occupying a given energy level at temperature T is known as
Fermi distribution function. It is given by
E →Energy of the level whose occupancy is
Define Fermi level and Fermi energy with its importance.
Fermi level is
the energy level at finite temperature above 0K in which the probability of the
electron occupation is ½ and it is also the level of maximum energy of the
filled states at 0K
Fermi energy is
the energy of the state at which the probability of the electron occupation
is ½ at any temperature above 0K.It is also the maximum energy of filled states
level and Fermi energy determine the probability of an electron occupying
a given energy level at a given temperature.
Define density of states. What is its use?
is defined as the number of available electron states per unit volume in an
energy interval E and E+dE. It is
denoted by Z (E). It is used to
determine Fermi energy at any temperature.
What are difference between Drift velocity and thermal velocity of an electron?
velocity is the average velocity acquired by the free electron, in the presence
of electric field.
electrons moving with drift velocity moves in the direction opposite to that of
the field direction.
velocity is very less, say in the order of 0.5 m/s.
velocity is the velocity of an electron without any external field.
direction of the electrons moving with thermal velocity is random.
velocity is very high, say in the order of 10 5
Distinguish between electrical conductivity and thermal conductivity.
S.No Electrical Conductivity
The co-efficient of electrical conductivity is defined as the quantity of
electricity flowing per unit area per unit time maintained at unit potential
Electrical conductivity is purely due to number of free electrons.
Conduction of electricity takes place from higher potential end to the lower
Unit: ohm -1 m-1
Co-efficient of thermal conductivity is defined as the quantity of heat
conducted per unit area per unit time maintained at unit temperature gradient.
conductivity is due to both free electrons and phonons.
of heat takes place from hot end to cold end
Wm -1 K-1