2 Marks Question & Answers

Part A '2' Marks Q & A

ANNA UNIVERSITY Q & A

1. Give any two postulates of classical free electron theory. 

• According to this theory, a metal consists of a very large number of free electrons. These free electrons move freely throughout the volume of the metal. They are fully responsible for the electrical conduction in the metal.

• Drude assumed that the free electrons in a metal form an electron gas. These free electrons move randomly in all possible directions just like the gas molecules move in a container.

2. Define mean free path.

The average distance travelled 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 electrons (vd) and collision time (τc).

3. Define relaxation time of an electron.

The average time taken by a free electron to reach its equilibrium state from its disturbed state due to application of an external electrical field is called relaxation time.

4. Define drift velocity of electron. How is it different from the thermal velocity of an electron?

The average velocity acquired by a free electron in a particular direction after a steady state is reached on the application of an electrical electrical field is called drift velocity. It is denoted as v and its value is very small (50 cm/s). 

The thermal velocity is random in nature and its value is very high (105 m/s)

5. Define mobility of electrons.

The magnitude of the drift velocity acquired by the electrons per unit electric field is defined as the mobility of electrons (μ)

where vd → Drift velocity of electrons

E → Electrical field.

6. Define electrical conductivity. What is its unit.

The amount of electrical charges (q) conducted per unit time (t) across unit area (A) of the conductor for unit applied electrical field (E) is defined as electrical conductivity.

Its unit is ohm-1 m-1 or mho m-1

7. What are the merits of classical free electron theory?

• It is used to verify Ohm's law.

• It is used to explain electrical and thermal conductivities of metals.

• It is used to derive Wiedemann - Franz law.

• It is used to explain the optical properties of metal.

8. What 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-metals) cannot be explained.

• The phenomena such as photo-electric effect, Compton effect and black body radiation cannot be explained on the basis of this theory because these phenomena are based on quantum theory.

9. Define Fermi distribution function.

The probability F (E) of an electron occupancy for a given energy level at temperature T is known as Fermi distribution function. It is given by

EF → Fermi level

K → Boltzmann's constant

T → Absolute temperature

E → Energy of the level whose occupancy is being considered.

10. Write down the expression for the Fermi distribution law and explain for the electrons in a metal.

Fermi distribution function is given by

where EF is called Fermi energy

if E < EF, all levels are filled with electrons

i.e., F (E) = 1

if E > EF, all levels are empty

i.e., F (E) = 0

if T > 0 K at EF, F (E) = 1/2

11. Define Fermi level and and Fermi energy with its importance.

Fermi level: It is the energy level at finite temperature above 0 K in which the probability of the electron occupation is 1/2 and it is also the level of maximum energy of the filled states at 0 K.

Fermi energy: It is the energy of the state at which the probability of the electron occupation is 1/2 at any temperature above OK. It is also the maximum energy of filled states at 0 K. 

Importance: Fermi level and Fermi energy determine the probability of an electron occupation for a given energy level at a given temperature.

12. Define density of states. What is its use?

It 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. 

13. Calculate the drift velocity of the free electrons with a mobility of 3.5 × 10-3 m2 V-1s-1 in copper for an electric field strength of 0.5 V/m

Given data

Mobility of free electrons (μ) = 3.5 × 10-3 m2 V-1s-1

Electric field strength of copper (E) = 0.5 Vm-1

Solution

Drift velocity vd = μ × E

= 3.5 × 10-3 × 0.5 = 1.75 × 10-3