Physics - Conducting Materials - Important Questions and Answers: Conducting Materials

**CONDUCTING MATERIALS**

**1. ****What
are the merits of classical free electron theory? **

(i) It
is used to verify Ohm’slaw.

(ii) It
is used to explain electrical and thermal conductivities of metals.

(iii)It
is used to derive Wiedemann –Franz law.

(iv)It
is used to explain the optical properties of metal.

**2. ****What
are the drawbacks of classical free electron theory? **

(i)
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.

(ii)
Electrical conductivity of
semiconductors and insulators (non –metal) could not be explained by this
theory.

(iii)
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.

**3. ****Define
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)

**λ=
vd ×τc**

**4. Define relaxation time of an
electron.**

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
time.**

**5. 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 field is called **drift velocity.**
It is denoted as vd..

The thermal velocity is
random in nature and its value is very high (10^{5} m/s), but the drift
velocity is unidirectional and its value is very small (50 cm/s).

**6. Define mobility of electrons.**

The
magnitude of the drift velocity per unit electric field is defined as the **mobility
of**

**electrons (μ)**

i.e.,
**μ= v _{d/E}**

Where vd→ drift velocity of electrons E→
lectricalE field.

**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).

**σ=
q/tAE**

**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
number.

**9. What is Lorentz number?**

The ratio
between thermal conductivity
(K) of a
metal to the
product of

electrical conductivity
(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**

**10.
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
being considered.

**11.
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
at 0K.

**Importance **Fermi
level and Fermi energy determine the probability of an electron** **occupying
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.
What are difference between Drift velocity and thermal velocity of an electron?**

**Drift Velocity**

Drift
velocity is the average velocity acquired by the free electron, in the presence
of electric field.

The
electrons moving with drift velocity moves in the direction opposite to that of
the field direction.

The
velocity is very less, say in the order of 0.5 m/s.

**Thermal Velocity**

Thermal
velocity is the velocity of an electron without any external field.

The
direction of the electrons moving with thermal velocity is random.

The
velocity is very high, say in the order of 10 5
m/s.

**14.
Distinguish between electrical conductivity and thermal conductivity.**

**S.No Electrical Conductivity**

1.
The co-efficient of electrical conductivity is defined as the quantity of
electricity flowing per unit area per unit time maintained at unit potential
gradient.

2.
Electrical conductivity is purely due to number of free electrons.

3.
Conduction of electricity takes place from higher potential end to the lower
potential end.

4.
Unit: ohm ^{-1} m^{-1}

**Thermal Conductivity **

The
Co-efficient of thermal conductivity is defined as the quantity of heat
conducted per unit area per unit time maintained at unit temperature gradient.

Thermal
conductivity is due to both free electrons and phonons.

Conduction
of heat takes place from hot end to cold end

Unit:
Wm ^{-1} K^{-1}

^{}

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Physics : Conducting Materials : Important Questions and Answers: Conducting Materials |

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