Question

With reference to free electron theory of conductivity, explain the terms
a. Drift Speed.
b. Relaxation Time.

Answer 1

Hint The average velocity gained by particles such as electrons in any material due to the presence of an electric field is termed as drift velocity.
Relaxation time is the time interval between two successive collisions of electrons inside a conducting material when a current is flowing through it.

 Complete step-by-step solution
(a) Drift speed: The free electron in metals moves constantly at random with high velocity inside the metal. They frequently collide with the positive ions present within the metal, thus changing their direction of motion. Hence they have no net motion in any particular direction when a potential difference is applied across a metal the free electrons drift with a small constant velocity in the direction opposite to the applied field. This is drift speed.
(b) Relaxation time: It is the average time interval between two successive collisions of a free electron with the positive ions in the metal.
The formulae for drift velocity is as follows-
\[A.v = - \dfrac{{(eE\tau )}}{m}\]
Where:
e = charge on an electron
E = electric field intensity
τ = relaxation time
m = mass of electron
Or
\[B.v = \dfrac{I}{{neA}}\]
Where:
I = current
n = number of electrons
A = area of cross section of wire
e = charge of electron

Note: Drude and Lorentz proposed free electron theory in 1900. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. The electron theory is applicable to all solids i.e., both metals and nonmetals. It explains the electrical, thermal and magnetic properties of solids etc.