Question

Using an expression for drift velocity show that the mobility of free electron is directly proportional to its relaxation time

Answer 1

Answer:

ANSWER

Drift velocity per unit electric field is called mobility of electron, i.e., μ=

E

V

d

=

ρneE

E

Now, ρ=

ne

2

τ

m

∴μ=

mne

ne

2

τ

=

m

eτ

Answer 2

Derivation for drift velocity to show that the mobility of free electron is directly proportional to its relaxation time

Given:

Using an expression for drift velocity we must have known the equation for drift velocity

To Find:

The mobility of free electron is directly proportional to its relaxation time

Solution:

When conductor is subjected to an electric field E, each electron experience a force ,

F = -eE and acquires an acceleration of ,

a = F/m

= -eE/m.......(1)

Here m= mass of electron, e= charge , E= Electric Field.

The average time difference between two consecutive collisions is known as relaxation time of electron,

ζ = (ζ1 + ζ2 +ζ3....../n)................(2)

As v=u+at then drift velocity $v_{d}$  is,

$v_{d}$ = $\frac{v1+v2+v3+.....vn}{n}$

Vd =[ (u1+u2+u3+...+un)+ a(ζ1 + ζ2 +ζ3......)]/n

Vd = 0+ a(ζ1 + ζ2 +ζ3......)/n

since initially velocity is zero,

Vd = 0 +aζ

Vd = (-eE/ m)ζ

According to drift velocity expression, the relaxation time is the time interval between successive collisions of an electron on increasing temperature, the electrons move faster and more collisions occur quickly.

Hence, relaxation time decreases with increase in temperature which implies that drift velocity also decreases with temperature.

​#SPJ2