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Get Answers to all your Questions
(1).Derive an expression for electrical conductivity of material in terms of relaxation time
(2).Define relaxation time
Answers (1)
1) Derive an expression for electrical conductivity of material in terms of relaxation time
According to the Drude model, the drift velocity is given by:
\[
v_d = \frac{-e E \tau}{m}
\]
(The negative sign indicates that the electrons move opposite to the electric field.)
Current density $J$ is given by:
\[
J = n e v_d
\]
Substituting the value of $v_d$:
\[
J = n e \left( \frac{-e E \tau}{m} \right) = \frac{-n e^2 \tau E}{m}
\]
Taking magnitude (ignoring negative sign):
\[
J = \frac{n e^2 \tau E}{m}
\]
From Ohm's law:
\[
J = \sigma E
\]
Comparing with the above equation:
\[
\sigma = \frac{n e^2 \tau}{m}
\]
\[
\boxed{\sigma = \frac{n e^2 \tau}{m}}
\]
This is the required expression for electrical conductivity in terms of relaxation time.
2) Relaxation time (τ) is defined as the average time interval between two successive collisions of a free electron in a conductor while an electric field is applied.
Key Points:
-
It indicates how quickly electrons lose their drift motion due to collisions.
-
Greater relaxation time means less frequent collisions, leading to better conductivity.
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