Question

What is the effect of heating of a conductor on the drift velocity of free electrons?

Answer 1

Hint:The drift velocity of free electrons is the average velocity with which free electrons get drifted in a metallic conductor in the presence of an external electric field.Drift velocity of free electrons in a conductor is directly proportional to it average relaxation time. As the temperature increases the average relaxation time decreases. So, the drift velocity of free electrons decreases.

Complete step by step answer:
The drift velocity of free electrons in a conductor is given by,
${\vec v_d} = - \left( {\dfrac{{e\overrightarrow E }}{m}} \right)\tau $
Where $e = $ charge of electron, $\overrightarrow E = $ External electric field, $m = $ mass of electron and $\tau = $ Average relaxation time.
Here, the relaxation time is the time gap between two successive collisions of free electrons in a conductor.Let’s see how the average relaxation time for a given conductor is qualitatively depend on its temperature.On increasing the temperature of a conductor, the thermal agitation of free electrons (random motion of free electrons) increases.

So, the number of collisions of free electrons increases i.e., the frequency of those collisions increases. Therefore, the time interval between two successive collisions or the relaxation time decreases. The drift velocity of free electrons $\left( {{{\vec v}_d}} \right)$ is directly proportional to the average relaxation time $\left( \tau \right)$. Therefore, the drift velocity of free electrons decreases as the average relaxation time decreases.

Hence, by heating a given conductor the drift velocity of free electrons decreases.

Note:Free electrons in a given metal are the electrons that are loosely bound to the outermost shell. These free electrons are responsible for the flow of electric current through the metal body. In some materials, the atoms have tightly bound electrons which cannot accelerate even if an external electric field is applied. These materials are called insulators.