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Relation between drift velocity of electron $({v_d}) $ and thermal velocity of electron $({v_t}) $ at room temperature is expressed as
A) ${v_d} = {v_t}$
B) ${v_d} > {v_t}$
C) ${v_d} < {v_t}$
D) ${v_d} = {v_t} = 0$

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Last updated date: 17th Apr 2024
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Answer
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Hint: Average speed obtained by charged particles, including electrons, in a material due to an electric field is the drift speed in physics. The electron in a conductor usually propagates at the Fermi speed arbitrarily, which corresponds to an average speed of zero. Thermal speed practically corresponds to the heat kinetic energy. For example, the heating of the gas may produce plasma, which removes the electrons from gas atoms when the temperature is high enough.

Complete step by step answer:
Subatomic particles like electrons always move randomly. When electrons are exposed to an electric field, they travel at random, but eventually migrate into the electrical realm. The net speed at which these electrons drift is referred to as drift speed.
Typical of the thermal acceleration of particles that make up gas, liquid, and others is thermal speed or thermal speed. Thus, thermal speed is implicitly a temperature variable. It measures the maximum width in the velocity distribution of particulate matter between Maxwell and Boltzmann.

Electrons with the Fermi energy carry considerable kinetic energy. Their mean thermal velocity at temperature $T$ should be

$\Rightarrow$\[{v_t} = \sqrt {\dfrac{{3kT}}{m}} \] which generally turns out to be quite large.
Where, ${v_t} $ is the thermal velocity, $T$ is the temperature and $m$ is the mass.
The average velocity with which electrons must pass along a conductor to carry a current is called drift velocity given by
$\Rightarrow$ \[{v_d} = \dfrac{I}{{enA}}\]
Which much less than thermal velocity.
Hence the correct option is C.

Note: Every substance above absolute zero temperature that can operate like metals has some free electrons that pass at an altered level. When a conductor is theoretically added, the electrons appear to change to positive potential; but, as they pass they collide with atoms and rebound or lose some of their kinetic energy If electrons have no electric field, they are randomly moving due to thermal motion in a semiconductor. The thermal speed is the average speed of this wave. An electrical field accelerates electrons and leads a component of the electron speed towards the electrical field. This level of electronic motion is called the drift level in the electrical field. This speed of drift contributes to an electric current.