Question

A metal wire is subjected to a constant potential difference. When the temperature of the metal wire increases, the drift velocity of the electron in it________.
Fill in the blank with the correct answer from the options given below.

• A. Increases, thermal velocity of the electrons decreases
• B. Decreases, thermal velocity of the electrons decreases
• C. Increases, thermal velocity of the electrons increases
• D. Decreases, thermal velocity of the electrons increases

Answer 1

The Correct Option is D

The drift velocity of an electron in a metal wire subjected to a constant potential difference is affected by temperature variations. The drift velocity \( v_d \) is defined by the equation:

\[ v_d = \frac{eE\tau}{m} \]

where:

• \( e \) represents the electron charge
• \( E \) signifies the electric field
• \( \tau \) denotes the mean free time between collisions
• \( m \) is the electron mass

An increase in temperature leads to more vigorous vibrations of lattice ions in the metal. This heightened vibration increases the frequency of electron collisions within the lattice, thereby reducing the mean free time \(\tau\). Since \(\tau\) is a factor in the drift velocity equation, a reduction in \(\tau\) results in a decreased drift velocity \(v_d\).

Additionally, the thermal velocity of electrons, which is the velocity component due to thermal agitation, rises with temperature as electrons acquire more kinetic energy. Consequently, the drift velocity of the electron decreases while its thermal velocity increases.

Therefore, the final conclusion is: Decreases, thermal velocity of the electrons increases