Question

Mobility \( \mu \) of an electron is related to average collision time \( \tau \) as: \[ \mu = \frac{e \tau}{m} \] (where \( e \) is the electronic charge, and \( m \) is the mass of the electron)

• A. \( \frac{1}{\tau} = m \mu \)
• B. \( \mu =\frac{m \tau}{e} \)
• C. \( \frac{1}{\mu} = \tau \)
• D. \( \mu = \frac{e \tau}{m} \)
• E. \( \mu \tau = e m \)

Hint:

The mobility of an electron is directly proportional to the average collision time and the electron charge, and inversely proportional to the mass of the electron.

Answer 1

The Correct Option is D

The mobility \( \mu \) of an electron is defined as the ratio of the drift velocity \( v_d \) to the applied electric field \( E \): \[ \mu = \frac{v_d}{E} \] The drift velocity \( v_d \) is related to the average collision time \( \tau \) by: \[ v_d = \frac{e \tau}{m} \] Thus, substituting for \( v_d \), we get: \[ \mu = \frac{e \tau}{m} \] Hence, the correct answer is (D).