Which of the following will increase the mobility of charge carriers?

The correct answer is Option (3) → increase in their average collision time

The mobility of a charge carrier is the drift speed per unit electric field. With the relaxation time \( \tau \) (average collision time) between collisions it is

    \( \displaystyle \mu = \frac{v_d}{E} = \frac{q\,\tau}{m} \)

Option (1) decrease in the charge of the mobile charge carriers — Incorrect. A smaller charge \( q \) gives a smaller \( \mu \).

Option (2) increase in the mass of the mobile charge carriers — Incorrect. A larger mass \( m \) gives a smaller \( \mu \).

Option (3) increase in their average collision time — Correct. \( \mu \propto \tau \): a longer time between collisions lets the carrier gain more drift speed per unit field.

Option (4) increase in the electric field — Incorrect. The drift speed is proportional to \( E \), so the ratio \( v_d/E \) does not depend on the field.

Note: A similar question was also asked in CUET (UG) 2025 on 22-05-2025 (Slot 1), and in CUET (UG) 2022 on 06-08-2022 (Slot 2).

NCERT (2026-27):
Mobility – “… An important quantity is the mobility μ defined as the magnitude of the drift velocity per unit electric field:

    \( \displaystyle \mu = \frac{|v_d|}{E} \qquad (3.24) \)

… Hence,

    \( \displaystyle \mu = \frac{v_d}{E} = \frac{e\tau}{m} \qquad (3.25) \)

where τ is the average collision time for electrons.”