Mobility of electrons
A. decreases with increase in potential difference
B. increases with increase in potential difference
C. does not depend on potential difference
D. decreases with increase in temperature of conductor
E. independent to the temperature of conductor
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → C and D only
The mobility of electrons is the drift speed per unit electric field, and it is fixed by the relaxation time \( \tau \), the average time between collisions:
\( \displaystyle \mu = \frac{v_d}{E} = \frac{e\tau}{m} \)
(A) decreases with increase in potential difference — Incorrect. In the Ohmic region \( v_d \propto E \), so the ratio \( v_d/E \) stays constant.
(B) increases with increase in potential difference — Incorrect. For the same reason.
(C) does not depend on potential difference — Correct. Mobility is a property of the material and its temperature, not of the applied voltage.
(D) decreases with increase in temperature of conductor — Correct. A hotter lattice vibrates more, so collisions are more frequent, \( \tau \) falls and the mobility decreases.
(E) independent to the temperature of conductor — Incorrect. \( \tau \), and hence \( \mu \), changes with temperature.
Note: It seems that there is a mistake in the original NTA paper, which prints statement (D) as “decreases with decrease in temperature of conductor” when it should read “decreases with increase in temperature of conductor”. As printed, (D) is false, because the mobility rises when a conductor is cooled, and no option would then be correct. The statement has been corrected here so that Option (3) is the only correct one.
NCERT (2026-27):
Mobility – “… An important quantity is the mobility μ defined as the magnitude of the drift velocity per unit electric field:
\( \displaystyle \mu = \frac{|\mathbf{v}_d|}{E} \qquad (3.24) \)
… Hence,
\( \displaystyle \mu = \frac{v_d}{E} = \frac{e\tau}{m} \qquad (3.25) \)
where τ is the average collision time for electrons.”
Temperature Dependence of Resistivity – “… As we increase temperature, average speed of the electrons, which act as the carriers of current, increases resulting in more frequent collisions. The average time of collisions τ, thus decreases with temperature.”