If the mass of the charge carriers increases by a factor of two, how will the conductivity of the material be affected?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → It will be halved
From the drift of electrons picture, the conductivity is \( \sigma=ne^2\tau/m \). For the same carrier density \( n \), charge \( e \) and relaxation time \( \tau \), the conductivity is inversely proportional to the mass of the charge carriers. So doubling \( m \) halves \( \sigma \).
\( \begin{aligned} \frac{\sigma'}{\sigma} &= \frac{m}{2m} \\ &= \frac{1}{2} \end{aligned} \)
NCERT (2026-27):
Drift of Electrons and the Origin of Resistivity – “… if we identify the conductivity σ as”
\( \displaystyle \sigma=\frac{ne^2}{m}\,\tau \)\( \qquad (3.23) \)