Metal X has twice as many free electrons per unit volume as metal Y. The relaxation time of the electrons in X is one-third of that in Y. The ratio of the resistivity of X to that of Y is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(3:2\)
The resistivity of a metal is \( \rho=m/(ne^{2}\tau) \). The electron mass \( m \) and charge \( e \) are the same in both metals, so \( \rho \) is inversely proportional to the product \( n\tau \).
\( \begin{aligned} \frac{\rho_X}{\rho_Y} &= \frac{n_Y\tau_Y}{n_X\tau_X} \\ &= \frac{n_Y\tau_Y}{2n_Y\times\frac{1}{3}\tau_Y} \\ &= \frac{3}{2} \end{aligned} \)
Therefore, \( \rho_X:\rho_Y=3:2 \).
NCERT (2026-27):
Temperature Dependence of Resistivity – “… From this equation, resistivity of a material is given by”
\( \rho=\frac{m}{ne^{2}\tau} \)\( \qquad (3.27) \)
“ρ thus depends inversely both on the number n of free electrons per unit volume and on the average time τ between collisions. …”