Q 11-12-112JEE MainJEE Main 2021 (25 Jul, Shift 2)Easy
A system consists of two types of gas molecules $A$ and $B$ having the same number density $2\times10^{25}$ m$^{-3}$. The diameter of $A$ and $B$ are $10$ Å and $5$ Å respectively. They suffer collisions at room temperature. The ratio of average distance covered by the molecule $A$ to that of $B$ between two successive collisions is ______ $\times10^{-2}$
Numerical value type. Enter your answer.
Answer: 25
Mean free path $\lambda = \dfrac{1}{\sqrt{2}\pi d^2 n}$; with equal $n$, $\lambda \propto \dfrac{1}{d^2}$.
$$\frac{\lambda_A}{\lambda_B} = \left(\frac{5}{10}\right)^2 = 0.25 = 25\times10^{-2}$$
Solution by Sreeraj P, M.Sc Physics