A system consists of two types of gas molecules $A$ and $B$ having same number density $2 imes 10^

Question

A system consists of two types of gas molecules $A$ and $B$ having same number density $2 	imes 10^{25} / \mathrm{m}^{3}$. The diameter of $A$ and $B$ are $10 \AA$ and $5 \AA$ respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule $A$ to that of $B$ between two successive collision is $\qquad$ $	imes 10^{-2}$.\

Professor PC Thomas Classes · Answer

(25): Number density, $n_{A}=n_{B}$\ $=2 	imes 10^{25} / \mathrm{m}^{3}$\ Diameter of $A, d_{A}=10 \AA$, diameter of $B$, $d_{B}=5 \AA$\ The formula of mean free path is\ $\lambda=\frac{1}{\sqrt{2} \pi \cdot d^{2} n}$\ where, $d$ is diameter and $n$ is number density.\ So, $\frac{\lambda_{A}}{\lambda_{B}}=\left(\frac{d_{B}}{d_{A}}ight)^{2} \cdot \frac{n_{B}}{n_{A}}=\left(\frac{5}{10}ight)^{2} 	imes 1=\frac{1}{4}$\ $	herefore \frac{\lambda_{A}}{\lambda_{B}}=25 	imes 10^{-2}$