Question

A system consists of two types of gas molecules $A$ and $B$ having the same number density $2\times {10}^{25}{\text{m}}^{-3}$. The diameter of $A$ and $B$ are $10\dot{A}$ and $5\dot{A}$ 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 $\times {10}^{-2}$

Answer 1

The average distance covered by a molecule between two successive collision is called as mean free path.

$\lambda =\frac{1}{\sqrt{2}\pi d^{2}n}$

$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{d_2^2{n}_2}{d_1^2{n}_1}$

Here, $n_1=n_2$, $d_2=5\dot{A},d_1=10\dot{A}$

$\Rightarrow \lambda ={\left(\frac{5}{10}\right)}^2=0.25=25\times {10}^{-2}\text{m}$

Hence, $25$ is the correct answer.