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A system consists

Question:

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

Solution:

$\because$ mean free path

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

$\frac{\lambda_{1}}{\lambda_{2}}=\frac{\mathrm{d}_{2}^{2} n_{2}}{\mathrm{~d}_{1}^{2} \mathrm{n}_{1}}$

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

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