A system consists of two types of gas molecules A and B having same… | JEE Main 2021 (25 Jul, Shift 2)

Q15JEE Main 2021 · 25 JUL · SHIFT 2Medium

Mean Free Path & Real Gases

A system consists of two types of gas molecules A and B having same number density 2 $\times$ 1025/m3. The diameter of A and B are 10 $\mathring{\text{A}}$ and 5 $\mathring{\text{A}}$ 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

Numerical answer type. Work it out, then open the answer.

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Answer: 25

$\lambda = \dfrac{1}{\sqrt{2}\,n\pi d^2}$ ; same $n$ , so $\lambda \propto \dfrac{1}{d^2}$ .
$\dfrac{\lambda_A}{\lambda_B} = \left(\dfrac{d_B}{d_A}\right)^2 = \left(\dfrac{5}{10}\right)^2 = 0.25$
$0.25 = 25\times10^{-2}$ , so the answer is 25.

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