Question:
A system consists of two types of gas molecules A and B having same number density \(2\times10^{25}/\mathrm{m^3}\). The diameter of A and B are \(10\ \mathrm{\AA}\) and \(5\ \mathrm{\AA}\) 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 ____________ \(\times 10^{-2}\)
A system consists of two types of gas molecules A and B having same number density \(2\times10^{25}/\mathrm{m^3}\). The diameter of A and B are \(10\ \mathrm{\AA}\) and \(5\ \mathrm{\AA}\) 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 ____________ \(\times 10^{-2}\)
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Average distance between collisions is the mean free path, lambda = 1/(sqrt(2) pi n d^2).
Updated On: Nov 4, 2026
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Correct Answer: 25
Solution and Explanation
Mean free path \(\lambda = \dfrac{1}{\sqrt2\,\pi n d^2}\). With equal \(n\) (and same temperature), \(\lambda \propto \dfrac{1}{d^2}\).
\(\dfrac{\lambda_A}{\lambda_B} = \left(\dfrac{d_B}{d_A}\right)^2 = \left(\dfrac{5}{10}\right)^2 = \dfrac14 = 0.25 = 25\times10^{-2}\).
Answer: 25
\(\dfrac{\lambda_A}{\lambda_B} = \left(\dfrac{d_B}{d_A}\right)^2 = \left(\dfrac{5}{10}\right)^2 = \dfrac14 = 0.25 = 25\times10^{-2}\).
Answer: 25
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