A system consists of two types of gas molecules A and B having same number density 2×1025/m3. The diameter of A and B are 10A0 and 5A0 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______×10−2

∵ mean free pathλ=12πd2nλ1λ2=d22n2d12n1=(510)2=0.25=25×10−2

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A system consists of two types of gas molecules A and B having same number density $2 \times 10^{25} / m^{3}$ . The diameter of A and B are $10 \overset{0}{A}$ and $5 \overset{0}{A}$ 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______ $\times 10^{- 2}$

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answer is 25.

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Detailed Solution

$∵$ mean free path

$λ = \frac{1}{\sqrt{2} π d^{2} n} \frac{λ_{1}}{λ_{2}} = \frac{d_{2}^{2} n_{2}}{d_{1}^{2} n_{1}}$

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

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