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Q.

Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters $1 A^{0}$ and $2 A^{0}$ . The gases may be considered under identical conditions of temperature, pressure and volume.

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a

1:4

b

4:1

c

1:2

d

2:1

answer is B.

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Detailed Solution

$\begin{array}{l} m e a n f r e e p a t h = λ = \frac{1}{\sqrt{2} {πnd}^{2}}; \Rightarrow λ_{1} α \frac{1}{d_{1}^{2}} and λ_{1} α \frac{1}{d_{1}^{2}} \\ h e r e n = n u m b e r o f c o l l i s i o n s; d = d i a m e t e r o f m o l e c u l e; g i v e n d_{1} = 1 A^{0} a n d d_{2} = 2 A^{0} \\ \Rightarrow \frac{λ_{1}}{λ_{2}} = {[\frac{d_{2}}{d_{1}}]}^{2} = {[\frac{2}{1}]}^{2} = \frac{4}{1} \end{array}$

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