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A monoatomic gas is expanded adiabatically to n times its initial volume. The ratio of final rate of collision of molecules with unit area of container walls to the initial rate will be

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$n^{\frac{- 4}{3}}$

$n^{\frac{4}{3}}$

$n^{\frac{2}{3}}$

$n^{\frac{- 5}{3}}$

answer is D.

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Detailed Solution

The rate of collision of molecules with unit area of walls of container is proportional to pressure.

Now, $P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$ $\Rightarrow \frac{P_{2}}{P_{1}} = {(\frac{V_{1}}{V_{2}})}^{γ}$

For mono atomic gas $γ = 1 + \frac{2}{3} = \frac{5}{3}$

$∴ \frac{P_{2}}{P_{1}} = {(\frac{V_{1}}{n V_{1}})}^{\frac{5}{3}} = n^{- \frac{5}{3}}$

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