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(C) The collision frequency $Z$ of gas molecules is given by the relation $Z \propto n \sigma v_{avg}$,where $n$ is the number density,$\sigma$ is the

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$\frac{2}{\sqrt{3}} Z$

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(C) The collision frequency $Z$ of gas molecules is given by the relation $Z \propto n \sigma v_{avg}$,where $n$ is the number density,$\sigma$ is the collision cross-section,and $v_{avg}$ is the average speed.In a closed chamber,the number density $n$ and the collision cross-section $\sigma$ remain constant.The average speed $v_{avg}$ is proportional to the square root of the absolute temperature,i.e.,$v_{avg} \propto \sqrt{T}$.Therefore,the collision frequency $Z \propto \sqrt{T}$.Given,$T_1 = 27^{\circ} C = 300 \ K$ and $T_2 = 127^{\circ} C = 400 \ K$.Using the ratio: $\frac{Z_2}{Z_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{400}{300}} = \sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}$.Thus,$Z_2 = \frac{2}{\sqrt{3}} Z$.

If the collision frequency of hydrogen molecules in a closed chamber at $27^{\circ} C$ is $Z$,then the collision frequency of the same system at $127^{\circ} C$ is :

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