Kinetic Theory

JEE Main level, single correct, medium

8 of 168

Question 8 of 168

If the collision frequency of hydrogen molecules in a closed chamber at 27∘C27^{\circ} \mathrm{C} is Z\mathrm{Z}, then the collision frequency of the same system at 127∘C127^{\circ} \mathrm{C} is :

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Answer: (B) 23Z\frac{2}{\sqrt{3}} \mathrm{Z}

Assuming mean free path constant.
f∝V∝Tf1f2=T1 T2=300400f2=43=f1=23Z\begin{aligned} & \mathrm{f} \propto \mathrm{V} \propto \sqrt{\mathrm{T}} \\ & \frac{\mathrm{f}_1}{\mathrm{f}_2}=\sqrt{\frac{\mathrm{T}_1}{\mathrm{~T}_2}}=\sqrt{\frac{300}{400}} \\ & \mathrm{f}_2=\sqrt{\frac{4}{3}}=\mathrm{f}_1=\frac{2}{\sqrt{3}} \mathrm{Z}\end{aligned}

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