If the collision frequency of hydrogen molecules in a closed chamber at 27°C is Z, then the collision frequency of the same system at 127°C is

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Solution

Q.
If the collision frequency of hydrogen molecules in a closed chamber at 27°C is Z, then the collision frequency of the same system at 127°C is [2024]

1 $\frac{3}{4} Z$

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

3 $\frac{4}{3} Z$

4 $\frac{2}{\sqrt{3}} Z$

Ans.
(4)

Collision frequency $\propto \sqrt{T} \Rightarrow \frac{f_{2}}{f_{1}} = \sqrt{\frac{T_{2}}{T_{1}}}$

$\Rightarrow \frac{f_{2}}{f_{1}} = \sqrt{\frac{400}{300}} \Rightarrow f_{2} = \frac{2}{\sqrt{3}} f_{1} = \frac{2}{\sqrt{3}} Z$

$f_{2} = \sqrt{\frac{4}{3}} = f_{1} = \frac{2}{\sqrt{3}} Z$

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