JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
If the collision frequency of hydrogen molecules in a closed chamber at \(27^{\circ} \mathrm{C}\) is \(\mathrm{Z}\), then the collision frequency of the same system at \(127^{\circ} \mathrm{C}\) is _______.
- A \(\frac{\sqrt{3}}{2} \mathrm{Z}\)
- B \(\frac{4}{3} \mathrm{Z}\)
- C \(\frac{2}{\sqrt{3}} \mathrm{Z}\)
- D \(\frac{3}{4} Z\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{\sqrt{3}} \mathrm{Z}\)
Step-by-step Solution
Detailed explanation
Assuming mean free path constant. \(\mathrm{f} \propto \mathrm{v} \propto \sqrt{\mathrm{T}}\) \(\frac{\mathrm{f}_1}{\mathrm{f}_2}=\sqrt{\frac{\mathrm{T}_1}{\mathrm{~T}_2}}=\sqrt{\frac{300}{400}}\) \(\mathrm{f}_2=\sqrt{\frac{4}{3}}=\mathrm{f}_1=\frac{2}{\sqrt{3}} \mathrm{Z}\)
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