If the collision frequency of hydrogen molecules in a closed chamber at 27 is Z, then the collision frequency of the same system at 127 is: (a) √(3)/2 Z (b) 2/√(3) Z (c) 3/4 Z (d) 4/3 Z

Answer: (b). Closed chamber: number density n fixed, so λ is fixed and f = ( v)/(λ) ∝ √(T). (f₂)/(f₁) = √((400)/(300)) = 2/√(3) So the answer is (b) 2/√(3)Z.

If the collision frequency of hydrogen molecules in a closed chamber… | JEE Main 2024 (5 Apr, Shift 1)

Q9JEE Main 2024 · 5 APR · SHIFT 1Medium

Mean Free Path & Real Gases

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

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Answer: (b)

Closed chamber: number density $n$ fixed, so $\lambda$ is fixed and $f = \dfrac{\bar v}{\lambda} \propto \sqrt{T}$ .
$\dfrac{f_2}{f_1} = \sqrt{\dfrac{400}{300}} = \dfrac{2}{\sqrt{3}}$
So the answer is (b) $\dfrac{2}{\sqrt{3}}Z$ .

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