Consider two boxes containing ideal gases A and B such that their… | JEE Main 2026 (22 Jan, Shift 2)

Q3JEE Main 2026 · 22 JAN · SHIFT 2Medium

Mean Free Path & Real Gases

Consider two boxes containing ideal gases $A$ and $B$ such that their temperatures, pressures and number densities are same. The molecular size of $A$ is half of that of $B$ and mass of molecule $A$ is four times that of $B$ . If the collision frequency in gas $B$ is $32 \times 10^{18}\text{/s}$ then collision frequency in gas $A$ is ______ /s.

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Answer: (d)

Collision frequency $f = \sqrt{2}\,n\pi d^2\,\bar v$ , with $\bar v \propto \sqrt{T/m}$ .
Same $n$ and $T$ : $f \propto \dfrac{d^2}{\sqrt{m}}$ .
$\dfrac{f_A}{f_B} = \left(\dfrac{1}{2}\right)^2 \times \dfrac{1}{\sqrt{4}} = \dfrac{1}{8}$
$f_A = \dfrac{32\times10^{18}}{8} = 4\times10^{18}$ /s
So the answer is (d).

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