JEE Main · 2026 · 22 Jan 2026 · Shift 2 · Heat & Thermodynamics

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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 1 0^{8} / s

then collision frequency in gas A is

____

/s.

(A) $32 \times 1 0^{8}$
(B) $4 \times 1 0^{8}$ ✓ Correct
(C) $2 \times 1 0^{8}$
(D) $8 \times 1 0^{8}$

Answer: (B)

Solution

The collision frequency is

z = 2 π d^{2} N \overset{v}{ˉ}

with the mean speed

\overset{v}{ˉ} = \frac{8 k _{B} T}{π m}

. At equal temperature and number density,

z \propto \frac{d ^{2}}{m}

. With

d_{A} = \frac{1}{2} d_{B}

and

m_{A} = 4 m_{B}

\frac{z _{A}}{z _{B}} = (\frac{d _{A}}{d _{B}})^{2} \frac{m _{B}}{m _{A}} = \frac{1}{4} \cdot \frac{1}{2} = \frac{1}{8} .

Hence

z_{A} = \frac{32 \times 1 0 ^{8}}{8} = 4 \times 1 0^{8} s^{- 1}

. The collision frequency in gas A is

4 \times 1 0^{8}

per second.

JEE Main · 2026 · 22 Jan 2026 · Shift 2 · Single correct option

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JEE Main · 2026 · 22 Jan 2026 · Shift 2 · Heat & Thermodynamics

Solution

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