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 × 10¹⁸/s then collision frequency in gas A i $s _____/s.$
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Question

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 × 10¹⁸/s then collision frequency in gas A i $s _____/s.$

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G1 Physics · Accepted Answer

For an ideal gas, collision frequency per molecule is proportional to Z ∝ d²/√M when temperature and number density are unchanged. Given, d(A) = d(B)/2, M(A) = 4M(B). Therefore, Z(A)/Z(B) = [d(A)/d(B)]² × √[M(B)/M(A)] = (1/2)² × √(1/4) = 1/4 × 1/2 = 1/8. Hence, Z(A) = Z(B)/8 = (32 × 10¹⁸)/8 = 4 × 10¹⁸ s⁻¹. Correct option: B.