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JEE Main202622 January 2026Evening ShiftPhysicsKinetic Theory of GasesActual

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 is _ _ _ _/ s .

Options

  1. A2 10⁸
  2. B8 10⁸
  3. C4 10⁸
  4. D32 10⁸

Correct answer

C. 4 10⁸

Step-by-step solution

Collision frequency (z) = 2 d^2 N 8RT M Temp, N are same Z d^2 M d_A = d_B 2 M_A = 4M_B Z_A Z_B = d_A^2 d_B^2 M_B M_A = ( M_B M_A ) ( d_A d_B )^2 = ( 1 4 ) ( 1 2 )^2 Z_A Z_B = 1 2 1 4 = 1 8 Z_A = 32 10^8 8 = 4 10^8 /s

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