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NEETPhysicsKinetic Theory of Gases

Two ideal gases A and B are maintained at the same temperature and pressure. If the diameter of a molecule of gas A is twice the diameter of a molecule of gas B, what is the ratio of the mean free path of gas A to that of gas B?

Options

  1. A1:2
  2. B2:1
  3. C1:4
  4. D4:1

Correct answer

C. 1:4

Step-by-step solution

The mean free path of a gas molecule is given by the formula: = 1 2 d^2 n where d is the molecular diameter and n is the number density of molecules. Since both gases are at the same temperature and pressure, their number density n is the same. Therefore, the mean free path is inversely proportional to the square of the molecular diameter: 1 d^2 Given that d_A = 2d_B , the ratio of their mean free paths is: _A _B = ( d_B d_A )^2 = ( d_B 2d_B )^2 = 1 4 Hence, the ratio is 1:4 . Answer: 1:4

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