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Physics · PYQ NEET UG 2026

हिन्दी

The mean free path of molecules in an ideal gas A is half that of another ideal gas B. The diameter of the spherical molecules of gas A is twice the diameter of the molecules of B. If number densities of the gases A and B are \( n_A \) and \( \nu_B \), respectively, then the correct option is :

  1. \( n_A = n_B \)
  2. \( n_A = 2n_B \)
  3. \( n_A = \frac{1}{4}n_B \)
  4. \( n_A = \frac{1}{2}n_B \)

Correct answer · Option 3

\( n_A = \frac{1}{4}n_B \)

Explanation

Mean free path \( \lambda = \frac{1}{\sqrt{2}\pi d^2 n \). Given \( \lambda_A = \frac{1}{2}\lambda_B \) and \( d_A = 2d_B \). Substituting these values yields \( n_A = \frac{1}{4}n_B \).

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