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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 n_B, respectively, then the correct option is :

Asked in Re-NEET 2026 · Mean free path and its dependence

• (1) n_A=n_B
• (2) n_A=2n_B
• (3) n_A=1/4n_B
• (4) n_A=1/2n_B

Step-by-step solution

Why the other options are wrong

• (1) Uses the diameter to the first power, λ∝1/(nd); the collision cross-section goes as d².
• (2) Leaves out the diameters and compares only the mean free paths.
• (3) Uses only the diameters, ((d_B)/(d_A))², forgetting that A's mean free path is half of B's.

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