Q.
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, the correct option is:
A) $n_A=n_B/2$
B) $n_A=n_B$
C) $n_A=2n_B$
D) $n_A=n_B/4$
Explanation
[Solution from source] $\lambda=1/(\sqrt2\pi d^2n)$, so $\lambda_A/\lambda_B=n_B/(4n_A)$. Setting this equal to 1/2 gives $n_A=n_B/2$. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.