Q. The ratio of most probable velocity to average velocity is
A) $\frac{\pi}{2}$
B) $\frac{2}{\pi}$
C) $\frac{\sqrt{\pi}}{2}$
D) $\frac{2}{\sqrt{\pi}}$
Explanation
(c)
We know, average velocity $v = \sqrt{\frac{8RT}{\pi M}}$
and most probable velocity $\alpha = \sqrt{\frac{2RT}{M}}$
so, their ratio $= \alpha\ :v = \sqrt{\frac{2RT}{M}}\ :\ \sqrt{\frac{8RT}{\pi M}}$
so, $\frac{\sqrt{\pi}}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.