The ratio of most probable velocity to average velocity is (Single option correct)

\frac{2}{\sqrt{π}}

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\frac{\sqrt{π}}{2}

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\frac{2}{π}

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\frac{π}{2}

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Solution

The correct option is A $\frac{\sqrt{π}}{2}$
Most probable velocity (MPV) $= \sqrt{\frac{2 R T}{M}}$
Average Velocity (avg.)= $\sqrt{\frac{8 R T}{π M}}$
$\Rightarrow$ Ratio $= \frac{M P V}{(a v g)} = \sqrt{\frac{2 \times π}{8}} = \frac{\sqrt{π}}{2}$
$(B) \frac{\sqrt{π}}{2}$

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