The ratio between most probable velocity, mean velocity and r.m.s velocity is :

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$\sqrt{2} : \sqrt{\frac{8}{π}} : \sqrt{3}$

$\sqrt{2} : \sqrt{3} : \sqrt{\frac{8}{π}}$

1 :2 :3

$1 : \sqrt{2} : \sqrt{3}$

answer is A.

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Detailed Solution

Most probable velocity = $\sqrt{\frac{2 RT}{M}}$
Average velocity = $\sqrt{\frac{8 RT}{πM}}$
Root mean square velocity = $\sqrt{\frac{3 RT}{M}}$
$∴$ Most probable : Average : Root mean square
velocity velocity velocity
$= \sqrt{\frac{2 RT}{M}} : \sqrt{\frac{8 RT}{πM}} : \sqrt{\frac{3 RT}{M}} = \sqrt{2} : \sqrt{\frac{8}{π}} : \sqrt{3}$

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