What is the relationship between the average velocity (v), root mean square velocity (u) and most probable velocity (a)

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$α : v : u :: 1.124 : 1.228 : 1$

$α : v : u :: 1 : 1.128 : 1.224$

$α : v : u :: 1.128 : 1 : 1.224$

$α : v : u :: 1.128 : 1.224 : 1$

answer is A.

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Detailed Solution

$\begin{array}{l} V_{2 :} : V_{ms} : V_{most probobic} = V : U : α \\ \sqrt{\frac{8 R T}{π M}} : \sqrt{\frac{3 R T}{M}} : \sqrt{\frac{2 R T}{M}} \\ α : V : U = \sqrt{2} : \sqrt{\frac{8}{π}} : \sqrt{3} = 1 : 1.128 : 1.224 . \end{array}$

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