Question

The ratio between most probable velocity, mean velocity
and r.m.s velocity is :
(a) √2 : √8 / π : √3 (b) √2 : √3 : √8/ π
(c) 1 : 2 : 3 (d) 1: √2 : √3

Answer 1

The ratio between most probable velocity, mean velocity  and r.m.s velocity is √2 : √ 8 / π : √3

Option (B) is correct.

Explanation:

Most probable velocity U (mp) =  √2RT / M

Mean velocity U (av) = √ 8RT / πM

Root mean square velocity U (rms) = √3RT / M

So

U(mp) :  U (av) : U (rms)  = √2RT / M : √8RT / πM : √3RT/M

= √2 - √ 8 / π - √3

Thus the ratio between most probable velocity, mean velocity  and r.m.s velocity is √2 : √ 8 / π : √3

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