The ratio among most probable velocity, mean velocity and root mean velocity is given by

Options

A. `1:2:3`
B. `1:sqrt2:sqrt3`
C. `sqrt2:sqrt3:sqrt((8)/(pi))`
D. `sqrt2:sqrt((8)/(pi)):sqrt3`

Answer

D

Explanation

Most probable velocity, `U_(mp)=sqrt((2RT)/(M))`
`"Mean velocity, U"_(av)=sqrt((8RT)/(piM))`
`"Root mean square velocity, U"_(rms)=sqrt((3RT)/(M))`
so, `U_(mp):U_(av):U_(rms)=sqrt((2RT)/(M)):sqrt((8RT)/(piM)):sqrt((3RT)/(M))`
`=sqrt2:sqrt((8)/(pi)):sqrt3`