`v_(rms), v_(av)` and `v_(mp)` are root mean square average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct ?

Options

A. `V_(rms)ltV_(av)ltV_(mp)`
B. `V_(rmr)gtV_(av)gtV_(mp)`
C. `V_(mp)ltV_(rms)ltV_(av)`
D. `V_(mp)gtV_(rms)gtV_(av)`

Answer

B

Explanation

`v_(rms)=sqrt(3K_(B)T)/(m)=1.73sqrt(K_(B)T)/(m)`
`v_(av)=sqrt(8K_(B)T)/(pim)`=1.60 `sqrt((K_(B)T)/(m)`
`v_(mp)=sqrt((2K_(B)T)/(m))=1.41sqrt((K_(B)T)/(m)` From these equations,`v_(rms)gtv_(av)gtv_(mp)`.