For a monatomic gas, kinetic energy `= E`. The relation with `rms` velocity is

Options

A. `u=((2E)/M)^(1//2)`
B. `u=((3E)/(2M))^(1//2)`
C. `u=((E)/(2M))^(1//2)`
D. `u=((E)/(3M))^(1//2)`

Answer

A

Explanation

`U_(rms)=sqrt((3pV)/M`
pV=nKt (K=Boltzmann's constant)
For a molecule, n = 1
`pV=KTrArrU_(rms)=sqrt((3KT)/(M))`
Kinetic energy` (E)=(3)/(2)`KT or `KT=(2)/(3)E`
`U_(rms)=sqrt((3xx(2)/(3)E)/(M))=sqrt((2E)/(M))`