The root mean square velocity of one mole of a monoatomic gas having molar mass M is `U_(r.m.s.)`. The relation between the average kinetic energy (E ) of the gas and `U_(rms)`is

Options

A. `U_("rms")=sqrt((3E)/(2M))`
B. `U_("rms")=sqrt((2E)/(3M))`
C. `u_("rms")=sqrt((2E)/(M))`
D. `u_("rms")=sqrt((E)/(3M))`

Answer

C

Explanation

R.M.S of one mole of a monoatomic gas is
`U_("rms")=sqrt((3RT)/(M)) `
Average K.E. is E `=(3)/(2)`RT or 2 E=3RT
`:. U_("rms") =sqrt((2E)/(M))`