The root mean square speed of one mole of a monoatomic gas having molecular mass `M` is `u_(rms)` The relation between the average kinetic energy `(E)` of the gas and `u_9rms)` 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

For 1 mole of the gas
`PV = (1)/(3) M u^(2)`
or `U_(r.m.s.) = sqrt((3PV)/(M)) = sqrt((3RT)/(M)) ( :. PV = RT)`
Kinetic energy, `E = (3)/(2) RT`
or `3RT = 2E`
`:. U_(r.m.s.) = sqrt((2E)/(M))`