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The root mean square velocity of one mol...

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

A

`U_("rms") = sqrt((3E)/(2M))`

B

`U_("rms") = sqrt((2E)/(3M))`

C

`U_("rms") = sqrt((2E)/(M))`

D

`U_("rms") = sqrt((E)/(3M))`

Text Solution

Verified by Experts

The correct Answer is:
C
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))`
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