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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 `U_(r.m.s.)`. The relation between the average kinetic energy (E ) of the gas and `U_(rms)`is

A

`u_("r.m.s")=sqrt((3E)/(2M))`

B

`u_("r.m.s")=sqrt((2E)/(3M))`

C

`u_("r.m.s")=sqrt((2E)/(M))`

D

`u_("r.m.s")=sqrt((E)/(3M))`

Text Solution

Verified by Experts

The correct Answer is:
C
`u_("r.m.s")=sqrt((3RT)/(M))`
Average kinetic energy, `E=(3)/(2)nRT`
For 1 mole of a gas,
`E=(3)/(2)RT`
`"or "RT=(2)/(3)E`
`therefore" "u_("r.m.s")=sqrt((3xx(2)/(3)E)/(M))=sqrt((2E)/(M))`
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