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The root mean square speed of one mole o...

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_("rms")` 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

`U_(rms) =sqrt((3RT)/(M), KE =(3)/(2) RT`
`therefore U_(rms) =sqrt((2E)/(M))`
Hence, (C ) is the correct answer.
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Knowledge Check

  • 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))`

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

  • For one mole of gas the average kinetic energy is given as E.The U_("rms") of gas is :

    A
    `sqrt((2E)/( M))`
    B
    `sqrt((3E)/( M))`
    C
    `sqrt((2E)/( 3M))`
    D
    `sqrt((3E)/( 2M))`

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