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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{\large\frac{3E}{2M}}\qquad(b)\;U_{rms}=\sqrt{\large\frac{2E}{3M}}\qquad(c)\;U_{rms}=\sqrt{\large\frac{2E}{M}}\qquad(d)\;U_{rms}=\sqrt{\large\frac{E}{3M}}$$

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$U_{rms}=\sqrt{\large\frac{3RT}{M}}$
and $K.E = \large\frac{3}{2}RT$
$U_{rms}=\sqrt{\large\frac{2E}{M}}$
Hence answer is (c)
answered Feb 14, 2014 by sharmaaparna1
 

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