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 $U_{r m s}$ is :

$U_{r m s} = \sqrt{\frac{E}{3 M}}$

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$U_{r m s} = \sqrt{\frac{2 E}{M}}$

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$U_{r m s} = \sqrt{\frac{2 E}{3 M}}$

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$U_{r m s} = \sqrt{\frac{3 E}{2 M}}$

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Solution

The correct option is B
$U_{r m s} = \sqrt{\frac{2 E}{M}}$

Average K.E. of gas per mole $E = \frac{3}{2} R T \Rightarrow R T = \frac{2 E}{3}$

$U_{r m s} = \sqrt{\frac{3 R T}{M}}$ Therefore $U_{r m s} = \sqrt{\frac{3 \times 2 E}{3 M}} = \sqrt{\frac{2 E}{M}}$

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