At a given temperature,the ratio of r.m.s. ve | vedclass

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(A) The $r.m.s.$ velocity of a gas molecule is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$T$ is th

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$\sqrt{2} : 1$

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(A) The $r.m.s.$ velocity of a gas molecule is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$T$ is the temperature,and $M$ is the molar mass.Since $T$ is constant,$v_{rms} \propto \frac{1}{\sqrt{M}}$.For hydrogen molecule $(H_2)$,$M_{H_2} = 2 \ g/mol$.For helium atom $(He)$,$M_{He} = 4 \ g/mol$.The ratio is $\frac{(v_{rms})_{H_2}}{(v_{rms})_{He}} = \sqrt{\frac{M_{He}}{M_{H_2}}} = \sqrt{\frac{4}{2}} = \sqrt{2} = \frac{\sqrt{2}}{1}$.Thus,the ratio is $\sqrt{2} : 1$.

At a given temperature,the ratio of $r.m.s.$ velocities of a hydrogen molecule and a helium atom will be:

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