The ratio of densities of O_2 and H_2 is 16 : | vedclass

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(C) The $rms$ velocity $(v_{rms})$ of a gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $d = \frac{PM}{RT}$,we have $M = \frac{dRT

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$1 : 4$

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(C) The $rms$ velocity $(v_{rms})$ of a gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $d = \frac{PM}{RT}$,we have $M = \frac{dRT}{P}$.Substituting $M$ in the $v_{rms}$ formula,we get $v_{rms} = \sqrt{\frac{3RT}{dRT/P}} = \sqrt{\frac{3P}{d}}$.Assuming constant pressure $(P)$ and temperature $(T)$,$v_{rms} \propto \frac{1}{\sqrt{d}}$.Therefore,$\frac{(v_{rms})_{O_2}}{(v_{rms})_{H_2}} = \sqrt{\frac{d_{H_2}}{d_{O_2}}}$.Given the ratio of densities $\frac{d_{O_2}}{d_{H_2}} = \frac{16}{1}$,so $\frac{d_{H_2}}{d_{O_2}} = \frac{1}{16}$.Thus,$\frac{(v_{rms})_{O_2}}{(v_{rms})_{H_2}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$ or $1 : 4$.

The ratio of densities of $O_2$ and $H_2$ is $16 : 1$. The ratio of their $rms$ velocities will be:

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