The ratio of r.m.s. velocities of oxygen and | vedclass

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

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$1 : 4$

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(D) The $r.m.s.$ velocity of a gas is given by the formula $\upsilon_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molar mass of the gas.Since the temperature $T$ is the same for both gases,we have $\upsilon_{rms} \propto \frac{1}{\sqrt{M}}$.Therefore,the ratio of the $r.m.s.$ velocities of oxygen $(O_2)$ and hydrogen $(H_2)$ is given by:$\frac{(\upsilon_{rms})_{O_2}}{(\upsilon_{rms})_{H_2}} = \sqrt{\frac{M_{H_2}}{M_{O_2}}}$.The molar mass of hydrogen $(H_2)$ is $M_{H_2} = 2 \ g/mol$ and the molar mass of oxygen $(O_2)$ is $M_{O_2} = 32 \ g/mol$.Substituting these values,we get:$\frac{(\upsilon_{rms})_{O_2}}{(\upsilon_{rms})_{H_2}} = \sqrt{\frac{2}{32}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$.Thus,the ratio is $1:4$.

The ratio of $r.m.s.$ velocities of oxygen and hydrogen at a given temperature is:

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