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(A) The root mean square velocity $(v_{rms})$ of a gas is given by the formula $v_{rms} = \sqrt{\frac{3P}{\rho}}$,where $P$ is the pressure and $\rho$

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$4$

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(A) The root mean square velocity $(v_{rms})$ of a gas is given by the formula $v_{rms} = \sqrt{\frac{3P}{\rho}}$,where $P$ is the pressure and $\rho$ is the density of the gas.Since the pressure $P$ is constant,we have $v_{rms} \propto \frac{1}{\sqrt{\rho}}$.Therefore,the ratio of the rms velocities of hydrogen $(v_H)$ and oxygen $(v_O)$ is given by $\frac{v_H}{v_O} = \sqrt{\frac{\rho_O}{\rho_H}}$.Given that the ratio of vapour density $\frac{\rho_H}{\rho_O} = \frac{1}{16}$,it follows that $\frac{\rho_O}{\rho_H} = 16$.Substituting this value,we get $\frac{v_H}{v_O} = \sqrt{16} = 4$.

If the ratio of vapour density for hydrogen and oxygen is $\frac{1}{16}$,then under constant pressure,the ratio of their rms velocities will be

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