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(B) The root mean square velocity $(V_{rms})$ of a gas is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M}}$.Since the temperature $(T)$ and gas c

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$0.5$

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(B) The root mean square velocity $(V_{rms})$ of a gas is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M}}$.Since the temperature $(T)$ and gas constant $(R)$ are the same for both gases, the relationship between velocity and molar mass $(M)$ is $V_{rms} \propto \frac{1}{\sqrt{M}}$.Let $V_H$ be the velocity of hydrogen $(M_H = 2 \,g/mol)$ and $V_O$ be the velocity of oxygen $(M_O = 32 \,g/mol)$.Then, $\frac{V_H}{V_O} = \sqrt{\frac{M_O}{M_H}}$.Substituting the given values: $\frac{2}{V_O} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$.Therefore, $V_O = \frac{2}{4} = 0.5 \,km/s$.

If the root mean square velocity of a hydrogen molecule at a given temperature and pressure is $2 \,km/s$, the root mean square velocity of oxygen at the same condition in $km/s$ is:

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