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(D) The mean velocity (average speed) of gas molecules is given by the formula: $v_{av} = \sqrt{\frac{8RT}{\pi M}}$.Since the temperature $T$ is the s

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$\sqrt{2}$ times that of helium

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(D) The mean velocity (average speed) of gas molecules is given by the formula: $v_{av} = \sqrt{\frac{8RT}{\pi M}}$.Since the temperature $T$ is the same for both gases,the mean velocity is inversely proportional to the square root of the molar mass $M$: $v_{av} \propto \frac{1}{\sqrt{M}}$.For hydrogen $(H_2)$,the molar mass $M_{H_2} = 2 	ext{ g/mol}$.For helium $(He)$,the molar mass $M_{He} = 4 	ext{ g/mol}$.Taking the ratio of the mean velocities:$\frac{v_{H_2}}{v_{He}} = \sqrt{\frac{M_{He}}{M_{H_2}}} = \sqrt{\frac{4}{2}} = \sqrt{2}$.Therefore,$v_{H_2} = \sqrt{2} \, v_{He}$.

Two vessels having equal volume contain molecular hydrogen at $1 \text{ atm}$ and helium at $2 \text{ atm}$ respectively. If both samples are at the same temperature,the mean velocity of hydrogen molecules is

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