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(C) The root mean square (rms) velocity of a gas is given by the formula: $v_{	ext{rms}} = \sqrt{\frac{3RT}{M}}$, where $R$ is the gas constant, $T$

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$\frac{c}{4}$

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(C) The root mean square (rms) velocity of a gas is given by the formula: $v_{	ext{rms}} = \sqrt{\frac{3RT}{M}}$, where $R$ is the gas constant, $T$ is the absolute temperature, and $M$ is the molar mass of the gas.Since $R$ and $T$ are constant for both gases, $v_{	ext{rms}} \propto \frac{1}{\sqrt{M}}$.For hydrogen gas $(H_2)$, $M_{H_2} = 2 	ext{ g/mol}$. Given $v_{	ext{rms}, H_2} = c$.For oxygen gas $(O_2)$, $M_{O_2} = 32 	ext{ g/mol}$.Taking the ratio: $\frac{v_{	ext{rms}, H_2}}{v_{	ext{rms}, O_2}} = \sqrt{\frac{M_{O_2}}{M_{H_2}}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$.Therefore, $v_{	ext{rms}, O_2} = \frac{v_{	ext{rms}, H_2}}{4} = \frac{c}{4}$.

If the rms velocity of hydrogen gas at a certain temperature is $c,$ then the rms velocity of oxygen gas at the same temperature is

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