If the root mean square (rms) speed of nitrog | vedclass

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(A) The root mean square (rms) speed of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$, where $R$ is the universal gas constan

Vedclass · Accepted Answer

$100 \sqrt{7} \ m \ s^{-1}$

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(A) The root mean square (rms) speed of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$, where $R$ is the universal gas constant, $T$ is the absolute temperature, and $M$ is the molar mass of the gas.For a given temperature $T$, the rms speed is inversely proportional to the square root of the molar mass: $v_{rms} \propto \frac{1}{\sqrt{M}}$.Therefore, the ratio of the rms speeds of Helium $(He)$ and Nitrogen $(N_2)$ is $\frac{v_{He}}{v_{N_2}} = \sqrt{\frac{M_{N_2}}{M_{He}}}$.The molar mass of Nitrogen $(N_2)$ is $M_{N_2} = 28 \ g \ mol^{-1}$ and the molar mass of Helium $(He)$ is $M_{He} = 4 \ g \ mol^{-1}$.Given $v_{N_2} = 100 \ m \ s^{-1}$, we substitute the values: $\frac{v_{He}}{100} = \sqrt{\frac{28}{4}} = \sqrt{7}$.Thus, $v_{He} = 100 \sqrt{7} \ m \ s^{-1}$.

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 \ m \ s^{-1}$, then the rms speed of Helium molecules at the same temperature is

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