(C) The root mean square velocity of one mole of a monoatomic gas is given by $V_{rms} = \sqrt{\frac{3RT}{M}} \dots (1)$.The average kinetic energy $(

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$V_{rms} = \sqrt{\frac{2E}{M}}$

(C) The root mean square velocity of one mole of a monoatomic gas is given by $V_{rms} = \sqrt{\frac{3RT}{M}} \dots (1)$.The average kinetic energy $(E)$ of one mole of a monoatomic gas is given by $E = \frac{3}{2}RT$.From this,we can express $RT$ as $RT = \frac{2E}{3} \dots (2)$.Substituting equation $(2)$ into equation $(1)$:$V_{rms} = \sqrt{\frac{3}{M} \times \frac{2E}{3}}$$V_{rms} = \sqrt{\frac{2E}{M}}$.

Class 11 Chemistry States of Matter Molecular speeds

Medium

The root mean square velocity of one mole of a monoatomic gas having molar mass $M$ is $V_{rms}$. The relation between the average kinetic energy $(E)$ and the $V_{rms}$ is

IIT 2004 All IIT

A
$V_{rms} = \sqrt{\frac{3E}{2M}}$
B
$V_{rms} = \sqrt{\frac{2E}{3M}}$
C
$V_{rms} = \sqrt{\frac{2E}{M}}$
D
$V_{rms} = \sqrt{\frac{E}{3M}}$

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The root mean square velocity of one mole of a monoatomic gas having molar mass $M$ is $V_{rms}$. The relation between the average kinetic energy $(E)$ and the $V_{rms}$ is

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The $RMS$ velocity of $CO$ gas molecules at $27^{\circ} C$ is approximately $1000 \ m / s$. For molecules at $600 \ K$, the $RMS$ velocity is approximately (in $m / s$)

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