If the r.m.s. speed of a chlorine molecule is $490\,m/s$ at $27^{\circ}C$,the r.m.s. speed of argon molecules at the same temperature will be $......\,m/s$ (Atomic mass of argon $= 39.9\,u$,molecular mass of chlorine $= 70.9\,u$). (in $.7$)

Nitrogen gas is at $300^{\circ} C$ temperature. The temperature (in $K$) at which the $rms$ speed of a $H_{2}$ molecule would be equal to the $rms$ speed of a nitrogen molecule is........ (Molar mass of $N_{2}$ gas = $28 \ g/mol$,Molar mass of $H_{2}$ gas = $2 \ g/mol$)

$A$ mixture of $2$ moles of helium gas (atomic mass $= 4 \ amu$) and $1$ mole of argon gas (atomic mass $= 40 \ amu$) is kept at $300 \ K$ in a container. The ratio of the rms speeds $\left(\frac{v_{\text{rms}} \text{ (helium)}}{v_{\text{rms}} \text{ (argon)}}\right)$ is:

The respective speeds of the five molecules are $1, 2, 3, 4$ and $5 \ km/s$. The ratio of their root mean square (rms) velocity to their average velocity is:

At what $^\circ C$ temperature will the molecules of nitrogen have the same $rms$ velocity as the molecules of oxygen at $127^\circ C$?

For a given gas at temperature $T$,the root mean square velocity is $\nu_{rms}$,the average velocity is $\nu_{av}$,and the most probable velocity is $\nu_{mp}$. Which of the following relations is correct?