The root mean square speed of molecules of nitrogen gas at $27^{\circ} C$ is approximately $.......m/s$. (Given: mass of a nitrogen molecule $= 4.6 \times 10^{-26} \, kg$ and Boltzmann constant $k_{B} = 1.4 \times 10^{-23} \, J K^{-1}$)

$A$ 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:

If the $rms$ speed of hydrogen gas is equal to the $rms$ speed of oxygen gas at $47^{\circ}C$,find the temperature of the hydrogen gas in $K$.

At a given temperature,the $rms$ velocity of a gas molecule of mass $m$ is proportional to:

The value closest to the thermal velocity of a Helium atom at room temperature $(300\,K)$ in $m/s$ is $[k_B = 1.4 \times 10^{-23}\,J/K; m_{He} = 7 \times 10^{-27}\,kg]$.

The speeds of $5$ gas molecules are $2, 3, 4, 5,$ and $6$ units respectively. What is the $rms$ speed of these molecules?