The root-mean-square (rms) speed of gas molecules is given by:

From kinetic theory, the average translational kinetic energy of a molecule is $\dfrac{1}{2} m \overline{v^2} = \dfrac{3}{2} kT$ giving $\overline{v^2} = \dfrac{3kT}{m} = \dfrac{3RT}{M}$, where $M$ is molar mass. The **rms** speed is the square root: $v_{\text{rms}} = \sqrt{\dfrac{3RT}{M}}$. Other useful speeds: most probable speed $v_p = \sqrt{\dfrac{2RT}{M}}$ (option C) average speed $\langle v\rangle = \sqrt{\dfrac{8RT}{\pi M}}$ (option D). Order: $v_p < \langle v\rangle < v_{\text{rms}}$.