The root mean square velocity ($v_{rms}$) of a gas molecule is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$ (or thermal speed $v \approx \sqrt{\frac{k_B T}{M}}$) . At a constant temperature ($T$), the velocity is inversely proportional to the square root of the molecular weight ($M$): $v_{rms} \propto \frac{1}{\sqrt{M}}$. Therefore, the ratio of the velocities is: $\frac{v_1}{v_2} = \frac{\sqrt{\frac{1}{M_1}}}{\sqrt{\frac{1}{M_2}}} = \sqrt{\frac{M_2}{M_1}}$.