Consider a mixture of gas molecules of types A, B and C having masses $$m_A < m_B < m_C$$. The ratio of their root mean square speeds at normal temperature and pressure is:

The root mean square speed of gas molecules is given by $$v_{rms} = \sqrt{\frac{3RT}{M}}$$, where $$M$$ is the molar mass of the gas and $$T$$ is the absolute temperature.

Since all gases A, B, and C are at the same temperature (normal temperature and pressure), the rms speed is inversely proportional to the square root of the molar mass: $$v_{rms} \propto \frac{1}{\sqrt{M}}$$.

Given that $$m_A < m_B < m_C$$, we have $$v_A > v_B > v_C$$, which means $$\frac{1}{v_A} < \frac{1}{v_B} < \frac{1}{v_C}$$.