Find the ratio of the root mean square speeds of oxygen molecules (O2) and ozone molecules (O3) at the same temperature.

The root mean square speed is inversely proportional to the square root of the molar mass ($v_{rms} \propto \frac{1}{\sqrt{M}}$). For oxygen ($M_1 = 32$) and ozone ($M_2 = 48$), the ratio is $\frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}} = \sqrt{\frac{48}{32}} = \sqrt{\frac{3}{2}}$.