Diffusion of ${\mathrm{CH}}_4 \left(\mathrm{g}\right)$ and ${\mathrm{O}}_2 \left(\mathrm{g}\right)$ occurs under similar conditions, then the ratio of their rates of diffusion is

Graham's Law: Under similar conditions of pressure, the rate of diffusion of different gases is inversely proportional to the square root of molecular mass of the respective gases.

$$\begin{gathered} \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\sqrt{\frac{{\mathrm{M}}_2}{{\mathrm{M}}_1}} \\ \Rightarrow \frac{{\displaystyle {\mathrm{r}}_1}}{{\displaystyle {\mathrm{r}}_2}}=\sqrt{\frac{{\mathrm{M}}_{{\mathrm{O}}_2}}{{\mathrm{M}}_{{\mathrm{CH}}_4}}}=\sqrt{\frac{{\displaystyle 32}}{{\displaystyle 16}}}=1.414 \end{gathered}$$