We know,

Using Graham's Law of diffusion

$\frac{{\mathrm{rate}}_1}{{\mathrm{rate}}_1} = \sqrt{\frac{{\mathrm{M}}_2}{{\mathrm{M}}_1}}$         .......$\left(\mathrm{I}\right)$

Let, the molecular mass of unknown gas is $\mathrm{x}$

The molecular mass of oxygen is $32 \mathrm{g}/\mathrm{mol}$

On putting in equation $\left(1\right)$, we get

$$\begin{gathered} \Rightarrow \frac{1}{4} = \sqrt{\frac{{\mathrm{M}}_2}{32}} \\ \Rightarrow {\mathrm{M}}_2 = 2 \raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right. \end{gathered}$$

Hence, the unkown gas is Hydrogen