Since the initial momentum of the system is zero. To keep the final momentum zero, the momentum of both parts should be equal and opposite in direction.

$\left|{\overrightarrow{P}}_1\right|=\left|{\overrightarrow{P}}_2\right|$

Here $\overrightarrow{P}$ is momentum

De-Broglie wavelength is given by $\lambda =\frac{h}{P}$

Hence, both will have same de Broglie wavelength.

Therefore, ${\lambda }_1:{\lambda }_2=1:1$.