A particle of mass M at rest splits up into two particles of masses $\displaystyle \mathrm{m}_{1}$ and $\displaystyle \mathrm{m}_{2}$ having non-zero velocities. Calculate the ratio of the de Broglie wavelengths associated with the two particles.

Calculating the ratio of de-Broglie ccording to law of conservation of m \[\begin{aligned} \mathrm{m}_{1} v_{1}-\mathrm{m}_{2} v_{2} & =0 \\ \mathrm{m}_{1} v_{1} & =\mathrm{m}_{2} v_{2} \\ \frac{v_{1}}{v_{2}} & =\frac{\mathrm{m}_{2}}{\mathrm{m}_{1}} \\ \frac{\lambda_{1}}{\lambda_{2}} & =\frac{h}{\mathrm{m}_{1} v_{1}} \times \frac{\mathrm{m}_{2} v_{2}}{h} \\ & =\frac{\mathrm{m}_{2} v_{2}}{\mathrm{m}_{1} v_{1}} \\ & =\frac{\mathrm{m}_{2}}{\mathrm{m}_{1}} \times \frac{\mathrm{m}_{1}}{\mathrm{m}_{2}} \\ & =1 \\ \lambda_{1}: \lambda_{2} & =1: 1 \end{aligned} \] from