Particle A of mass m A = m 2 moving along the x -axis with velocity v 0 collides elastically with another…

${\mathrm{v}}_1=\frac{2\left(\mathrm{m}/3\right)0}{\left(\frac{\mathrm{m}}{2}+\frac{\mathrm{m}}{3}\right)}+\frac{\left(\frac{\mathrm{m}}{2}-\frac{\mathrm{m}}{3}\right)\mathrm{v}}{\left(\frac{\mathrm{m}}{2}+\frac{\mathrm{m}}{3}\right)}=\frac{\mathrm{v}}{5}$

For particle $\mathrm{A}$,

Initial de-Broglie wavelength

${\mathrm{\lambda }}_0=\frac{\mathrm{h}}{\frac{\mathrm{m}}{2}\mathrm{v}}=\frac{2\mathrm{h}}{\mathrm{mv}}$

Final de-Broglie wavelength after collision.

${\mathrm{\lambda }}_1=\frac{\mathrm{h}}{\frac{\mathrm{m}}{2}\frac{\mathrm{v}}{5}}=\frac{10\mathrm{h}}{\mathrm{mv}}=5{\mathrm{\lambda }}_0$

Change in De-Broglie wavelength $\mathrm{\Delta \lambda }={\mathrm{\lambda }}_{\mathrm{i}}-{\mathrm{\lambda }}_0=4{\mathrm{\lambda }}_0$