A particle A with a mass m${}_{A}$ is moving with a velocity v and hits particle B (mass m${}_{B}$) at rest (one-dimensional motion). Find the change in the de-Broglie wavelength of the particle A. Treat collision as elastic.

Hint: The de-Broglie wavelength depends on the momentum of the particle.

Step 1: Conserve the momentum.

As collision is elastic, hence laws of conservation of momentum and kinetic energy are obeyed.

According to the law of conservation of momentum,

Step 2: Conserve the kinetic energy.

According to the law of conservation of kinetic energy,

Step 3: Find the final velocities of A and B.

Dividing Eq. (ii) by Eq. (i) ;

we get,

Step 4: Find the change in wavelength of particle A.

Solving Eqs. (i) and (ii), we get;