A particle A with a mass m is moving with a velocity v and hits particle B (mass m) 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) ;
Step 4: Find the change in wavelength of particle A.
Solving Eqs. (i) and (ii), we get;