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

Mass of particle A = m_A, Mass of particle B = m_B

Initial velocity of A = v, initial velocity of B = 0

Initially, only particle A is moving.

After collision, let the velocity of the particle A be v₁ and that of particle B be v₂.

Then

Using conservation of momentum, Initial momentum will be same as final momentum.

Eq. 1 Since, this is an elastic collision, the Kinetic Energy shall also remain conserved.

Eq. 2

Dividing the above equation by Eq. 1, we get

Using these values in Eq. 2

Initial de-Broglie wavelength for particle A (_i), with initial momentum as p_i

Final de-Broglie wavelength for particle A , with final momentum as p_f

Change in de-Broglie wavelength (∆λ)