A particle A with a mass mA is moving with a velocity v and hits a particle B (mass mB) 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 = mA, Mass of particle B = mB

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 pi



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



Change in de-Broglie wavelength (∆λ)



1