Q. 234.5( 2 Votes )

# Two particles A and B of de Broglie wavelengths λ_{1} and λ_{2} combine to form a particle C. The process conserves momentum. Find the de Broglie wavelength of the particle C. (The motion is one dimensional).

Answer :

(Since the motion is one-dimensional, we will take into account only the magnitude of the momentum). Momentum of particle A (p_{A}) with wavelength will be given as

Momentum of particle B (p_{B} ) with wavelength will be given as

The momentum of the system before collision =

The momentum of the system after collision = where is the momentum of particle C.

Let _{3} be the de-Broglie wavelength of particle C, then

Using conservation of momentum

This result is true considering both particles are moving in one direction. If they are moving in opposite direction, we can take one direction as positive and the other as negative and repeat the above steps.

If they are moving in opposite directions then

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