Two particles A and B of de Broglie wavelengths

Question:

Two particles A and B of de Broglie wavelengths λ1 and λ2 combine to form a particle C. The process conserves momentum. Find the de Broglie wavelength of the particle C. (The motion is one dimensional).

Solution:

According to de-Broglie wavelengths,

λ=h/p

p=h/ λ

p1 = h/ λ1

p2 = h/ λ2

p3 = h/ λ3

There are 4 possible cases and they are:

Case 1: When p1 and p2 are positive, then λ3 = λ1 λ1/ λ1+ λ2

Case 2: When p1 and p2 are negative, then λ3 = λ1 λ2/ λ1+ λ2

Case 3: When p1 > 0 and p2 < 0, then λ3 = λ1 λ2/ λ2 – λ1

Case 4: When p1 < 0 and p2 > 0, then λ3 = λ1 λ2/ λ1- λ2

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