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