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Question:

A nucleus A, with a finite de Broglie wavelength λA, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de Broglie wavelengths λB and λC of B and C are respectively:-

2λA,λA

λA,2λA

λA,λA/2

λA/2,λA

Solution:

Correct option is D. λA/2,λA
Let mass of B and C is m each.
By momentum conservation
2mv0=mv - mv/2
v=4v0
PA=2mv0
PB=4mv0
PC=2m
De- Broglie wavelength λ=h/p
λA=h/2mv0;
λB=h/4mv0;
λC=h/2mv0