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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 deBroglie wavelengths λB and λC of B and C are respectively :-

A
2λA,λA
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B
λA,2λA
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C
λA,λA2
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D
λA2,λA
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Solution

The correct option is C λA2,λA
let mass of B and C is m each.
By momentum conservation
2mv0=mvmv2
v=4v0
PA=2mv0PB=4mv0Pc=2mv0
De- Broglie wavelength λ=hp
λA=h2mv0;λB=h4mv0;λc=h2mv0

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