A nucleus A , with a finite de-broglie wavelength λ A , undergoes spontaneous fission into two nuclei B…

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:
  1. λA,λA2
  2. λA2,λA
  3. λA,2λA
  4. 2λA,λA

Solution

hλA=hλB-hλC …(i)
Also λC=2λB ...(ii)
From equation (i) & (ii),
1λA=1λB-12λB
λB=λA2;λC=λA

Asked in: JEE Main 2019 (08 Apr Shift 2)

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