In a nuclear fission reaction of an isotope of mass M , three similar daughter nuclei of same mass are…

In a nuclear fission reaction of an isotope of mass M, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect ΔM will be :
  1. 2cΔMM
  2. ΔMc23
  3. c2ΔMM
  4. c3ΔMM

Solution

Let the reaction be, (P)(X)+(Y)+(Z)

Let mass of each daughter nuclei be m, then mass defect can be written as M=M-3m.

Now the energy released will be in the form of kinetic energy of the daughter nuclei. Therefore, 

ΔMc2=12mV2+12mV2+12mV2V=2ΔMc23m=2ΔMc2M-Mc2ΔMM

Asked in: JEE Main 2024 (30 Jan Shift 2)

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