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JEE Main 202430 JanuaryEvening Shift
Exam
JEE Main
Year
2024
Date
30 January
Shift
Evening Shift
Subject
Physics
Chapter
Nuclear Physics

JEE Main 2024 · 30 January · Evening Shift · Physics · Nuclear Physics

In a nuclear fission reaction of an isotope of mass M , three...

In a nuclear fission reaction of an isotope of mass MM, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect \DeltaM\DeltaM will be :

Options

  1. A2c\DeltaMM\sqrt{\dfrac{2c\DeltaM}{M}}
  2. B\DeltaMc23\dfrac{\DeltaM{c}^{2}}{3}
  3. Cc2\DeltaMMc\sqrt{\dfrac{2\DeltaM}{M}}
  4. Dc3\DeltaMMc\sqrt{\dfrac{3\DeltaM}{M}}

Correct answer

C. c2\DeltaMMc\sqrt{\dfrac{2\DeltaM}{M}}

Step-by-step solution

Let the reaction be, (P)→(X)+(Y)+(Z)( P ) \to ( X ) + ( Y ) + ( Z )

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

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

\DeltaMc2=12mV2+12mV2+12mV2⇒V=2\DeltaMc23m=2\DeltaMc2M−∆M≈c2\DeltaMM\DeltaM{c}^{2} = \dfrac{1}{2}m{V}^{2} + \dfrac{1}{2}m{V}^{2} + \dfrac{1}{2}m{V}^{2} ⇒ V = \sqrt{\dfrac{2\DeltaM{c}^{2}}{3m}} = \sqrt{\dfrac{2\DeltaM{c}^{2}}{M - ∆ M}} \approx c\sqrt{\dfrac{2\DeltaM}{M}}

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