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Concepts Of Physics MCQ Edition [Volume 1]PhysicsCentre of Mass, Linear momentum, Collision

During a gamma decay process, a nucleus of mass M undergoes a decrease in its internal energy, emitting a gamma photon with energy E and linear momentum E/c while the nucleus recoils. Determine the decrease in the internal energy.

Options

  1. AE - E^2 2Mc^2
  2. BE + E^2 Mc^2
  3. CE^2 2Mc^2
  4. DE + E^2 2Mc^2

Correct answer

D. E + E^2 2Mc^2

Step-by-step solution

By conservation of linear momentum, the momentum of the recoiling nucleus is equal in magnitude to the momentum of the emitted gamma photon. p = E c The recoil kinetic energy of the nucleus is given by: K = p^2 2M = 1 2M ( E c )^2 = E^2 2Mc^2 By conservation of energy, the decrease in the internal energy of the nucleus U is equal to the sum of the energy of the gamma photon and the recoil kinetic energy of the nucleus. U = E + K U = E + E^2 2Mc^2

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