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A nucleus of mass M + Δ m is at rest and decays into two daughter nuclei of equal mass M 2 each. Speed of light is c. The speed of daughter nuclei is

Options

  1. Ac Δ m M + Δ m
  2. Bc Δ m M + Δ m
  3. Cc 2 Δ m M
  4. Dc Δ m M

Correct answer

C. c 2 Δ m M

Step-by-step solution

The decrease in mass Δ m will appear as the kinetic energy of the two daughter nuclei. Since the two nuclei formed are of equal masses, they will share the available energy equally among themselves. If v is the speed of a daughter nucleus, then 1 2 M 2 v 2 = 1 2 Δ m c 2 or v = c 2 Δ m M

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