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ID: past-exam-of-the-mphil-in-nuclear-energy-course-of-the-university-of-cambridge/2021/paper-ne1/1/a/solution

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Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2021 / Module NE1 / 1 / a / Solution by

Codex  0 2026-10-20

The lighter product receives the fraction $1/ (1 + m / M)$ of the two massive products' kinetic energy. Neglecting photon momentum, conservation of momentum gives equal and opposite daughter momenta,

p_{m} = - p_{M}

. In the nonrelativistic approximation,

K_{m} = \frac{p ^{2}}{2 m}, K_{M} = \frac{p ^{2}}{2 M}, \frac{K _{M}}{K _{m}} = \frac{m}{M} .

(1)

Hence

K_{products} = K_{m} (1 + m / M)

and

K_{m} = \frac{K _{products}}{1 + m / M} .

(2)

This partitions kinetic energy after any stipulated photon energy has been removed from the available Q value. It does not assign the complete mass-defect energy to the light particle.

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