 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2002/ib/paper-4/9d/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the University of Cambridge / 2002 / ib / Paper 4 / 9D / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-14

Work in the parent's rest frame. Momentum conservation makes the final spatial momenta equal and opposite:

p_{m} = - p_{0}

with magnitude

p

. The massless energy is

E_{0} = p c

, while the massive energy–momentum relation is

E_{m}^{2} = m^{2} c^{4} + p^{2} c^{2}

. Conservation of energy gives

E_{m} + p c = M c^{2}

. Squaring

E_{m} = M c^{2} - p c

and cancelling the

p^{2} c^{2}

terms gives

p = \frac{M ^{2} - m ^{2}}{2 M} c, E_{0} = \frac{M ^{2} - m ^{2}}{2 M} c^{2}, E_{m} = \frac{M ^{2} + m ^{2}}{2 M} c^{2} .

The two directions are arbitrary but opposite in this frame. These are total energies, including the massive daughter's rest energy, as required for relativistic two-body decay.

 Read the full article

 New to topics? Read the docs here!