 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ia/paper-4/12b/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Squaring

p_{H} = p_{1} + p_{2}

gives

m^{2} c^{4} = 2 E_{1} E_{2} (1 - cos θ) = 4 E_{1} E_{2} sin^{2} (θ /2)

, proving the formula. If the rest-frame photons are along

\pm y

, an

x

-boost gives equal energies and

sin (θ /2) = 1/ γ

, hence

v = c cos (θ /2)

 New to topics? Read the docs here!