 Solution

ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2022/6/a/solution

p = γm v

γ = (1 - v^{2} / c^{2})^{- 1/2}

. Equal speeds imply equal Lorentz factors, so the pion and proton momenta are in the ratio of their rest masses:

p_{π} = p_{p} \frac{m _{π}}{m _{p}} = 400 \frac{0.14}{0.94} ≃ 59.6 GeV / c .

The common dimensionless product is

γ v / c = p_{p} / (m_{p} c) = 400/0.94 ≃ 425.53

γ ≃ 425.53

and

v / c ≃ 0.99999724

 New to topics? Read the docs here!