An ultrarelativistic <electron> has <kinetic energy> much larger than its rest <energy>: $(\gamma-1)m_ec^2\gg m_ec^2$, equivalently $\gamma\gg1$. Its <speed> obeys $v/c=\sqrt{1-\gamma^{-2}}\simeq1-1/(2\gamma^2)$ and its total <energy> is approximately $pc$. At $\gamma=10^6$, $E=\gamma m_ec^2\simeq511\ \mathrm{GeV}$.

Solution

Past exam of the astrophysics course of the University of Oxford / 2022 / 4 / a / Solution

 Solution (source code)