Problem No 9 | IPhO Estonia 2012

Problem No 9

Electron, initially at rest, is accelerated with a voltage $U=km_0c^2/e$ , where $m_0$ is the electron's rest mass, $e$ – the elementary charge, $c$ – the speed of light, and $k$ – a dimensionless number. The electron hits a motionless positron and annihilates creating two photons. The direction of one emitted photon defines the direction of the other one. Find the smallest possible value $\alpha_{\min}$ of the angle $\alpha$ between the directions of the two emitted photons (express it in terms of $k$ and provide a numrical value for $k=1$ ).