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).