When an electron and positron annihilate, both their masses are destroyed, creating two equal energy photons to preserve momentum.

(a) Confirm that the annihilation equation e⁺ + e^- → γ + γ conserves charge, electron family number, and total number of nucleons. To do this, identify the values of each before and after the annihilation.

(b) Find the energy of each y ray, assuming the electron and positron are initially nearly at rest.

(c) Explain why the two y rays travel in exactly opposite directions if the center of mass of the electron-positron system is initially at rest.