An electron and a positron travelling at small speeds collide and annihilate each other. Determine the energy of the resulting gamma photon.

Step-by-step solution

The annihilation of an electron and a positron at small speeds (negligible kinetic energy) produces two gamma photons to conserve linear momentum. The initial momentum is approximately zero, so the two photons must travel in opposite directions with equal momenta, and therefore equal energies. The total initial energy of the system is the sum of the rest mass energies of the electron and the positron: E_ initial = m_e c^2 + m_e c^2 = 2m_e c^2 The rest mass energy of an electron (or positron) is: m_e c^2 = 0.51 MeV