Final answer:
When a positron and an electron meet, they annihilate, converting their mass into energy, specifically gamma ray photons, as per the equation E = mc². The total energy released is the combined mass of the electron and positron times the square of the speed of light.
Step-by-step explanation:
When a positron and an electron meet, they annihilate, converting all of their mass into energy. This process is a spectacular demonstration of the mass-energy equivalence principle encapsulated by Einstein's famous equation, E = mc². The annihilation of an electron-positron pair produces gamma ray photons, which are a form of electromagnetic energy. The total energy released is equal to the mass of both particles multiplied by the square of the speed of light, as the rest mass of the particles is entirely converted into energy.
To find the energy released (part a), we would use the rest mass of the electron (which is the same as the positron) and the equation E = mc². Since photons as gamma rays are emitted, they carry away the energy in the form of electromagnetic radiation. Giving this energy to a proton or another electron (parts b and c) would result in these particles gaining kinetic energy and thus speed, with the velocities depending on their respective masses and the energy transferred to them.