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The collision of a positron and an electron is either a scattering event or a mutual annihilation event. Remember that the positron is antimatter; it's the antiparticle of the electron. It has a positive charge and will be attracted to electrons (or anything else negative). If a positron has extremely high energy, it will have to "slow down" before it and an electron can "mutually capture" each other and annihilate each other. Let's look at a positron with high kinetic energy that is moving very quickly through some medium like air or water. In scattering, the positron whizzes by an electron of an atom and some energy is exchanged. The positron will give a bit of energy to the electron, and how much will be determined by the energies of the positron and the electron, and some "probabilities" regarding the scattering, which could be either inelastic or elastic scattering. The net result is that the positron will leave the area moving a bit less rapidly. It lost energy (has less kinetic energy), and it is slowing down. As it slows, it experiences an increasing probability that it will be able to combine with an electron. The more it slows down, the more likely the "combining event" will become. When the positron "bumps into" an electron after slowing down, that positron and the electron will "combine" themselves, and all of their mass will be converted into energy. This energy will be carried off by a pair of electromagnetic rays, two gamma rays. And they'll have considerable energy and be moving in opposite directions. Conservation laws will have been upheld in the reaction. The combination of matter and antimatter results in mutual annihilation, and the two particles completely disappear, having had all of their mass converted into energy.

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