Final answer:
The kinetic energy of the positron, when a photon decays into an electron-positron pair, is found to be 1.146 MeV when the photon energy is 2.55 MeV and the electron's kinetic energy is 0.382 MeV.
Step-by-step explanation:
The question asks about the kinetic energy of a positron, given that an electron-positron pair is produced by a 2.55 MeV photon, and the kinetic energy of the electron is 0.382 MeV.
In such pair production interactions, the initial photon energy is converted into the rest mass energies of the electron and positron (each having a rest mass energy of 0.511 MeV) plus their kinetic energies. All these values must add up to the initial photon energy.
The kinetic energy of the positron can be found using the conservation of energy principle. The initial energy of the photon (2.55 MeV) is equal to the sum of the rest mass energies of the electron and positron (2 * 0.511 MeV) plus their kinetic energies.
We have the kinetic energy of the electron (0.382 MeV), so we can find the kinetic energy of the posiron (KEpositron) by the following calculation:
KEpositron = Total photon energy - (Electron rest mass + Positron rest mass) - Electron kinetic energy
KEpositron = 2.55 MeV - (0.511 MeV + 0.511 MeV) - 0.382 MeV
KEpositron = 2.55 MeV - 1.404 MeV
KEpositron = 1.146 MeV