An electron-positron pair is created in a particle detector....

An electron-positron pair is created in a particle detector. If the tracks of the particles indicate that each one has a kinetic energy of $0.22 \mathrm{MeV},$ what is the energy of the photon that created the two particles?

Key Concepts

Pair Production

Pair production is a quantum electrodynamics process in which a high-energy photon is converted into a particle and its antiparticle, such as an electron and a positron. This process requires the photon to have sufficient energy to create the rest mass of both particles, and typically occurs near a nucleus that helps conserve momentum.

Rest Mass Energy

The rest mass energy is the intrinsic energy of a particle at rest, given by Einstein’s equation E = mc². For electrons and positrons, this energy is approximately 0.511 MeV each. In pair production, the total rest mass energy required is the sum of the rest energies of both particles, forming the baseline energy requirement for the photon.

Conservation of Energy

Conservation of energy is a fundamental principle stating that the total energy before and after a transformation must remain the same. In the context of pair production, the energy of the incoming photon must be equal to the sum of the rest mass energies of the electron and positron plus any additional kinetic energy they acquire.

Kinetic Energy

Kinetic energy in this context is the energy associated with the motion of the electron and positron after their creation. It is the surplus energy over and above the rest mass energy of the particles. The total photon energy must account for both the kinetic energies measured and the intrinsic rest mass energies of the particles.

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