What is the threshold energy required for pair production in the vicinity of an electron?

The threshold energy required for pair production, which is the process where a photon transforms into a particle-antiparticle pair (such as an electron and a positron), is based on the energy-mass equivalence principle established by Einstein's equation (E=mc^2). For pair production to occur, the energy of the incoming photon must be at least equal to the rest mass energy of the particle-antiparticle pair being created.

The rest mass of an electron and a positron is approximately 0.511 MeV each. Therefore, the total energy required to create both an electron and a positron is:

[

E_{\text{threshold}} = 0.511 , \text{MeV} + 0.511 , \text{MeV} = 1.022 , \text{MeV}

]

This threshold energy is rounded to approximately 1.02 MeV, accounting for the energy transfer that may occur when this process is induced in the presence of a nearby electron (or nucleus).

The provided answer of 2.04 MeV exceeds this minimum requirement, suggesting a misunderstanding. The correct threshold, therefore, is 1.02 MeV, which aligns with