Question

A high-energy photon in the vicinity of a nucleus can create an electron-positron pair by pair production:

γ → e⁻ + e⁺.

(1) What minimum energy photon is required?
_____________MeV

(2) Why is the nucleus needed?

a)Electrons can only exist inside the nucleus. b)Positrons can only exist inside the nucleus. c)The nucleus is required to absorb the energy so that conservation of energy is not violated. d)The nucleus is required to absorb the momentum so that conservation of momentum is not violated.

Answer 1

If the photon is near an atomic nucleus, the energy of a photon can be converted into an electron-positron pair:

γ → e− + e+

The photon's energy is converted to particle's mass through Einstein’s equation, E=mc²; where E is energy, m is mass and c is the speed of light. The photon must have higher energy than the sum of the rest mass energies of an electron and positron (2 * 0.511 MeV = 1.022 MeV) for the production to occur. The photon must be near a nucleus in order to satisfy conservation of momentum, as an electron-positron pair producing in free space cannot both satisfy conservation of energy and momentum.^[1] Because of this, when pair production occurs, the atomic nucleus receives some recoil. The reverse of this process is electron positron annihilation.

So the answers are 1) 1.022 MeV

and d)The nucleus is required to absorb the momentum so that conservation of momentum is not violated.