Question

It is possible for an electron and a positron to orbit around their stationary center of mass until they annihilate each other, creating two photons of equal energy moving in opposite directions. A positron is a particle that has the same mass as an electron and equal but opposite charge. The amount of kinetic energy of the electron– positron pair before annihilation is negligible compared to the energy of the photons created.

(a) Calculate, in eV, the rest energy of a positron.

(b) Determine, in eV, the energy each emitted photon must have.

(c) Calculate the wavelength of each created photon.

(d) Calculate the magnitude of the momentum of each photon.

(e) Determine the total momentum of the two-photon system.

Answer 1

This is the process of pair–production, creation of particles from energy

(a) E = mc² = (9.11 x 10^–31)(3 x 10⁸)² = 8.2 x 10^–14 J *1eV/1.6 x 10^–19 J = 5.12 x 10⁵ eV

(b) To cause pair production, 2x the energy of a single electron must be present since 2 ‘electron–like’ particles are created. 2 Eelectron = 1.02 x 10⁶ eV

(c) E = hc / λ … 1.02 x 10⁶ = 1240 / λ … 1.22 x 10^–3 nm

(d) p = h / λ … 4.14 x 10^–15 / 1.22 x 10^–3 … 3.39 x 10^–12 eV-s/nm