Question

In the vicinity of a heavy nucleus, a high-energy photon can be converted into two particles: an electron and a positron. A positron has the same mass as the electron and equal but opposite charge. This process is called pair production.

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

(b) Determine the minimum energy, in eV, that a photon must have to give rise to pair production.

(c) Calculate the wavelength corresponding to the photon energy found in part (b).

(d) Calculate the momentum of the photon.

Answer 1

(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) The total energy before is 2x the energy from part “a” since there are two particles of the same mass. After the annihilation, there are two photons that split this total energy, so each photon simply has the energy of one of the two particles = 5.12 x 10⁵ eV.

(c) E = hc / λ … 5.12 x 10⁵ = 1240 / λ … λ = 2.42 x 10^–3 nm

(d) p = h / λ … 4.14 x 10^–15 / 2.42 x 10^–3 = 1.71 x 10^–12 eV-s / nm