Fig 23.4: Pair production, as a photon is converted into an electron and a positron
The photon has momentum in the direction it is travelling before the interaction.When the electron and positron are produced, they each travel at an angle as shown in Fig 23.4.The electron/positron pair carry the same momentum in the x-direction as the photon had before the interaction. The pair carry equal amounts of momentum in opposite directions in the y-direction.Therefore the total momentum before the interaction is equal to the total momentum after.
Pair Annihilation PAIR ANNIHILATION
Pair annihilation is the formation of two photons when a particle–antiparticle pair collide; the pair convert all their mass into energy.
The laws of conservation hold true for pair annihilation Mass-energy:
The mass of the particles is converted into the energy of the photons in accordance with the equation E mc2.
Photon () Photon () Electric charge: Electron (e–) Positron (e+)
Fig 23.5: Pair annihilation, as an electron and positron produce two photons
Electron and positron have opposite charges and the photons have no charge, therefore the total charge before and after the interaction is zero. Momentum:
The particle–antiparticle pair are moving in opposite directions before they collide, meaning that the total momentum beforehand is zero. The photons travel in opposite directions after, therefore the total momentum before and after is zero.
SAMPLE PROBLEM 23F
A -photon with a frequency of 3.0 1020 Hz produces an electron/positron pair when fired at a nucleus of a large atom.The positron collides with an electron in a neighbouring atom and both are annihilated, producing a pair of photons. Calculate:
(i) the speed of the electron and positron produced by the 3.0 1020 Hz photon (ii) the frequency of each photon produced when an electron and positron annihilate each other.
(Mass of electron 9.1094 1031 kg; speed of light 2.9979 108 m s1; Planck’s constant 6.6 1034 J s.)
