JEE Main & Advanced Physics Nuclear Physics And Radioactivity Pair Production and Pair-Annihilation

When an energetic g-ray photon falls on a heavy substance. It is absorbed by some nucleus of the substance and an electron and a positron are produced. This phenomenon is called pair production and may be represented by the following equation         

\[\underset{(\gamma -\text{photon)}}{\mathop{h\nu }}\,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\underset{(\text{Positron)}}{\mathop{_{1}{{\beta }^{0}}}}\,\,\,\,\,\,\,\,+\,\,\,\,\,\,\,\underset{(\text{Electron)}}{\mathop{_{-1}{{\beta }^{0}}}}\,\]

The rest-mass energy of each of positron and electron is

\[{{E}_{0}}={{m}_{0}}{{c}^{2}}=(9.1\times {{10}^{31}}kg)\times {{(3.0\times {{10}^{8}}m/s)}^{2}}\] \[=8.2\times {{10}^{14}}J=\mathbf{0}.\mathbf{51}MeV\]

Hence, for pair-production it is essential that the energy of g-photon must be at least \[2\times 0.51\text{ }=1.02MeV\]. If the energy of \[\gamma -\]photon is less than this, it would cause photo-electric effect or Compton effect on striking the matter.

The converse phenomenon pair-annihilation is also possible. Whenever an electron and a positron come very close to each other, they annihilate each other by combining together and two \[\gamma -\]photons (energy) are produced. This phenomenon is called pair annihilation and is represented by the following equation.

\[\underset{(\text{Positron)}}{\mathop{_{+1}{{\beta }^{0}}}}\,\,\,\,\,\,\,\,\,+\,\,\,\,\,\,\,\underset{(\text{E}lectron\text{)}}{\mathop{_{-1}{{\beta }^{0}}}}\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\underset{(\gamma \text{-photon})}{\mathop{h\nu }}\,\,\,\,\,+\,\,\,\underset{(\gamma \text{-photon})}{\mathop{h\nu }}\,\]