19.7 Annihilation Reactions

19.7 Annihilation Reactions

We have already discussed annihilation of positron-electron pair in the last chapter. Infact, annihilation is an event taking place whenever a particle and its antiparticle come close to each other. In elementary particles research, very high energies are required for investigations. Instead of collisions at their rest mass energies, they are accelerated to nearly the speed of light and then collided. At CERN's Large Hadron Collider (LHC), proton $p$ -antiproton $\bar{p}$ and other heavy nuclei are collided at nearly with the speed of light to create conditions similar to early universe. $p$ -$\bar{p}$ and other heavy particles collision at energies of the order of $\mathrm{TeV}$ offer insight to early universe conditions. During such collisions electro-weak force mediation particles $W^{+}$, $W^{-}$ and $Z$ bosons predicted by Prof. Abdus Salam have been discovered, along with top and bottom quarks and most significant Higgs bosons in July, $2012$.

For your information

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Schematic diagram of $p^{-}$ and $p$ collision Image of a $7\,\mathrm{TeV}$ proton-proton collision in CMS producing more than $100$ charged particles

Example 19.4

Calculate the energy of the gamma ray photons emitted during the annihilation of an electron-positron pair .

Solution

Mass of positron $= 9.1 \times 10^{-31}\,\mathrm{kg}$ Mass of electron $= 9.1 \times 10^{-31}\,\mathrm{kg}$ Using Einstein mass-energy relation $E = 2mc^{2}$ $= 2 \times 9.1 \times 10^{-31}\,\mathrm{kg} \times (3 \times 10^{8}\,\mathrm{m\,s^{-1}})^{2}$ $E = 1.64 \times 10^{-13}\,\mathrm{J}$ In $\mathrm{eV}$, $E = (1.64 \times 10^{-13}\,\mathrm{J}) / (1.6 \times 10^{-19}\,\mathrm{J\,(eV)^{-1}})$ $= 1.02\,\mathrm{MeV}$ Hence $2\gamma$-ray photons will be emitted each with $0.51\,\mathrm{MeV}$ energy travelling in opposite directions to conserve momentum.