Question

An electron-position pair annihilates at rest to produce y-rays. Calculate the energy produced in $MeV$ if the rest mass of electron is $9.1\times {10}^{-31}kg$ .

Answer 1

Since the charges of the electron and positron are equal and opposite that is they are particle and antiparticle is the result of the collision of at low energy

$e^{-}+e^{+}=\gamma +\gamma$

The energy of the photon must be such that the two particle are created

$E=2m{c}^2$

The energy of the photon must be combined energy of the electron and positron.

$E=2\times 9.1\times {10}^{-31}\times {\left(3\times {10}^8\right)}^2$

$E=163.8\times {10}^{33}J$

$E=26.4\times {10}^{9}MeV$