question_answer

What is the minimum amount of energy released in the annihilation of an electron-positron pair?

Answer:

                The energy released in the annihilation is minimum when both electron and positron are at rest. Hence,        \[{{E}_{\min }}=2{{m}_{0}}{{c}^{2}}\] (where, \[{{m}_{0}}=\]rest mass of electron or positron) \[{{E}_{\min }}=2\times 9.1\times {{10}^{-31}}\times {{(3\times {{10}^{8}})}^{2}}J\] \[=\frac{2\times 9.1\times {{10}^{-31}}\times {{(3\times {{10}^{8}})}^{2}}}{1.6\times {{10}^{-31}}}\text{MeV}\] \[=1.02\text{MeV}\text{.}\]