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The minimum energy required for the pair production to take place is when both the electron and positron are at rest so that the energy required is equal to the sum of the rest mass of the electron and positron.
so, the minimum energy required for the pair production is,
rest mass energy of electron + rest mass energy of positron,
or, E= m0+ m0,
since the rest mass energy of electron/positron = 0.51 MeV,
so, E= 0.51 MeV + 0.51 MeV,
or E= 1.02 MeV
So, the minimum energy for the pair production is 1.02 MeV.
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