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What will be the total energy shared between an electron and positron, that have been created through pair production from a 10 MeV photon

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Answer:

The total energy that an electron and positron share is 5 Mev    

Explanation:

One of the potential ways that gamma rays interact with matter is by the formation of positron-electron pairs.

The pair production requires a minimum gamma-energy of 1.02 MeV since an electron's rest mass is equal to 0.511 MeV of energy. The electron-positron pair receives any extra kinetic energy from the pair-producing gamma ray.

The reaction is represented by γ =(. - 1e⁰) +  (. + 1e⁰)

E = m₀C² + [tex]KE_{electron}[/tex] + m₀C² + [tex]KE_{positron}[/tex]

10 MeV = 2m₀C² + [tex]KE_{electron}[/tex] + [tex]KE_{positron}[/tex]

[ 2m₀C²= 1.02 ] and since the mass of electron and positron is the same, the Kinetic energy (KE), 1/2 mv² will also be the same

Therefore,

KE = 1/2(10 - 1.02)

    =4.49 MeV

[ 2m₀C²= 1.02 so, m₀C² = 1.02/ 2 = 0.51]

Total energy shared = m₀C² + KE

                                  =  0.51 + 4.49

                                  = 5 Mev

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