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Question

How much energy must a gamma ray photon have, if it is to materialize into a pair of electron and positron, with each particle having a K.E of 1 MeV?

A
1.0 MeV
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B
2 MeV
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C
3.02 MeV
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D
0.5 MeV
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Solution

The correct option is C 3.02 MeV
By conservation of energy,

Egamma=Eelectron+Epositron+2K.E

Mass of electron and positron are same,

Me=Mp=9.1×1031 kg

By, Einstein's Mass-Energy relation,

E=Mc2

Eelectron=Epositron=9.1×1031×(3×108)2

Eelectron=9.1×9×1015 J

Eelectron=81.9×10151.6×1013 MeV

Eelectron=0.512 MeV

Egamma=(2×0.51 MeV)+(2×1 MeV)

Egamma=3.02 MeV

Hence, option (D) is correct.

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