Question

A gamma ray photon creates an electron-positron pair. If the rest mass energy of an electron is 0.5 MeV and the total kinetic energy of the electron-positron pair is 0.78 MeV, then the energy of the gamma ray photon must be(a) 0.78 MeV(b) 1.78 MeV(c) 1.28 MeV(d) 0.28 MeV

Answer 1

answer : option (b) 1.78 MeV

explanation : $\gamma(\textbf{photon})\rightarrow _1\beta^0(\textbf{positron})+_{-1}\beta^0(\textbf{electron})$

here it is clear that,

energy of $\gamma$ photon = rest mass energy + total kinetic energy

rest mass energy = rest mass energy of electron + rest mass energy of positron

[ rest mass energy of electron= rest mass energy of positron ]

so, rest mass energy = 0.5 + 0.5 = 1MeV

so, energy of $\gamma$ photon = 1MeV + 0.78 MeV = 1.78 MeV

Answer 2

Answer:

B) 1.78 MeV.

Explanation:

Energy of an electron = 0.5 MeV (Given)

Total kinetic energy of the electron-positron pair = 0.78 MeV (Given)

Thus, energy of g-ray photon -

γ photon → 1β0(positron) + –1β0(electron)

The energy of γ photon = rest mass energy + kinetic energy

= 0.5 + 0.5 + 0.78 ----- (rest mass of positron

= rest mass of electron)

= 1.78 MeV.  

Thus,  the energy of the gamma ray photon will be 1.78 MeV.