Question

Calculate the minimum amount of energy which a gamma ray photon should have for the production of an electron and a positron pair..

Answer 1

The equation representing pair production is given by,

hv = _-1β⁰ + ₁β⁰

This equation follows Einstein's- mass energy relation. So, for this process to occur, energy of photon should be at least equal to the rest mass energy of electron and position.

Therefore hv = 2m_oc²    ...(Here m_o is the rest mass energy of electron)

`= 2 xx 9.1 xx 10^-31 "kg" xx (3 xx 10^8)^2 ("ms"^-1)^2`

`= 2 xx 8.2 xx 106-14`J

`= (16.4 xx 10^-14)/(1.6 xx 10^-19 "J"//"eV")`

= 1.02 × 10⁶ eV

= 1.02 MeV