Question

A positron and an electron with negligible kinetic energy meet and annihilate one another, producing two γ-rays of equal energy. What is the wavelength of these γ-rays?

Answer 1

In the annihilation process energy released is equal to the sum of rest mass energy of positron and electron which is 2mc². Because of momentum and energy conservation, the two photons must carry equal energy. Therefore each gamma ray carries energy 

E_γ = mc² = 0.511 MeV 

The wavelength of each photon 

λ = 1, 241/(0.511 × 10⁶)nm = 2.428 × 10⁻³nm = 2.428 × 10⁻¹²m