(3-15) Energy of electron at rest = energy of positron at rest = mc2
= 9.11 x 10-31 x (3.00 x 108)2 = 8.20 x 10-14 J
So each of the photons produced in the mutual annihilation should have this energy.
photon energy E = hc/ λ where λ is the wavelength, h is Planck’s constant and c is the speed of light. So we would predict:
λ = hc/E = 6.626 x 10-34 x 3.00 x 108 / 8.20 x 10-14 = 2.42 x 10-12 m
which accords with what is actually observed: so it works!