Pair Production and Annihilation

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When a photon, with the help of a nucleus experiences pair production to make a positron and an electron, the energy of the photon will equal the rest mass of both the electron and positron together right?

Then when the electron and positron annihilate, the two photons produces will each have energy equal to the rest mass of a positron/electron.

The new photons will have half the energy of the original photon each.



Is this correct?

mathman

Not quite true. The incoming photon will in general have more energy than that required to create the pair. The extra energy ends up as kinetic energy of the pair.

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Should it be expected that the parent photon will have a smaller wavelength than the two daughter photons?

mathman

Since wavelength is inversely proportional to energy, the parent photon has less than half the wavelength of the daughters.

Small correction, the extra energy of the photon in pair production goes into kinetic energy of the nucleus.