Final answer:
(a) The average energy of charged particles resulting from pair production in the nuclear field for hν = 2 MeV is 1 MeV, and for hν = 20 MeV is 10 MeV.
Step-by-step explanation:
The average energy of charged particles resulting from pair production is determined by the energy of the photons initiating the process. For pair production to occur in an electron field, the photon must have a minimum energy of 1.022 MeV (twice the rest mass energy of an electron).
In a nuclear field, the energy threshold is the same, but the presence of the field allows energy conservation. For photons with an energy of 2 MeV and 20 MeV, the average energy of the resulting charged particles would depend on the specific process and the distribution of excess energy between them.
However, for a narrow beam containing 10²⁰ photons at 6 MeV impinging perpendicularly on a layer of lead 12 mm thick and with a density of 11.3 g/cm³, the number of pair production events would depend on the cross-sectional area of the photons and the lead's thickness and density, which affects the mean free path of photons in lead.