(a) The rest mass energy of an electron is `m_(0)c^(2)=0.51MeV`. Can a photon of this energy create an electron in free space?
(A) A single photon of energy `2m_(0)c^(2)` or greater has enough energy to form an electron `(e^(-))`. Positron `(e^(+))` pair. But prove that this process cannot occur in free space.
(c) The pair production is possibel in presence of a third particle. Assume that a photon having frequency v collides with a nucleus of rest mass `M_(0)` (at rest) and creates an `e^(-),e^(+)` pair at rest. Calculate the mass `M_(0)` of the nucleus.
Neglect relativistic effect in all questions.

Answer

(a) No (b) `m_(0)=(h^(2)v^(2))/(2c^(2)[hv-2m_(0)c^(2)])`