Question

2. A positron is the anti-particle of an electron. It has exactly the same mass as an electron but the opposite electric charge. Prove, using conservation of energy and momentum that it is impossible for an electron and positron to be formed from the "decay" of a single (high-energy) photon. (Note: this process can occur in the presence of other particles).

Answer 1

From Conservation of energy,

but since m_e = m_p , p_e = p_p

so,

=>

also, from the conservation of linear momentum,

where the angle will be the same for both due to their equal masses.

substitute this above to get:

and since , for the above condition to satify, p² must be negative (or p must be imaginary) or their rest masses must be negative either of which cannot happen.

Thus it is impossible for an electron and positron to be formed from a decay of a single photon.