Answer
(a) If only one photon is produced, then momentum will not be conserved. However, if two photons are produced, and these photons move away in opposite directions, then momentum is still zero, and momentum is conserved.
(b) $E = 8.19\times 10^{-14}~J$
Work Step by Step
(a) Initially, the momentum is zero since the electron and positron are at rest. If only one photon is produced, then momentum will not be conserved. However, if two photons are produced, and these photons move away in opposite directions, then momentum is still zero, and momentum is conserved.
(b) We can find the energy of each photon:
$E = m_e~c^2$
$E = (9.1\times 10^{-31}~kg)(3.0\times 10^8~m/s)^2$
$E = 8.19\times 10^{-14}~J$
