Final answer:
In pair production, a high-energy photon near a nucleus can create an electron-positron pair, with the particles being emitted at approximately 180 degrees to each other due to momentum conservation. They carry half of the photon's energy each, and upon annihilation, they produce two gamma-ray photons with energy equivalent to their rest mass.
Step-by-step explanation:
In the process of pair production, when a high-energy photon interacts near a nucleus, it can transform into an electron-positron pair. The equation indicating this process is γ → e⁻ + e⁺, where γ represents the photon, e⁻ the electron, and e⁺ the positron. The conservation of energy and momentum in this situation dictates that the electron and positron are emitted at approximately 180 degrees to each other. This is to ensure that the total momentum before and after the process remains zero. Each of the produced particles (electron and positron) carries away half of the photon's energy. Upon annihilation of an electron and a positron, two gamma-ray photons (y-rays) are produced, each possessing the energy equivalent to the rest mass of the electron or positron, according to the equation E = mc², which portrays the mass-energy equivalence.
The sum of the opposite charges on the electron and positron is equal to the zero charge of the photon. This means, since an electron has a negative charge and a positron has a positive charge, and since photons are electrically neutral, the total charge before and after pair production or annihilation must be zero, satisfying charge conservation as well. Therefore, the correct statement regarding the relationship between the mass and charge in pair production is that during the particle production, the total energy of the photon is converted to the mass of an electron and a positron, with the sum of the opposite charges on the electron and positron being equal to the zero charge of the photon, as outlined in option (c).