In positron-emission tomography (PET) used in medical research and diagnosis, compounds containing unstable nuclei that
emit positrons are introduced into the brain, destined for a site of interest in the brain. When a positron is emitted, it goes
only a short distance before coming nearly to rest. It forms a bound state with an electron, called “positronium,” which is
rather similar to a hydrogen atom. The binding energy of positronium is very small compared to the rest energy of an
electron. After a short time the positron and electron annihilate. In the annihilation, the positron and the electron disappear,
and all of their rest energy goes into two photons (particles of light) that have zero mass; all their energy is kinetic energy
These high-energy photons, called “gamma rays,” are emitted at nearly 180 to each other. What energy of gamma ray (in
MeV, million electron volts) should each of the detectors be made sensitive to? (The mass of an electron or positron is 9 ×
10−31 kg.)