Suppose that positron–electron annihilations occur on the line 3 cm from the center of the line connecting two detectors. Will the resultant photons be counted as having arrived at these detectors simultaneously?

(a) No, because the time difference between their arrivals is 100 ms;

(b) No, because the time difference is 200 ms;

(c) yes, because the time difference is 0.1 ns;

(d) yes, because the time difference is 0.2 ns.

In the imaging method called positron emission tomography (PET), a patient is injected with molecules containing atoms that have nuclei with an excess of protons. As they decay into neutrons, these protons emit positrons. An emitted positron travels a short distance and slows to near-zero velocity; when it encounters an electron, they may annihilate each other and emit two photons in opposite directions. The patient is enclosed in a circular array of detectors, with the tissue to be imaged centered in the array. If two photons of the proper energy strike two detectors simultaneously (within 10 ns), we can conclude that the photons were produced by positron electron annihilation somewhere along a line connecting the detectors. By observing many such simultaneous events, we can create a map of the distribution of positron-emitting atoms in the tissue. However, photons can be absorbed or scattered as they pass through tissue. The number of photons remaining after they travel a distance x through tissue is given by N = N₀e^-µx, where N₀ is the initial number of photons and m is the attenuation coefficient, which is approximately 0.1 cm^-1 for photons of this energy. The index of refraction of biological tissue for x rays is 1.