A patient is administered a radioactive tracer for a PET scan. The physical half-life of the radionuclide is 210 minutes210\text{ minutes}210 minutes. The biological half-life of this radionuclide in the body is 140 minutes140\text{ minutes}140 minutes. Calculate the effective half-life of this tracer in the body.
The decay of the radionuclide inside the body results in the emission of a positron. Describe the physical process in which gamma-ray photons are created following this emission, and explain why two photons must be emitted in opposite directions.
The patient's chest, which has a width of 0.30 m0.30\text{ m}0.30 m, is positioned centrally between two opposing detectors of the PET scanner. Assuming the speed of the gamma-ray photons is 3.0×108 m s−13.0 \times 10^8\text{ m s}^{-1}3.0×108 m s−1, find the range of the time interval Δt\Delta tΔt between the triggering of the two detectors that the scanner must be capable of measuring to determine the position of emission within the chest.
