In a medical technique called PET (positron emission tomography) scanning, glucose is tagged with F-18, and its progress through the body can be tracked. F-18 undergoes positron emission with a half-life of 1.83hours, but the scanner does not detect the positrons directly. Instead, it detects the gamma rays produced when the positron collides with a nearby electron - the two particles annihilate one another, and their combined mass is completely converted into energy.
a) Calculate the amount of energy produced (in J) when one positron and one electron annihilate one another. Each particle has a mass of 9.1*10^-31kg.
b) If that energy is carried away by two gamma rays photons, what is the wavelength of each photon?
c) The F-18 used in PET studies must be produced in a cyclotron. Assuming the F-18 can be transported at 50.0 miles/ hour, how close must the hospital be to the cyclotron in order to make sure that 85% of the F-18 remains wen it gets there?