Solved: Irradiating Ourselves! The radiocarbon in our

Chapter 43, Problem 43.55

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Irradiating Ourselves! The radiocarbon in our bodies is one of the naturally occurring sources of radiation. Let’s see how large a dose we receive. \(^{14}C\) decays via \(\beta^-\) emission, and 18% of our body’s mass is carbon. (a) Write out the decay scheme of carbon-14 and show the end product. (A neutrino is also produced.) (b) Neglecting the effects of the neutrino, how much kinetic energy (in MeV) is released per decay? The atomic mass of \(^{14}C\) is 14.003242 u. (c) How many grams of carbon are there in a 75-kg person? How many decays per second does this carbon produce? (Hint: Use data from Example 43.9.) (d) Assuming that all the energy released in these decays is absorbed by the body, how many MeV/s and J/s does the \(^{14}C\) release in this person’s body? (e) Consult Table 43.3 and use the largest appropriate RBE for the particles involved. What radiation dose does the person give himself in a year, in Gy, rad, Sv, and rem?