The equation for the decay of a positive pion to muon and a neutrino.

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Chapter 39, Problem 23E

To determine

The equation for the decay of a positive pion to muon and a neutrino.

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Beams of p- mesons are used in radiation therapy for certain cancers. The energy comes from the complete decay of the p- to stable particles. (a) Write out the complete decay of a p- meson to stable particles. What are these particles? (b) How much energy is released from the complete decay of a single p- meson to stable particles? (You can ignore the very small masses of the neutrinos.) (c) How many p- mesons need to decay to give a dose of 50.0 Gy to 10.0 g of tissue? (d) What would be the equivalent dose in part (c) in Sv and in rem? Consult Table 43.3 and use the largest appropriate RBE for the particles involved in this decay.

One proposed proton decay is p+ Se+ + π0 , which violates both baryon and lepton number conservation, so the proton lifetime is expected to be very long. Suppose the proton half-life were 1.0 x 1018 y. (a) Calculate the energy deposited per kilogram of body tissue (in rad) due to the decay of the protons in your body in one year. Model your body as consisting entirely of water. Only the two protons in the hydrogen atoms in each H2O molecule would decay in the manner shown; do you see why? Assume that the π0 decays to two g rays, that the positron annihilates with an electron, and that all the energy produced in the primary decay and these secondary decays remains in your body. (b) Calculate the equivalent dose (in rem) assuming an RBE of 1.0 for all the radiation products, and compare with the 0.1 rem due to the natural background and the 5.0 rem guideline for industrial workers. Based on your calculation, can the proton lifetime be as short as 1.0 x 1018 y?

If a muon at rest decays into an electron and two neutrinos, what is the total kinetic energy of the decay products? Assume that the neutrinos have zero rest mass. Express your answer in millions of electron volts to four significant figures.