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Essential University Physics: Volume 2 (3rd Edition)
3rd Edition
ISBN: 9780321976420
Author: Richard Wolfson
Publisher: PEARSON
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Question
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.
Chapter 39 Solutions
Essential University Physics: Volume 2 (3rd Edition)
Ch. 39 - Prob. 1FTDCh. 39 - Prob. 2FTDCh. 39 - Prob. 3FTDCh. 39 - Prob. 4FTDCh. 39 - Prob. 5FTDCh. 39 - Prob. 6FTDCh. 39 - Prob. 7FTDCh. 39 - Prob. 8FTDCh. 39 - Name the fundamental force involved in (a) binding...Ch. 39 - Prob. 10FTD
Ch. 39 - Prob. 11FTDCh. 39 - Prob. 12FTDCh. 39 - Prob. 13FTDCh. 39 - Prob. 14FTDCh. 39 - Describe the origin of the cosmic microwave...Ch. 39 - Prob. 16FTDCh. 39 - Prob. 17FTDCh. 39 - The radiation that we observe as the cosmic...Ch. 39 - Prob. 19FTDCh. 39 - Prob. 20FTDCh. 39 - Prob. 21ECh. 39 - Prob. 22ECh. 39 - Prob. 23ECh. 39 - Prob. 24ECh. 39 - Prob. 25ECh. 39 - Prob. 26ECh. 39 - Prob. 27ECh. 39 - Prob. 28ECh. 39 - Prob. 29ECh. 39 - Prob. 30ECh. 39 - Prob. 31ECh. 39 - Prob. 32ECh. 39 - Prob. 33ECh. 39 - Prob. 34ECh. 39 - Prob. 35ECh. 39 - Prob. 36ECh. 39 - Prob. 37ECh. 39 - Prob. 38PCh. 39 - Prob. 39PCh. 39 - Prob. 40PCh. 39 - Prob. 41PCh. 39 - Prob. 42PCh. 39 - Prob. 43PCh. 39 - Prob. 44PCh. 39 - Prob. 45PCh. 39 - Prob. 46PCh. 39 - Prob. 47PCh. 39 - Prob. 48PCh. 39 - Prob. 49PCh. 39 - Prob. 50PCh. 39 - Prob. 51PCh. 39 - Prob. 52PCh. 39 - Prob. 53PCh. 39 - Prob. 54PCh. 39 - Prob. 55PCh. 39 - Prob. 56PCh. 39 - Prob. 57PCh. 39 - Prob. 58PCh. 39 - Prob. 59PCh. 39 - Prob. 60PCh. 39 - Prob. 61PPCh. 39 - Prob. 62PPCh. 39 - Prob. 63PPCh. 39 - Prob. 64PP
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- (a) Show that the conjectured decay of the proton, violates conservation of baryon number and conservation of lepton number. (b) What is the analogous decay process for the antiproton?arrow_forwardThe K0 meson is an uncharged member of the particle “zoo” that decays into two charged pions according to K0 → π+ + π−. The pions have opposite charges, as indicated, and the same mass, mπ = 140 MeV/c2. Suppose that a K0 at rest decays into two pions in a bubble chamber in which a magnetic field of 2.0 T is present (see Fig. P2.22). If the radius of curvature of the pions is 34.4 cm, find (a) the momenta and speeds of the pions and (b) the mass of the K0 meson.arrow_forwardA proton and an antiproton collide headon, with each having a kinetic energy of 7.00 TeV (such as in the LHC at CERN). How much collision energy is available, taking into account the annihilation of the two masses? (Note that this is not significantly greater than the extremely relativistic kinetic energy.)arrow_forward
- (a) Is the decay possible considering the appropriate conservation laws? State why or why not. (b) Write the decay in terms of the quark constituents of the particles.arrow_forward(a) Is a hadron always a baryon? (b) Is a baryon always a hadron? (c) Can an unstable baryon decay into a meson, leaving no other baryon?arrow_forwardBased on quark composition of a proton, show that its charge is +1.arrow_forward
- (a) What is the uncertainty in the energy released in the decay of a due to its short lifetime? (b) Is the uncertainty in 1his energy greater than or lees than the uncertainty in the mass of the tau neutrino? Discuss the source of the uncertainty.arrow_forwardOne decay mode for the etazero meson is (a) Write the decay in terms at the quark constituents. (b) How much energy is released? (c) What is the ultimate release of energy, given the decay mode for the pi zero isarrow_forward(a) Find the charge, baryon number, strangeness, charm, and bottomness of the particle from its quark composition. (b) Do the same for the particle.arrow_forward
- The highest energy beams at LEP achieved had E=104.5 GeV. As2...(a) Calculate how much larger was the synchrotron energy loss at this energy, relative to the synchrotron energy loss at E=45.1 GeV. (b) If protons had been used instead of electrons, how much smaller would the energy loss have been, for a beam energy of E=104.5 GeV?arrow_forwardAccelerators such as the Triangle Universities Meson Facility (TRIUMF) in British Columbia produce secondary beams of pions by having an intense primary proton beam strike a target. Such “meson factories” have been used for many years to study the interaction of pions with nuclei and,hence, the strong nuclear force. One reaction that occurs isπ+ + p → Δ++ → π+ + p , where the Δ++ is a very short-lived particle. The graph shows the probability of this reaction as a function of energy. The width of the bump is the uncertainty in energy due to the short lifetime of the Δ++ .(a) Find this lifetime.(b) Verify from the quark composition of the particles that thisreaction annihilates and then re-creates a d quark and a d antiquark by writing the reaction and decay in terms ofquarks.(c) Draw a Feynman diagram of the production and decay ofthe Δ++ showing the individual quarks involved.arrow_forwardA proton‑antiproton annihilation takes place, leaving two photons with a combined energy of 2.50 GeV. Find the kinetic energy Kp of the proton if the proton had the same kinetic energy as the antiproton. Find the kinetic energy Kp′ of the proton if the proton had 1.25 times as much kinetic energy as the antiproton.arrow_forward
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