30_InstSolManual_PDF_Part11

30_InstSolManual_PDF_Part11 - Nuclear and High-Energy...

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Solve: (a) In the lab frame the initial momentum of the system is zero, since the electron and positron have equal speeds in opposite directions. According to momentum conservation, the final momentum of the system must also be zero. A photon has momentum, so the momentum of a single photon is not zero. (b) For the two photons to have zero total momentum they must have the same magnitude of momentum and move in opposite directions. Since equal p means equal E . (c) so so and These are gamma ray photons. Reflect: The total charge of the electron/positron system is zero and the photons have no charge, so charge is con- served in the particle-antiparticle annihilation. 30.44. Set Up: Section 30.7 says that a charged pion decays into a muon plus a neutrino. The muon in turn decays into an electron or positron plus two neutrinos. Solve: (a) (b) If we neglect the mass of the neutrinos, the mass decrease is (c) The total energy delivered to the tissue is The number of mesons required is (d) The RBE for the electrons that are produced is 1.0, so the equivalent dose is
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