2. Suppose that the difference between the square of the mass of the electron neutrino and that of the muon neutrino is m?, - m, = a? and that between muon and tau neutrino is m? - m, = b. (a) What are the dimensions of a and b?
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- 4. Suppose some object in space emits a muon and a photon at the same time. The muon's decay timescale is 2.2 usec. This is actually a characteristic decay time, but for this problem, we will assume it's the maximum lifetime of the muon. Let this object in space be at a distance of 100 light years from Earth. How much sooner will the photon, which moves at the speed of light, arrive at Earth than the muon?Answers to d and e please99Mo beta decays with a half-life of 66 h to 99Tc*, an isotope that is widely used in medical imaging. The 99Mo itself is created in a nuclear reactor by bombarding 235U nuclei with neutrons. One particular 99Mo was created in this way 66 h ago, while another was created just now. Which nucleus is morelikely to decay in the next 66 h?
- A nuclei has a mass of 6.51×10-27 kg. What is its mass in Mev/c²? 3.65x10³ Mev/c² 3.92 Mev/² 7.85x10³ Mev/c² Question 3 Is the following decay possible? 232Th (Z=90) 236µ (Z = 92) + a 000 It's impossible to tell No YesSupply the missing neutrinos in the following reactions or decays. (a) µ+ → e+ + ? (b) ? + p → n + e+ (c) π- → µ- + ? (d) K- → µ- + ? (e) ? + n → p + µ-14. In the β+ decay of nitrogen-12 (12.01864 u) into carbon-12 (12.00000 u), a positron with energy of 11.0 MeVis emitted. What is the energy of the electron neutrino? Assume the mass of the positron is 5.485799 x 10-4 u(same as an electron).
- 3. What magnetic field is required for the 7.0-TeV protons in the 4.25-km radius Large Hadron Collider (LHC)? 4. Show that the energy of a particle (charge q.) in a synchotron, in the relativistic limit (v z c), is given by E = Brc, where E is measured in eV, B is the magnetic field, and r is the radius of the orbit.9. Which of the following reactions and decays are possible? For those forbidden, explain what laws are violated? (а) п- +р+п + п?. (b) a+ +p → n+ 7º. (c) n+ +p→p+ e+. (d) p→ e+ + ve. (e) p→n + e+ + Ve- 10. Draw the two Feynman diagrams for electron-electron scattering at the first-order. Draw three distinct second-order diagrams.7. What are the wavelengths of the two photons produced when a proton and antiproton annihilate? 8. The A° cannot decay by the following reactions. What conservation laws are violated in each of the reactions? (а) Л° - п+п-. (b) A° + p+ K¯. (c) A° + n+ + T¯.
- 5. Pion beams (*) are used to treat cancer in radiation therapy. The energy comes from the decay of the pions. Negative pions usually decay into a muon and a muon antineutrino. (a) (b) Write out the complete decay of a л into stable particles. How much energy is released from a complete decay? Assume the neutrino masses are negligible. (c) How many pions need to decay to give a dose of 50.0 Gy to 10.0 grams of tissue?A yoyo of radius R and mass M is released from rest with the string vertical and its top end fixed up a support as shown below. How fast is the center of mass of the yoyo moving when it has fallen a distance of 47 cm. Ignore the mass of the string and express your answer if m/s5. How much energy is released in the decay + → µt + v„? 6. How much energy is required to produce a neutron-antineutron pair?