Chapter #14 Solutions - Modern Physics for Scientists and Engineers - Andrew Rex, Stephen T. Thornton - 3rd Edition

 

1. What are the frequencies of two photons produced when a proton and antiproton annihilate each other at rest? Get solution

1q. What are the characteristics of the following conservation laws: mass-energy, electric charge, linear momentum, angular momentum, baryon number, lepton number? Explain how they are related to fundamental laws of nature. Get solution

2. The mass of the charged pion is 140 MeV/c 2. Determine the range of the nuclear force if the pion is the mediator. Get solution

2q. Why are storage rings useful for high-energy accelerators? Get solution

3. The strong interaction must interact within the time it takes a high-energy nucleon to cross the nucleus. Use an appropriate speed and distance to estimate the time for the strong interaction to occur. Get solution

3q. Why are colliding beams useful for particle physics experiments? Get solution

4. To probe another particle with linear dimensions D, the wavelength of the probing particle must be λ ≤ D. To learn details, the wavelength should be substantially less, perhaps as small as 0.10D. Calculate the kinetic energies of an electron and a proton needed to probe the details of a neutron. Assume the diameter of the neutron is 1.5 fm. Get solution

4q. Can a baryon be produced when an antibaryon interacts with a meson? Explain. Get solution

5. Some details of elementary particles may need to be probed on distance scales as small as 10-18 m. Calculate the kinetic energies of an electron and a proton necessary to probe details this small. (Hint: See Problem 4, but we don’t need to divide by the factor of 10 to determine the wavelength.) Problem 4 To probe another particle with linear dimensions D, the wavelength of the probing particle must be λ ≤ D. To learn details, the wavelength should be substantially less, perhaps as small as 0.10D. Calculate the kinetic energies of an electron and a proton needed to probe the details of a neutron. Assume the diameter of the neutron is 1.5 fm. Get solution

5q. What kinds of neutrinos are produced in the reaction ...? Explain. Get solution

6. The omega meson ω (mass = 782 MeV/c 2) is believed to be the mediator for a short-range repulsive force. Estimate the range of this force. Get solution

6q. What mediating particles are exchanged between two positrons? Between two quarks? Get solution

7. Suppose that the Higgs boson is discovered and that it has a mass of 150 GeV/c 2. Physicists believe it may be the mediator of a new force. Use its mass to determine the range of the force. Get solution

7q. Which families of particles seem to be truly elementary? Get solution

8. Supply the missing neutrinos in the following reactions or decays. ... Get solution

8q. How can you determine whether particles are mesons or baryons by looking at their quark structure? Get solution

9. Estimate the approximate number of baryons in planet Earth. Get solution

9q. Does it appear that the total baryon number of the universe is zero? What would that mean? Get solution

10. The mass of the Ω- baryon is 1672.45 × 0.29 MeV/c 2, where the latter number represents the experimental uncertainty. The lifetime is quoted as 8.21 × 10-11 s. (a) What is the intrinsic value of its resonance width ... based on its lifetime? (b) How does this compare with the experimental uncertainty in the mass-energy? Get solution

10q. Explain how a magnet may be used to distinguish a range of energies for protons. How can a mono-energetic beam of protons be obtained? Get solution

11. The values of the mean lifetime arc not listed in the 2004 Review of Particle Physics (see http://pdg.lbLgov) for the ... and upsilon ... mesons. We have listed approximate values in Table 14.4. The 2004 Review gives the full-width ... values of 91.0 keV and 53.0 keV, respectively, for the two mesons. Determine their lifetimes. ... Get solution

11q. Why is it a problem when a particle gets out of phase with the frequency of a pulsed accelerator? Get solution

12. Consider the two following reactions: ... Do both of these reactions obey the conservation rules? Does this explain why K0 is not its own antiparticle? Get solution

12q. Explain why electron accelerators that are not linear must have large radii. The largest such accelerator is the LHC at CERN, which has a radius of 4.3 km. Get solution

13. Explain why each of the following reactions is forbidden. ... Get solution

13q. The next proposed accelerator is an electron-positron collider that may be many kilometers long. Why must it be so long? Why can’t it be circular to save space? Get solution

14. Explain why each of the following reactions is forbidden. ... Get solution

16. A ... of kinetic energy 600 MeV decays in flight into ... rays of equal energies. Determine the angles of the ... Get solution

17. Complete the following reactions. ... Get solution

18. Show that electric charge, baryon number, and strangeness for the neutron, ..., and for ... are all equal to the sum of their quark configurations. Get solution

19. Show that electric charge, baryon number, and strangeness for the π-, K-, and D0 are all equal to the sum of their quark configurations. Get solution

20. Determine the quark composition of the D0, D-, and D+ charmed mesons. Get solution

21. Determine the quark composition of the B+, B-, and B0 mesons. Get solution

22. What kind of particle would you expect to be made of the ...u configuration? Get solution

23. The Ω- baryon decays primarily through the following reaction: ...Subsequently the ...and K- also decay by the first reaction listed for each in the Table 14.4 column Main Decay Modes. (a) Are these strong or weak decay interactions? (b) Write out each reaction using its particle symbols and its quark composition. ... Get solution

24. Consider particles with the following quark composition. Determine their quantum numbers and the particle names. ... Get solution

25. Assume the half-life of the proton is 1033y. Flow many decays per year would you expect in a tank of water containing 100,000 gallons of water? Assume the bound protons can decay. Get solution

26. Some GUT theories allow the proton to be unstable. What conservation laws are broken in the following proton decays? ... Get solution

27. Assume that half of the mass of a 50-kg person consists of protons. If the half-life of the proton is 1052 years, calculate the number of proton decays per day from the body. Get solution

28. A ... particle of kinetic energy 3 GeV is produced inside a bubble chamber. Ignoring energy losses, what is the ... travels in the detector? Get solution

29. In modern collider experiments the beam energy K has much greater energy than its rest energy (K >> mc 2 ) . If two particles each of mass m collide head-on with each having beam energy K, the energy in the center of mass Ecm = 2K. Show that two particles of the same mass m colliding head-on with each having kinetic energy K (K >> mc 2 ) have the same center-of-mass energy as the same particle of energy Klab in a fixed-target accelerator colliding with the same target particle, where ... Get solution

30. CERN constructed the first proton-proton collider, called the Intersecting Storage Rings (ISR), in 1971. Each proton beam had a kinetic energy of 31 GeV. Calculate how much energy a fixed-target accelerator would need to have the same energy available in the center-of-mass energy. Get solution

31. Calculate the speed of the 7.0-TeV protons that are produced in the LHC at CERN. Get solution

32. A cyclotron is used to accelerate protons to 60 MeV. If these protons are elastically scattered from deuterons ... what are the maximum energies of the ... Get solution

33. Calculate the minimum kinetic energy of a proton to be scattered from a fixed proton target to produce an antiproton. Get solution

34. A magnetic field of 1 T is used to accelerate 10-MeV protons in a cyclotron. (a) What is the radius of the magnet? (b) What is the cyclotron frequency? Get solution

35. Show that for higher particle energies, the simple cyclotron frequency in Equation (14.8) becomes limited by relativistic effects. Show that Equation (14.9) is the correct orbital frequency: ... ... ... Get solution

36. Show that Equation (14.10) is the correct relativistic result for the amount of energy available in the center-of-mass system when the reaction m1 + m2 ... anything occurs with a bombarding particle of mass m1 and kinetic energy K on a fixed target of mass m2. Show that it reduces in the nonrelativistic limit to Equation (13.12). ... ... Get solution

37. In a fi xed-target experiment with m1 = m2 = m, derive approximate expressions for Ecm in the following limiting cases: (a) K mc2 and (b) K >> mc2. Discuss your results in both cases. Get solution

38. Calculate the electron velocity in the 50-GeV beam at SLAC. Get solution

39. What is the ratio of cyclotron frequencies calculated relativistically and nonrelativistically for (a) a 10-MeV proton, (b) a 100-MeV proton, and (c) a 1-GeV proton? Get solution

41g. Consider the reaction ...?. (a) Determine the quantum numbers for the missing particle or particles (baryon, lepton, charge, spin, and so on). (b) Consider whether one or two particles is needed to complete the reaction. What are possible particles? Get solution

42g. Determine which of the following decays is not allowed and explain why. ... Get solution

43g. Consider the following reaction: ....How much bombarding energy is required for this reaction (a) if the second proton is a stationary target and (b) if the protons collide head-on? Get solution

44g. Determine which of the following decays is not allowed and explain why. ... Get solution

45g. Determine which of the following decays or reactions is not allowed and explain why. ... Get solution

46g. Determine which of the following decays or reactions is not allowed and explain why. ... Get solution

47g. Determine which of the following decays or reactions is not allowed and explain why. ... Get solution

48g. What is the relation between the de Broglie wavelength λ, mass m, and kinetic energy K for (a) a lowenergy proton, and (b) a very high energy proton? Get solution

49g. Consider the 7.0-TeV protons that are produced in the LHC collider at CERN. (a) Find the available center-of-mass energy if these protons collide with other protons in a fixed-target experiment. (b) Compare your results in (a) with the center-of-mass energy available in a colliding-beam experiment. Get solution