14. (Ill) What magnetic field intensity is needed at the

1. (I) What is the total energy of a proton whose kinetic energy is 6.35 GcV?

2. (I) Calculate the wavelength of 35-GeV electrons.

3. (I) What strength of magnetic field is used in a cyclotron in which protons make 2.8 X 107 revolutions per second?

4. (I) What is the time for one complete revolution for a very high-energy proton in the 1.0-km-radius Fermilab accelerator?

5. (I) If particles are accelerated by the cyclotron of Example 32-2. what must be the frequency of the voltage applied to the dees?

6. (II) (a) If the cyclotron of Example 32-2 accelerated a particles, what maximum energy could they attain? What would their speed be? (b) Repeat for deuterons (2H). (c) In each case, what frequency of voltage is required?

7. (II) Which is better for picking out details of the nucleus: 30-McV alpha particles or 30-McV protons? Compare each of their wavelengths with the size of a nucleon in a nucleus.

8. (II) Ilie voltage across the dees of a cyclotron is 55 kV. How many revolutions do protons make to reach a kinetic energy of 25 MeV?

9. (II) What is the wavelength (= maximum resolvable distance) of 7.0-TeV protons?

10. (II) A cyclotron with a radius of 1.0 m is to accelerate deuterons (?H) to an energy of 12 MeV. (a) What is the required magnetic field? (b) What frequency is needed for the voltage between the dees? (c) If the potential difference between the dees averages 22 kV. how many revolutions will the particles make before exiting? (d) How much time does it take for one deutcron to go from start to exit, (e) Estimate how far it travels during this time.

11. (II) The 4.25-km-radius tunnel that will be used to house the magnets for the Large Hadron Collider (LHC) calls for proton beams of energy 7.0 TeV. What magnetic field will be required?

12. (II) The 1.0-km radius Fermilab Tevatron takes about 20 seconds to bring the energies of the stored protons from 150GeV to 1.0 TeV. The acceleration is done once per turn. Estimate the energy given to the protons on each turn. (You can assume that the speed of the protons is essentially c the whole time.)

13. (Ill) Show that the energy of a particle (charge e) in a synchrotron, in the relativistic limit (i> c), is given by E (in eV) = Brc. where B is magnetic field strength and r the radius of the orbit (SI units).

14. (Ill) What magnetic field intensity is needed at the 1.0-km-radius Fermilab synchrotron for 1.0-TeV protons?

15. (I) How much energy is released in the decay ?r+ -> See Table 32-2.

16. (I) About how much energy is released when a A" decays to n + ir? (See Table 32-2.)

17. (I) How much energy is required to produce a neutron-antineutron pair?

18. (I) Estimate the range of the strong force if the mediating particle were the kaon instead of the pion.

19. (II) Two protons are heading toward each other with equal speeds. What minimum kinetic energy must each have if a ir meson is to be created in the process? (See Table 32-2.)

20. (II) What minimum kinetic energy must two neutrons each have if they are traveling at the same speed toward each other, collide, and produce a K'K pair in addition to themselves? (See Table 32-2.)

21. (II) Estimate the range of the weak force using Eq. 32-3. given the masses of the W and Z particles as about 80 to 90GcV/c2.

22. (II) What are the wavelengths of the two photons produced when a proton and antiproton at rest annihilate?

23. (II) The A cannot decay by the following reactions. What conservation law is violated in each of the reactions? (a) Au > n + tt~ (/>) A0 p + K-(c) A" > TT+ + TT~

24. (II) For the decay A p + j~, calculate (a) the {9-value (energy released), and (b) the kinetic energy of the p and assuming the A0 decays from rest. (Use relativistic formulas.)

25. (II) (a) Show, by conserving momentum and energy, that it is impossible for an isolated electron to radiate only a single photon. (b) With this result in mind, how can you defend the photon exchange diagram in Fig. 32-7?

26. (II) What would be the wavelengths of the two photons produced when an electron and a positron, each with 420 keV of kinetic energy, annihilate head on?

27. (II) In the rare decay n~ > e+ + rc, what is the kinetic energy of the positron? Assume the tt~ decays from rest.

28. (II) Which of the following reactions and decays are possible? For those forbidden, explain what laws are violated. (tf) 7T~ + p > n + TJU (b) 77+ + p > n + 7T (c) 7T+ + P > P + C+ (d) p -> e+ + uc (e) ft* > e+ + Up (f) p -> n + e+ + i'c

29. (II) Calculate the kinetic energy of each of the two products in the decay > A0 + xr-. Assume the decays from rest.

30. (Ill) Could a 7t* meson be produced if a 100-MeV proton struck a proton at rest? What minimum kinetic energy must the incoming proton have?

31. (Ill) Calculate the maximum kinetic energy of the electron in the decay ix~ > e + vc + u^. [Hint: in what direction do the two neutrinos move relative to the electron in order to give the latter the maximum kinetic energy? Both energy and momentum are conserved; use relativistic formulas.)

32. (I) Use Fig. 32-11 to estimate the energy width and then the lifetime of the A resonance using the uncertainty principle.

33. (I) The measured width of the J/i/> meson is 88 keV. Estimate its lifetime.

34. (I)T he measured width of the 0 (3685) meson is 277 keV. Estimate its lifetime.

35. (I) What is the energy width (or uncertainty) of (a) tj. and (b) S? See Table 32-2.

36. (I) Hie B meson is a bu quark combination, (a) Show that this is consistent for all quantum numbers. (b) What are the quark combinations for B+. B. B"?

37. (II) Which of the following decays are possible? For those that are forbidden, explain which laws are violated. (a) H - + tt~ (b) Ct~ -> 2 + tt~ + (c) 2 -> A0 + y + y

38. (II) What are the quark combinations that can form (a) a neutron. (b) an antineutron, (c) a A0, (d) a 2?

39. (II) What particles do the following quark combinations produce: {a) uud. (b) uus. (c) us. (d) dii. (e) cs?

40. (II) What is the quark combination needed to produce a D meson (Q = B = S = 0, c = +1)?

41. (II) The Dj meson has S = c = +1, B = 0. What quark combination would produce it?

42. (II) Draw a possible Feynman diagram using quarks (as in Fig. 32-13c) for the reaction tt~ + p > 77 + n.

43. (II) Draw a Feynman diagram for the reaction n + -> p + ix~.

44. What is the total energy of a proton whose kinetic energy is 25 GeV? What is its wavelength?

45. Assume there are 5.0 x 1013 protons at 1.0 TeV stored in the 1.0-km-radius ring of the Tevatron. (<7) How much current (amperes) is carried by this beam? (b) How fast would a 1500-kg car have to move to carry the same kinetic energy as this beam?

46. Protons are injected into the 1.0-km-radius Fermilab Tevatron with an energy of 150 GeV. If they are accelerated by 2.5 MV each revolution, how far do they travel and approximately how long does it take for them to reach 1.0 TeV?

47. (<?) How much energy is released when an electron and a positron annihilate each other? (/>) How much energy is released when a proton and an antiproton annihilate each other? (All particles kl 0.) (d) 77+ + p - 1 + 77

48. Which of the following reactions arc possible, and by what interaction could they occur? For those forbidden, explain why. (a) tt + p > K+ + 2" (b) tt+ + p -> K+ + S + (c) tt~ + p A0 + K + 7T (<?) 7T + p > p + e + Tfc

49. Which of the following reactions are possible, and by what interaction could they occur? For those forbidden, explain why. (a) n~ + p K + p + 7r" (b) K + p > A0 + tt (c) K+ + n 2+ + 7T + y (d) K* -> 77 + 77 + 7T+ (e) tt* > e+ + i>c

50. One decay mode for a ->r* is tt+ > /x+ + . What would be the equivalent decay for a tt-? Check conservation rules.

51. Symmetry breaking occurs in the electroweak theory at about 10_,sm. Show that this corresponds to an energy that is on the order of the mass of the W1.

52. The mass of a can be measured by observing the reaction 7r_ + p > 77" + n at very low incident tt~ kinetic energy (assume it is zero). The neutron is observed to be emitted with a kinetic energy of 0.60 MeV. Use conservation of energy and momentum to determine the 77 mass.

53. Calculate the Q-value for each of the reactions, tq. 32-4, for producing a pion.

54. Calculate the (M'alue for the reaction tt~ + p > A0 + K, when negative pions strike stationary protons. Estimate the minimum pion kinetic energy needed to produce this reaction. [Hint: assume A0 and K move off with the same velocity.)

55. How many fundamental fermions are there in a water molecule?

56. A proton and an antiproton annihilate each other at rest and produce two pions. 77 and 77+. What is the kinetic energy of each pion ?

57. (a) Show that the so-called unification distance of 10-32 m in grand unified theory is equivalent to an energy of about 10l6GeV. Use the uncertainty principle, and also de Broglies wavelength formula, and explain how they apply. (b) Calculate the temperature corresponding to 1016 GeV.

58. For the reaction p + p 3p + p, where one of the initial protons is at rest, use relativistic formulas to show that the threshold energy is 6mpc2, equal to three times the magnitude of the (M'alue of the reaction, where mp is the proton mass. [Hint: assume all final particles have the same velocity !

59. The lifetimes listed in Table 32-2 are in terms of proper time. measured in a reference frame where the particle is at rest. If a tau lepton is created with a kinetic energy of 450 MeV, how long would its track be as measured in the lab, on average, ignoring any collisions?

60. Identify the missing particle in the following reactions. (d) p + p > p + n + 77 * + ? (b) p + ? > n + p.+

61. Use the quark model to describe the reaction P + n > 77 4- 77.

62. What fraction of the speed of light c is the speed of a 7.0-TcV proton?