Quantum Physics

Problems 100740. Assume binding energies can be neglected. Find themasses of the u and d quarks from the masses of theproton and neutron.ADDITIONAL PROBLEMS41. A 0 particle traveling through matter strikes a protonand a , and a gamma ray, as well as a thirdparticle, emerges. Use the quark model of each todetermine the identity of the third particle.42. It was stated in the text that the reactionoccurs with high probability,whereas the reactionnever occurs.Analyze these reactions at the quark level andshow that the first conserves the net number of eachtype of quark while the second does not. p : K 0 043. Two protons approach each other with equal andopposite velocities. Find the minimum kinetic energyof each of the protons if they are to produce a meson at rest in the reactionp p : p n 44. Name at least one conservation law that preventseach of the following reactions from occurring:(a) p : 0(b) : e(c) p : Find the energy released in the fu-45.sion reaction p : K 0 nH 3 2He : 4 2He e 46. Occasionally, high-energy muons collide with electronsand produce two neutrinos according to thereaction e : 2. What kind of neutrinos arethese?47. Each of the following decays is forbidden. For eachprocess, determine a conservation law that is violated:(a) : e (b) n : p e e(c) 0 : p 0(d) p : e 0(e) 0 : n 048. Two protons approach each other with 70.4 MeV ofkinetic energy and engage in a reaction in which aproton and a positive pion emerge at rest. Whatthird particle, obviously uncharged and thereforedifficult to detect, must have been created?49. The atomic bomb dropped on Hiroshima on August6, 1945, released 5 10 13 J of energy (equivalent tothat from 12 000 tons of TNT). Estimate (a) thenumber of23592U nuclei fissioned and (b) the mass ofthis235U.50. A 0 particle at rest decays according to 0 : 0 . Find the gamma-ray energy. [Hint: remember toconserve momentum.]51. If baryon number is not conserved, then one possiblemechanism by which a proton can decay isp : e Show that this reaction violates the conservation ofbaryon number. (b) Assuming that the reaction occursand that the proton is initially at rest, determinethe energy and momentum of the photon afterthe reaction. [Hint: recall that energy andmomentum must be conserved in the reaction.](c) Determine the speed of the positron after thereaction.52. Classical general relativity views the space–timemanifold as a deterministic structure completelywell defined down to arbitrarily small distances.On the other hand, quantum general relativity forbidsdistances smaller than the Planck lengthL (G/c 3 ) 1/2 . (a) Calculate the value of L. Theanswer suggests that, after the Big Bang (when allthe known Universe was reduced to a singularity),nothing could be observed until that singularitygrew larger than the Planck length, L. Since the sizeof the singularity grew at the speed of light, we caninfer that during the time it took for light to travelthe Planck length, no observations were possible.(b) Determine this time (known as the Planck timeT), and compare it to the ultra-hot epoch discussedin the text. (c) Does your answer to part (b) suggestthat we may never know what happened between thetime t 0 and the time t T ?53.92(a) Show that about 1.0 10 10 J would be releasedby the fusion of the deuterons in 1.0 gal of water.Note that 1 out of every 6 500 hydrogen atoms is adeuteron. (b) The average energy consumption rateof a person living in the United States is about 1.0 10 4 J/s (an average power of 10 kW). At this rate,how long would the energy needs of one person besupplied by the fusion of the deuterons in 1.0 gal ofwater? Assume that the energy released perdeuteron is 1.64 MeV.54. Calculate the mass of 235 U required to provide thetotal energy requirements of a nuclear submarine