Quantum Physics

970 Chapter 29 Nuclear Physics39. Identify the unknown particles X and X in the followingnuclear reactions:424 1X 2He : 12Mg 0n235 190192U 0n : 38Sr X 2n 0122H 1 : 1H X X40. The first nuclear reaction utilizing particle acceleratorswas performed by Cockcroft and Walton. Acceleratedprotons were used to bombard lithium nuclei,producing the following reaction:1 7H Li :4He 41 32 2HeSince the masses of the particles involved in the reactionwere well known, these results were used toobtain an early proof of the Einstein mass–energyrelation. Calculate the Q value of the reaction.1041. (a) Suppose 5 B is struck by an alpha particle, releasinga proton and a product nucleus in the reaction.What is the product nucleus? (b) An alpha particleand a product nucleus are produced when 6 C13is struck by a proton. What is the product nucleus?742. (a) Determine the product of the reaction 3Li 42He : ? n. (b) What is the Q value of the reaction?19743. Natural gold has only one isotope: 79 Au . If goldis bombarded with slow neutrons, e particlesare emitted. (a) Write the appropriate reactionequation. (b) Calculate the maximum energy of198the emitted beta particles. The mass of 80 Hg is197.966 75 u.44. Find the threshold energy that an incident neutronmust have to produce the reaction1 42 30n 2He : 1H 1H45.When 18 O is struck by a proton, 18 Fand another particle are produced. (a) What is theother particle? (b) The reaction has a Q value of2.453 MeV, and the atomic mass of 18 O is17.999 160 u. What is the atomic mass of 18 F?Section 29.7 Medical Applications of Radiation46. In terms of biological damage, how many rad ofheavy ions is equivalent to 100 rad of x-rays?47. A person whose mass is 75.0 kg is exposed to awhole-body dose of 25.0 rads. How many joules ofenergy are deposited in the person’s body?48. A 200-rad dose of radiation is administered to a patientin an effort to combat a cancerous growth. Assumingall of the energy deposited is absorbed by thegrowth, (a) calculate the amount of energy deliveredper unit mass. (b) Assuming the growth has a mass of0.25 kg and a specific heat equal to that of water,calculate its temperature rise.49. A “clever” technician decides to heat some water forhis coffee with an x-ray machine. If the machineproduces 10 rad/s, how long will it take to raise thetemperature of a cup of water by 50°C. Ignore heatlosses during this time.50. An x-ray technician works 5 days per week, 50 weeksper year. Assume that the technician takes an averageof eight x-rays per day and receives a dose of5.0 rem/yr as a result. (a) Estimate the dose in remper x-ray taken. (b) How does this result comparewith the amount of low-level background radiationthe technician is exposed to?51.A patient swallows a radiopharmaceuticaltagged with phosphorus-32 ( 15P), a emit-32ter with a half-life of 14.3 days. The average kineticenergy of the emitted electrons is 700 keV. If the initialactivity of the sample is 1.31 MBq, determine(a) the number of electrons emitted in a 10-dayperiod, (b) the total energy deposited in the bodyduring the 10 days, and (c) the absorbed dose ifthe electrons are completely absorbed in 100 g oftissue.52. A particular radioactive source produces 100 mrad of2-MeV gamma rays per hour at a distance of 1.0 m.(a) How long could a person stand at this distancebefore accumulating an intolerable dose of 1 rem?(b) Assuming the gamma radiation is emitteduniformly in all directions, at what distance woulda person receive a dose of 10 mrad/h from thissource?ADDITIONAL PROBLEMS53. A 200.0-mCi sample of a radioactive isotope is purchasedby a medical supply house. If the sample hasa half-life of 14.0 days, how long will it keep beforeits activity is reduced to 20.0 mCi?54. A sample of organic material is found to contain 18 gof carbon. The investigators believe the material to be20 000 years old, based on samples of pottery found atthe site. If so, what is the expected activity of theorganic material? Take data from Example 29.7.55. Deuterons that have been accelerated are used tobombard other deuterium nuclei, resulting in thereaction2 23 11H 1H : 2He 0nDoes this reaction require a threshold energy? If so,what is its value?56. Free neutrons have a characteristic half-life of 12min. What fraction of a group of free neutrons at athermal energy of 0.040 eV will decay before travelinga distance of 10.0 km?