?30PE energy produced by the fusion of a 1.00-kg mixture

1CQ Problem In terms of radiation dose, what is the major difference between medical diagnostic uses of radiation and medical therapeutic uses?

1PE Problem A neutron generator uses an ? source, such as radium, to bombard beryllium, inducing the reaction 4 He + 9Be ? 12C + n . Such neutron sources are called RaBe sources, or PuBe sources if they use plutonium to get the ? s. Calculate the energy output of the reaction in MeV.

61PE Problem Integrated Concepts One scheme to put nuclear weapons to nonmilitary use is to explode them underground in a geologically stable region and extract the geothermal energy for electricity production. There was a total yield of about 4,000 MT in the combined arsenals in 2006. If 1.00 MT per day could be converted to electricity with an efficiency of 10.0%: (a) What would the average electrical power output be? (b) How many years would the arsenal last at this rate?

Problem 2CQ One of the methods used to limit radiation dose to the patient in medical imaging is to employ isotopes with short half-lives. How would this limit the dose?

Problem 3CQ Isotopes that emit ? radiation are relatively safe outside the body and exceptionally hazardous inside. Yet those that emit ? radiation are hazardous outside and inside. Explain why.

Problem 2PE Neutrons from a source (perhaps the one discussed in the preceding problem) bombard natural molybdenum, which is 24 percent 98 Mo . What is the energy output of the reaction 98 Mo + n ? 99 Mo + ? ? The mass of 98 Mo is given in Appendix A: Atomic Masses, and that of 99 Mo is 98.907711 u.

Problem 3PE The purpose of producing 99 Mo (usually by neutron activation of natural molybdenum, as in the preceding problem) is to produce 99m Tc. Using the rules, verify that the ? ? decay of 99 Mo produces 99m Tc . (Most 99m Tc nuclei produced in this decay are left in a metastable excited state denoted 99m Tc .)

4CQ Problem Why is radon more closely associated with inducing lung cancer than other types of cancer?

4PE Problem (a) Two annihilation ? rays in a PET scan originate at the same point and travel to detectors on either side of the patient. If the point of origin is 9.00 cm closer to one of the detectors, what is the difference in arrival times of the photons? (This could be used to give position information, but the time difference is small enough to make it difficult.) (b) How accurately would you need to be able to measure arrival time differences to get a position resolution of 1.00 mm?

5CQ Problem The RBE for low-energy ? s is 1.7, whereas that for higher-energy ? s is only 1. Explain why, considering how the range of radiation depends on its energy.

Table 32.1 indicates that \(7.50 \ mCi\) of \({ }^{99 m} \mathrm{Tc}\) is used in a brain scan. What is the mass of technetium? Equation Transcription: Text Transcription: 7.50 mCi ^99m Tc

8CQ Problem Are some types of cancer more sensitive to radiation than others? If so, what makes them more sensitive?

8PE Problem What is the dose in mSv for: (a) a 0.1 Gy x-ray? (b) 2.5 mGy of neutron exposure to the eye? (c) 1.5 mGy of ? exposure?

7CQ Problem What radioisotope could be a problem in homes built of cinder blocks made from uranium mine tailings? (This is true of homes and schools in certain regions near uranium mines.)

9CQ Problem Suppose a person swallows some radioactive material by accident. What information is needed to be able to assess possible damage?

(a) Neutron activation of sodium, which is \(100\%\ ^{23}\mathrm{Na}\), produces \({ }^{24} \mathrm{Na}\), which is used in some heart scans, as seen in Table 32.1. The equation for the reaction is \({ }^{23} \mathrm{Na}+n \rightarrow{ }^{24} \mathrm{Na}+\gamma\). Find its energy output, given the mass of \({ }^{24} \mathrm{Na}\) is \(23.990962 \ u\). (b) What mass of \({ }^{24} \mathrm{Na}\) produces the needed \(5.0-mCi\) activity, given its half-life is \(15.0 \ h\)? Equation Transcription: Text Transcription: 100% ^23 Na ^24 Na ^23 Na + n rightarrow ^24 Na + gamma ^24 Na 23.990962 u ^24 Na 5.0-mCi 15.0 h

9PE Problem Find the radiation dose in Gy for: (a) A 10-mSv fluoroscopic x-ray series. (b) 50 mSv of skin exposure by an ? emitter. (c) 160 mSv of ? – and ? rays from the 40 K in your body.

The activities of \({ }^{131} \mathrm{I}\) and \({ }^{123} \mathrm{I}\) used in thyroid scans are given in Table 32.1 to be \(50\) and \(70\ \mu\mathrm{Ci}\), respectively. Find and compare the masses of \({ }^{131} \mathrm{I}\) and \({ }^{123} \mathrm{I}\) in such scans, given their respective half-lives are \(8.04 \ d\) and \(13.2 \ h\). The masses are so small that the radioiodine is usually mixed with stable iodine as a carrier to ensure normal chemistry and distribution in the body. Equation Transcription: Text Transcription: ^131 I ^123 I 50 70 mu Ci ^131 I ^123 I 8.04 d 13.2 h

Which methods of radiation protection were used in the device shown in the first photo in Figure 32.35? Which were used in the situation shown in the second photo? Figure 32.35 (a) This x-ray fluorescence machine is one of the thousands used in shoe stores to produce images of feet as a check on the fit of shoes. They are unshielded and remain on as long as the feet are in them, producing doses much greater than medical images. Children were fascinated with them. These machines were used in shoe stores until laws preventing such unwarranted radiation exposure were enacted in the \(1950s\). (credit: Andrew Kuchling ) (b) Now that we know the effects of exposure to radioactive material, safety is a priority. (credit: U.S. Navy) Equation Transcription: Text Transcription: 1950s

10CQ Problem Radiotherapy is more likely to be used to treat cancer in elderly patients than in young ones. Explain why. Why is radiotherapy used to treat young people at all?

10PE Problem How many Gy of exposure is needed to give a cancerous tumor a dose of 40 Sv if it is exposed to ? activity?

11CQ Problem Does food irradiation leave the food radioactive? To what extent is the food altered chemically for low and high doses in food irradiation?

11PE Problem What is the dose in Sv in a cancer treatment that exposes the patient to 200 Gy of ? rays?

12CQ Problem Compare a low dose of radiation to a human with a low dose of radiation used in food treatment.

13CQ Problem Suppose one food irradiation plant uses a 137Cs source while another uses an equal activity of 60Co . Assuming equal fractions of the ? rays from the sources are absorbed, why is more time needed to get the same dose using the 137Cs source?

13PE Problem A plumber at a nuclear power plant receives a whole-body dose of 30 mSv in 15 minutes while repairing a crucial valve. Find the radiation-induced yearly risk of death from cancer and the chance of genetic defect from this maximum allowable exposure.

12PE Problem One half the ? rays from 99m Tc are absorbed by a 0.170-mm-thick lead shielding. Half of the ? rays that pass through the first layer of lead are absorbed in a second layer of equal thickness. What thickness of lead will absorb all but one in 1000 of these ? rays?

14CQ Problem Why does the fusion of light nuclei into heavier nuclei release energy?

14PE Problem In the 1980s, the term picowave was used to describe food irradiation in order to overcome public resistance by playing on the well-known safety of microwave radiation. Find the energy in MeV of a photon having a wavelength of a picometer.

15CQ Problem Energy input is required to fuse medium-mass nuclei, such as iron or cobalt, into more massive nuclei. Explain why.

15PE Problem Find the mass of 239 Pu that has an activity of 1.00 ?Ci.

16CQ Problem In considering potential fusion reactions, what is the advantage of the reaction 2H + 3H ? 4He + n over the reaction 2H + 2H ? 3He + n?

16PE Problem A beam of 168-MeV nitrogen nuclei is used for cancer therapy. If this beam is directed onto a 0.200-kg tumor and gives it a 2.00-Sv dose, how many nitrogen nuclei were stopped? (Use an RBE of 20 for heavy ions.)

17CQ Problem Give reasons justifying the contention made in the text that energy from the fusion reaction 2H + 2H ? 4He + ? is relatively difficult to capture and utilize.

17PE Problem (a) If the average molecular mass of compounds in food is 50.0 g, how many molecules are there in 1.00 kg of food? (b) How many ion pairs are created in 1.00 kg of food, if it is exposed to 1000 Sv and it takes 32.0 eV to create an ion pair? (c) Find the ratio of ion pairs to molecules. (d) If these ion pairs recombine into a distribution of 2000 new compounds, how many parts per billion is each?

18CQ Problem Explain why the fission of heavy nuclei releases energy. Similarly, why is it that energy input is required to fission light nuclei?

18PE Problem Calculate the dose in Sv to the chest of a patient given an x-ray under the following conditions. The x-ray beam intensity is 1.50 W/m2 , the area of the chest exposed is 0.0750 m2 , 35.0% of the x-rays are absorbed in 20.0 kg of tissue, and the exposure time is 0.250 s.

19PE Problem (a) A cancer patient is exposed to ? rays from a 5000-Ci 60Co transillumination unit for 32.0 s. The ? rays are collimated in such a manner that only 1.00% of them strike the patient. Of those, 20.0% are absorbed in a tumor having a mass of 1.50 kg. What is the dose in rem to the tumor, if the average ? energy per decay is 1.25 MeV? None of the ? s from the decay reach the patient. (b) Is the dose consistent with stated therapeutic doses?

20CQ Problem The ruins of the Chernobyl reactor are enclosed in a huge concrete structure built around it after the accident. Some rain penetrates the building in winter, and radioactivity from the building increases. What does this imply is happening inside?

19CQ Problem Explain, in terms of conservation of momentum and energy, why collisions of neutrons with protons will thermalize neutrons better than collisions with oxygen.

20PE Problem What is the mass of 60Co in a cancer therapy transillumination unit containing 5.00 kCi of 60Co ?

21CQ Problem Since the uranium or plutonium nucleus fissions into several fission fragments whose mass distribution covers a wide range of pieces, would you expect more residual radioactivity from fission than fusion? Explain.

21PE Problem Large amounts of 65Zn are produced in copper exposed to accelerator beams. While machining contaminated copper, a physicist ingests 50.0 ?Ci of 65Zn . Each 65Zn decay emits an average ? -ray energy of 0.550 MeV, 40.0% of which is absorbed in the scientist’s 75.0-kg body. What dose in mSv is caused by this in one day?

22CQ Problem The core of a nuclear reactor generates a large amount of thermal energy from the decay of fission products, even when the power-producing fission chain reaction is turned off. Would this residual heat be greatest after the reactor has run for a long time or short time? What if the reactor has been shut down for months?

23CQ Problem How can a nuclear reactor contain many critical masses and not go supercritical? What methods are used to control the fission in the reactor?

23PE Problem (a) Background radiation due to 226Ra averages only 0.01 mSv/y, but it can range upward depending on where a person lives. Find the mass of 226Ra in the 80.0-kg body of a man who receives a dose of 2.50-mSv/y from it, noting that each 226Ra decay emits a 4.80-MeV ? particle. You may neglect dose due to daughters and assume a constant amount, evenly distributed due to balanced ingestion and bodily elimination. (b) Is it surprising that such a small mass could cause a measurable radiation dose? Explain.

22PE Problem Naturally occurring 40 K is listed as responsible for 16 mrem/y of background radiation. Calculate the mass of 40 K that must be inside the 55-kg body of a woman to produce this dose. Each 40 K decay emits a 1.32-MeV ? , and 50% of the energy is absorbed inside the body.

24CQ Problem Why can heavy nuclei with odd numbers of neutrons be induced to fission with thermal neutrons, whereas those with even numbers of neutrons require more energy input to induce fission?

24PE Problem The annual radiation dose from 14C in our bodies is 0.01 mSv/y. Each 14C decay emits a ? – averaging 0.0750 MeV. Taking the fraction of 14C to be 1.3×10–12 N of normal 12C , and assuming the body is 13% carbon, estimate the fraction of the decay energy absorbed. (The rest escapes, exposing those close to you.)

25CQ Problem Why is a conventional fission nuclear reactor not able to explode as a bomb?

25PE Problem If everyone in Australia received an extra 0.05 mSv per year of radiation, what would be the increase in the number of cancer deaths per year? (Assume that time had elapsed for the effects to become apparent.) Assume that there are 200×10?4 deaths per Sv of radiation per year. What percent of the actual number of cancer deaths recorded is this?

Verity that the total number of nucleons, total charge, and electron family number are conserved for each of the fusion reactions in the proton-proton cycle in \(^1\mathrm{H}+^1\mathrm{H}\ \rightarrow\ ^2\mathrm{H}+e^++v_{\mathrm{e}},\ \ \ ^1\mathrm{H}+^2\mathrm{H}\ \rightarrow\ ^3\mathrm{He}+\gamma\), and \(^3\mathrm{He}+^3\mathrm{He}\ \rightarrow\ ^4\mathrm{He}+^1\mathrm{H}+^1\mathrm{H}\). (List the value of each of the conserved quantities before and after each of the reactions.) Equation Transcription: Text Transcription: ^1 H + ^1 H rightarrow ^2 H + e^+ + v_e, ^1 H + ^2 H rightarrow ^3He + gamma ^3 He + ^3He rightarrow ^4 He + ^1 H + ^1 H

26CQ Problem What are some of the reasons that plutonium rather than uranium is used in all fission bombs and as the trigger in all fusion bombs?

27CQ Problem Use the laws of conservation of momentum and energy to explain how a shape charge can direct most of the energy released in an explosion in a specific direction. (Note that this is similar to the situation in guns and cannons—most of the energy goes into the bullet.)

27PE Problem Calculate the energy output in each of the fusion reactions in the proton-proton cycle, and verify the values given in the above summary.

Show that the total energy released in the proton-proton cycle is \(26.7 \ MeV\), considering the overall effect in \(^1\mathrm{H}+^1\mathrm{H}\ \rightarrow\ ^2\mathrm{H}+e^++v_{\mathrm{e}}\), \(^1\mathrm{H}+^2\mathrm{H}\ \rightarrow\ ^3\mathrm{He}+\gamma\), and \(^3\mathrm{He}+^3\mathrm{He}\ \rightarrow\ ^4\mathrm{He}+^1\mathrm{H}+^1\mathrm{H}\) and being certain to include the annihilation energy. Equation Transcription: Text Transcription: 26.7 MeV ^1 H + ^1 H rightarrow ^2 H + e^+ + v_e ^1 H + ^2 H rightarrow ^3 He + gamma ^3 He + ^3 He rightarrow ^4 He + ^1 H + ^1 H

29CQ Problem Fallout from nuclear weapons tests in the atmosphere is mainly 90Sr and 137Cs , which have 28.6- and 32.2-y half-lives, respectively. Atmospheric tests were terminated in most countries in 1963, although China only did so in 1980. It has been found that environmental activities of these two isotopes are decreasing faster than their half-lives. Why might this be?

Verify by listing the number of nucleons, total charge, and electron family number before and after the cycle that these quantities are conserved in the overall proton-proton cycle in \(2e^-+4^1\mathrm{H}\ \rightarrow\ ^4\mathrm{He}+2v_{\mathrm{e}}+6\gamma\). Equation Transcription: Text Transcription: 2e^- + 4^1 H rightarrow ^4 He + 2v_e + 6 gamma

30PE Problem The energy produced by the fusion of a 1.00-kg mixture of deuterium and tritium was found in Example Calculating Energy and Power from Fusion. Approximately how many kilograms would be required to supply the annual energy use in the United States? Example 32.2: Calculating Energy and Power from Fusion (a) Calculate the energy released by the fusion of a 1.00-kg mixture of deuterium and tritium, which produces helium. There are equal numbers of deuterium and tritium nuclei in the mixture. (b) If this takes place continuously over a period of a year, what is the average power output?

31PE Problem Tritium is naturally rare, but can be produced by the reaction n + 2H ? 3 H + ? . How much energy in MeV is released in this neutron capture?

32PE Problem Two fusion reactions mentioned in the text are n + 3He ? 4 He + ? and n + 1H ? 2 H + ? . Both reactions release energy, but the second also creates more fuel. Confirm that the energies produced in the reactions are 20.58 and 2.22 MeV, respectively. Comment on which product nuclide is most tightly bound, 4 He or 2 H .

Problem 33PE (a) Calculate the number of grams of deuterium in an 80,000-L swimming pool, given deuterium is 0.0150% of natural hydrogen. (b) Find the energy released in joules if this deuterium is fused via the reaction 2 H + 2H ? 3 He + n . (c) Could the neutrons be used to create more energy? (d) Discuss the amount of this type of energy in a swimming pool as compared to that in, say, a gallon of gasoline, also taking into consideration that water is far more abundant.

34PE Problem How many kilograms of water are needed to obtain the 198.8 mol of deuterium, assuming that deuterium is 0.01500% (by number) of natural hydrogen?

Problem 35PE The power output of the Sun is 4×1026 W . (a) If 90% of this is supplied by the proton-proton cycle, how many protons are consumed per second? (b) How many neutrinos per second should there be per square meter at the Earth from this process? This huge number is indicative of how rarely a neutrino interacts, since large detectors observe very few per day.

37PE Problem (a) Find the total energy released in MeV in each carbon cycle (elaborated in the above problem) including the annihilation energy. (b) How does this compare with the proton-proton cycle output?

38PE Problem Verify that the total number of nucleons, total charge, and electron family number are conserved for each of the fusion reactions in the carbon cycle given in the above problem. (List the value of each of the conserved quantities before and after each of the reactions.)

Another set of reactions that result in the fusing of hydrogen into helium in the Sun and especially in hotter stars is called the carbon cycle. It is \(^{12}\mathrm{C}+^1\mathrm{H}\ \rightarrow\ ^{13}\mathrm{~N}+\gamma\), \(^{13}\mathrm{N}\quad\ \ \ \ \ \ \rightarrow^{13}\mathrm{C}+e^++v_e\), \(^{13}\mathrm{C}+^1\mathrm{H}\ \rightarrow\ ^{14}\mathrm{N}+\gamma\), \(^{14}\mathrm{N}+^1\mathrm{H}\ \rightarrow\ ^{15}\mathrm{O}+\gamma\), \(^{15}\mathrm{O}\quad\ \ \ \ \ \ \rightarrow\ ^{15}\mathrm{N}+e^++v_e\), \(^{15}\mathrm{N}+^1\mathrm{H}\ \rightarrow\ ^{12}\mathrm{C}+^4\mathrm{He}\). Write down the overall effect of the carbon cycle (as was done for the proton-proton cycle in \(2e^-+4^1\mathrm{H}\ \rightarrow\ ^4\mathrm{He}+2v_e+6\gamma\)). Note the number of protons \(({ }^{1} \mathrm{H})\) required and assume that the positrons \((e^{+})\) annihilate electrons to form more \(\gamma\) rays. Equation Transcription: Text Transcription: ^12 C + ^1 H rightarrow ^13 N + gamma ^13 N rightarrow ^13 C + e^+ + v_e ^13 C + ^1 H rightarrow ^14 N + gamma ^14 N + ^1 H rightarrow ^15 O + gamma ^15 O rightarrow ^15 N + e^+ + v_e ^15 N + ^1 H rightarrow ^12 C + ^4He 2e^- + 4^1 H rightarrow ^4 He + 2v_e + 6 gamma ^1 H e^+ gamma

39PE Problem Integrated Concepts The laser system tested for inertial confinement can produce a 100-kJ pulse only 1.00 ns in duration. (a) What is the power output of the laser system during the brief pulse? (b) How many photons are in the pulse, given their wavelength is 1.06 µm ? (c) What is the total momentum of all these photons? (d) How does the total photon momentum compare with that of a single 1.00 MeV deuterium nucleus?

40PE Problem Integrated Concepts Find the amount of energy given to the 4 He nucleus and to the ? ray in the reaction n + 3 He ?4 He + ? , using the conservation of momentum principle and taking the reactants to be initially at rest. This should confirm the contention that most of the energy goes to the ? ray.

42PE Problem Integrated Concepts (a) Estimate the years that the deuterium fuel in the oceans could supply the energy needs of the world. Assume world energy consumption to be ten times that of the United States which is 8×1019 J/y and that the deuterium in the oceans could be converted to energy with an efficiency of 32%. You must estimate or look up the amount of water in the oceans and take the deuterium content to be 0.015% of natural hydrogen to find the mass of deuterium available. Note that approximate energy yield of deuterium is 3.37×1014 J/kg. (b) Comment on how much time this is by any human measure. (It is not an unreasonable result, only an impressive one.)

41PE Problem Integrated Concepts (a) What temperature gas would have atoms moving fast enough to bring two 3 He nuclei into contact? Note that, because both are moving, the average kinetic energy only needs to be half the electric potential energy of these doubly charged nuclei when just in contact with one another. (b) Does this high temperature imply practical difficulties for doing this in controlled fusion?

44PE Problem (a) Calculate the energy released in the neutron-induced fission reaction n + 235U ? 92 Kr + 142Ba + 2n, given m( 92 Kr) = 91.926269 u and m( 142Ba) = 141.916361 u . (b) Confirm that the total number of nucleons and total charge are conserved in this reaction.

(a) Calculate the energy released in the neutron-induced fission (similar to the spontaneous fission in Example 32.3) \(n+^{238}\mathrm{U}\ \rightarrow\ ^{96}\mathrm{Sr}+^{140}\mathrm{Xe}+3n\), given \(m\left(^{96}\mathrm{Sr}\right)=95.921750\mathrm{\ u}\) and \(m\left({ }^{140} \mathrm{Xe}\right)=139.92164\). (b) This result is about \(6 \ MeV\) greater than the result for spontaneous fission. Why? (c) Confirm that the total number of nucleons and total charge are conserved in this reaction. Equation Transcription: Text Transcription: n + ^238 U rightarrow ^96 Sr + ^140 Xe + 3n m (^96 Sr) = 95.921750 u m (^140 Xe) = 139.92164 6 MeV

(a) Calculate the energy released in the neutron-induced fission reaction \(n+^{239}\mathrm{Pu}\ \rightarrow\ ^{96}\mathrm{Sr}+^{140}\mathrm{Ba}+4n\), given \(m\left(^{96}\mathrm{Sr}\right)=95.921750\mathrm{\ u}\) and \(m\left(^{140}\mathrm{Ba}\right)=139.910581\mathrm{\ u}\). (b) Confirm that the total number of nucleons and total charge are conserved in this reaction. Equation Transcription: Text Transcription: n + ^239 Pu rightarrow ^96 Sr + ^140 Ba + 4n m (^96 Sr) = 95.921750 u m (^140 Ba) = 139.910581 u

46PE Problem Confirm that each of the reactions listed for plutonium breeding just following Example 32.4 conserves the total number of nucleons, the total charge, and electron family number. Example 32.4: Calculating Energy from a Kilogram of Fissionable Fuel Calculate the amount of energy produced by the fission of 1.00 kg of 235 U , given the average fission reaction of 235 U produces 200 MeV

Breeding plutonium produces energy even before any plutonium is fissioned. (The primary purpose of the four nuclear reactors at Chernobyl was breeding plutonium for weapons. Electrical power was a by-product used by the civilian population.) Calculate the energy produced in each of the reactions listed for plutonium breeding just following Example 32.4. The pertinent masses are \(m\left(^{239}\mathrm{U}\right)=239.054289\mathrm{\ u}\), \(m\left(^{239}\mathrm{Np}\right)=239.052932\mathrm{\ u}\), and \(m\left(^{239}\mathrm{Pu}\right)=239.052157\mathrm{\ u}\). Equation Transcription: Text Transcription: m (^239 U) = 239.054289 u m (^239 Np) = 239.052932 u m (^239 Pu) = 239.052157 u

48PE Problem The naturally occurring radioactive isotope 232Th does not make good fission fuel, because it has an even number of neutrons; however, it can be bred into a suitable fuel (much as 238 U is bred into 239 P ). (a) What are Z and N for 232Th ? (b) Write the reaction equation for neutron captured by 232Th and identify the nuclide A X produced in n + 232Th ? A X + ? . (c) The product nucleus ? ? decays, as does its daughter. Write the decay equations for each, and identify the final nucleus. (d) Confirm that the final nucleus has an odd number of neutrons, making it a better fission fuel. (e) Look up the half-life of the final nucleus to see if it lives long enough to be a useful fuel.

49PE Problem The electrical power output of a large nuclear reactor facility is 900 MW. It has a 35.0% efficiency in converting nuclear power to electrical. (a) What is the thermal nuclear power output in megawatts? (b) How many 235 U nuclei fission each second, assuming the average fission produces 200 MeV? (c) What mass of 235 U is fissioned in one year of full-power operation?

50PE Problem A large power reactor that has been in operation for some months is turned off, but residual activity in the core still produces 150 MW of power. If the average energy per decay of the fission products is 1.00 MeV, what is the core activity in curies?

51PE Problem Find the mass converted into energy by a 12.0-kT bomb.

52PE Problem What mass is converted into energy by a 1.00-MT bomb?

53PE Problem Fusion bombs use neutrons from their fission trigger to create tritium fuel in the reaction n + 6 Li ?3 H +4 He . What is the energy released by this reaction in MeV?

55PE Problem A radiation-enhanced nuclear weapon (or neutron bomb) can have a smaller total yield and still produce more prompt radiation than a conventional nuclear bomb. This allows the use of neutron bombs to kill nearby advancing enemy forces with radiation without blowing up your own forces with the blast. For a 0.500-kT radiation-enhanced weapon and a 1.00-kT conventional nuclear bomb: (a) Compare the blast yields. (b) Compare the prompt radiation yields.

54PE Problem It is estimated that the total explosive yield of all the nuclear bombs in existence currently is about 4,000 MT. (a) Convert this amount of energy to kilowatt-hours, noting that 1 kW ? h = 3.60×106 J . (b) What would the monetary value of this energy be if it could be converted to electricity costing 10 cents per kW·h?

56PE Problem (a) How many 239 Pu nuclei must fission to produce a 20.0-kT yield, assuming 200 MeV per fission? (b) What is the mass of this much 239 Pu ?

57PE Problem Assume one-fourth of the yield of a typical 320-kT strategic bomb comes from fission reactions averaging 200 MeV and the remainder from fusion reactions averaging 20 MeV. (a) Calculate the number of fissions and the approximate mass of uranium and plutonium fissioned, taking the average atomic mass to be 238. (b) Find the number of fusions and calculate the approximate mass of fusion fuel, assuming an average total atomic mass of the two nuclei in each reaction to be 5. (c) Considering the masses found, does it seem reasonable that some missiles could carry 10 warheads? Discuss, noting that the nuclear fuel is only a part of the mass of a warhead.

58PE Problem This problem gives some idea of the magnitude of the energy yield of a small tactical bomb. Assume that half the energy of a 1.00-kT nuclear depth charge set off under an aircraft carrier goes into lifting it out of the water—that is, into gravitational potential energy. How high is the carrier lifted if its mass is 90,000 tons?

59PE Problem It is estimated that weapons tests in the atmosphere have deposited approximately 9 MCi of 90Sr on the surface of the earth. Find the mass of this amount of 90Sr .

60PE Problem A 1.00-MT bomb exploded a few kilometers above the ground deposits 25.0% of its energy into radiant heat. (a) Find the calories per cm2 at a distance of 10.0 km by assuming a uniform distribution over a spherical surface of that radius. (b) If this heat falls on a person’s body, what temperature increase does it cause in the affected tissue, assuming it is absorbed in a layer 1.00-cm deep?