13. Suppose one food irradiation plant uses a 137 Cs source while another uses an equal activity of 60 Co . Assuming equal fractions of the γ rays
from the sources are absorbed, why is more time needed to get the same dose using the 137 Cs source?
1176 CHAPTER 32 | MEDICAL APPLICATIONS OF NUCLEAR PHYSICS
14. Why does the fusion of light nuclei into heavier nuclei release energy?
15. Energy input is required to fuse medium-mass nuclei, such as iron or cobalt, into more massive nuclei. Explain why.
16. In considering potential fusion reactions, what is the advantage of the reaction 2 H + 3H → 4 He + n over the reaction
2 H + 2H → 3He + n?
17. Give reasons justifying the contention made in the text that energy from the fusion reaction 2 H + 2H → 4 He + γ is relatively difficult to
capture and utilize.
18. Explain why the fission of heavy nuclei releases energy. Similarly, why is it that energy input is required to fission light nuclei?
19. Explain, in terms of conservation of momentum and energy, why collisions of neutrons with protons will thermalize neutrons better than collisions
with oxygen.
20. 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?
21. 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.
22. 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?
23. How can a nuclear reactor contain many critical masses and not go supercritical? What methods are used to control the fission in the reactor?
24. 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?
25. Why is a conventional fission nuclear reactor not able to explode as a bomb?
26. 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?
27. 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.)
28. How does the lithium deuteride in the thermonuclear bomb shown in Figure 32.33 supply tritium (3 H) as well as deuterium (2 H) ?
29. Fallout from nuclear weapons tests in the atmosphere is mainly 90 Sr and 137 Cs , 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?
CHAPTER 32 | MEDICAL APPLICATIONS OF NUCLEAR PHYSICS 1177
Problems & Exercises
12. One half the γ rays from 99m Tc are absorbed by a 0.170-mm-thick
lead shielding. Half of the γ rays that pass through the first layer of lead
32.1 Medical Imaging and Diagnostics
are absorbed in a second layer of equal thickness. What thickness of
1. A neutron generator uses an α source, such as radium, to bombard
lead will absorb all but one in 1000 of these γ rays?
beryllium, inducing the reaction 4 He + 9Be → 12 C + n . Such neutron 13. A plumber at a nuclear power plant receives a whole-body dose of 30
sources are called RaBe sources, or PuBe sources if they use plutonium
mSv in 15 minutes while repairing a crucial valve. Find the radiation-
to get the α s. Calculate the energy output of the reaction in MeV.
induced yearly risk of death from cancer and the chance of genetic defect
from this maximum allowable exposure.
2. Neutrons from a source (perhaps the one discussed in the preceding
14. In the 1980s, the term picowave was used to describe food irradiation
problem) bombard natural molybdenum, which is 24 percent 98 Mo .
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
What is the energy output of the reaction 98 Mo + n → 99 Mo + γ ?
a wavelength of a picometer.
The mass of 98 Mo is given in Appendix A: Atomic Masses, and that
15. Find the mass of 239 Pu that has an activity of 1.00 μCi .
of 99 Mo is 98.907711 u.
32.3 Therapeutic Uses of Ionizing Radiation
3. The purpose of producing 99 Mo (usually by neutron activation of
16. A beam of 168-MeV nitrogen nuclei is used for cancer therapy. If this
natural molybdenum, as in the preceding problem) is to produce
beam is directed onto a 0.200-kg tumor and gives it a 2.00-Sv dose, how
99m Tc. Using the rules, verify that the β− decay of 99Mo produces many nitrogen nuclei were stopped? (Use an RBE of 20 for heavy ions.)
99m
17. (a) If the average molecular mass of compounds in food is 50.0 g,
Tc . (Most 99m Tc nuclei produced in this decay are left in a
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
metastable excited state denoted 99m Tc .)
takes 32.0 eV to create an ion pair? (c) Find the ratio of ion pairs to
4. (a) Two annihilation γ rays in a PET scan originate at the same point
molecules. (d) If these ion pairs recombine into a distribution of 2000 new
compounds, how many parts per billion is each?
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
18. Calculate the dose in Sv to the chest of a patient given an x-ray under
times of the photons? (This could be used to give position information,
the following conditions. The x-ray beam intensity is 1.50 W/m2 , the
but the time difference is small enough to make it difficult.)
area of the chest exposed is 0.0750 m2 , 35.0% of the x-rays are
(b) How accurately would you need to be able to measure arrival time
absorbed in 20.0 kg of tissue, and the exposure time is 0.250 s.
differences to get a position resolution of 1.00 mm?
19. (a) A cancer patient is exposed to γ rays from a 5000-Ci 60 Co
5. Table 32.1 indicates that 7.50 mCi of 99m Tc is used in a brain scan.
transillumination unit for 32.0 s. The γ rays are collimated in such a
What is the mass of technetium?
manner that only 1.00% of them strike the patient. Of those, 20.0% are
6. The activities of 131 I and 123 I used in thyroid scans are given in
absorbed in a tumor having a mass of 1.50 kg. What is the dose in rem to
the tumor, if the average γ energy per decay is 1.25 MeV? None of the
Table 32.1 to be 50 and 70 μCi , respectively. Find and compare the
β s from the decay reach the patient. (b) Is the dose consistent with
masses of 131 I and 123 I in such scans, given their respective half-
stated therapeutic doses?
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
20. What is the mass of 60 Co in a cancer therapy transillumination unit
chemistry and distribution in the body.
containing 5.00 kCi of 60 Co ?
7. (a) Neutron activation of sodium, which is 100% 23 Na , produces
24 Na
21. Large amounts of 65 Zn are produced in copper exposed to
, which is used in some heart scans, as seen in Table 32.1. The
accelerator beams. While machining contaminated copper, a physicist
equation for the reaction is 23 Na + n → 24 Na + γ . Find its energy
ingests 50.0 μCi of 65 Zn . Each 65 Zn decay emits an average γ -
output, given the mass of 24 Na is 23.990962 u.
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?
(b) What mass of 24 Na produces the needed 5.0-mCi activity, given its
22. Naturally occurring 40 K is listed as responsible for 16 mrem/y of
half-life is 15.0 h?
background radiation. Calculate the mass of 40 K that must be inside
32.2 Biological Effects of Ionizing Radiation
the 55-kg body of a woman to produce this dose. Each 40 K decay
8. What is the dose in mSv for: (a) a 0.1 Gy x-ray? (b) 2.5 mGy of
emits a 1.32-MeV β , and 50% of the energy is absorbed inside the
neutron exposure to the eye? (c) 1.5 mGy of α exposure?
body.
9. Find the radiation dose in Gy for: (a) A 10-mSv fluoroscopic x-ray
series. (b) 50 mSv of skin exposure by an α emitter. (c) 160 mSv of β–
23. (a) Background radiation due to 226 Ra averages only 0.01 mSv/y,
and γ rays from the 40 K in your body.
but it can range upward depending on where a person lives. Find the
mass of 226 Ra in the 80.0-kg body of a man who receives a dose of
10. How many Gy of exposure is needed to give a cancerous tumor a
dose of 40 Sv if it is exposed to α activity?
2.50-mSv/y from it, noting that each 226 Ra decay emits a 4.80-MeV α
11. What is the dose in Sv in a cancer treatment that exposes the patient
particle. You may neglect dose due to daughters and assume a constant
to 200 Gy of γ rays?
amount, evenly distributed due to balanced ingestion and bodily
1178 CHAPTER 32 | MEDICAL APPLICATIONS OF NUCLEAR PHYSICS
elimination. (b) Is it surprising that such a small mass could cause a
(d) Discuss the amount of this type of energy in a swimming pool as
measurable radiation dose? Explain.
compared to that in, say, a gallon of gasoline, also taking into
consideration that water is far more abundant.
24. The annual radiation dose from 14 C in our bodies is 0.01 mSv/y.
34. How many kilograms of water are needed to obtain the 198.8 mol of
Each 14 C decay emits a β– averaging 0.0750 MeV. Taking the
deuterium, assuming that deuterium is 0.01500% (by number) of natural
hydrogen?
fraction of 14 C to be 1.3×10–12 N of normal 12 C , and assuming
35. The power output of the Sun is 4×1026 W .
the body is 13% carbon, estimate the fraction of the decay energy
absorbed. (The rest escapes, exposing those close to you.)
(a) If 90% of this is supplied by the proton-proton cycle, how many
25. If everyone in Australia received an extra 0.05 mSv per year of
protons are consumed per second?
radiation, what would be the increase in the number of cancer deaths per
(b) How many neutrinos per second should there be per square meter at
year? (Assume that time had elapsed for the effects to become
the Earth from this process? This huge number is indicative of how rarely
apparent.) Assume that there are 200×10−4 deaths per Sv of radiation a neutrino interacts, since large detectors observe very few per day.
per year. What percent of the actual number of cancer deaths recorded is
36. Another set of reactions that result in the fusing of hydrogen into
this?
helium in the Sun and especially in hotter stars is called the carbon cycle.
It is
12 C + 1H → 13N + γ,
26. Verify that the total number of nucleons, total charge, and electron
family number are conserved for each of the fusion reactions in the
13 N
→ 13 C + e+ + ve,
proton-proton cycle in
13 C + 1H → 14N + γ,
1 H + 1H → 2H + e+ + v e, 1H + 2H → 3He + γ,
14 N + 1H → 15O + γ,
and
15 O
→ 15 N + e+ + ve,
3 He + 3He → 4He + 1H + 1H.
15 N + 1H → 12C + 4He.
(List the value of each of the conserved quantities before and after each
of the reactions.)
Write down the overall effect of the carbon cycle (as was done for the
27. Calculate the energy output in each of the fusion reactions in the
proton-proton cycle in 2 e− + 41 H → 4 He + 2 ve + 6γ ). Note the
proton-proton cycle, and verify the values given in the above summary.
number of protons ( 1 H ) required and assume that the positrons ( e+ )
28. Show that the total energy released in the proton-proton cycle is 26.7
annihilate electrons to form more γ rays.
MeV, considering the overall effect in 1 H + 1H → 2 H + e+ + v e ,
1
37. (a) Find the total energy released in MeV in each carbon cycle
H + 2H → 3 He + γ , and 3 He + 3He → 4 He + 1H + 1H and
(elaborated in the above problem) including the annihilation energy.
being certain to include the annihilation energy.
(b) How does this compare with the proton-proton cycle output?
29. Verify by listing the number of nucleons, total charge, and electron
38. Verify that the total number of nucleons, total charge, and electron
family number before and after the cycle that these quantities are
family number are conserved for each of the fusion reactions in the
conserved in the overall proton-proton cycle in
carbon cycle given in the above problem. (List the value of each of the
2 e− + 41 H → 4 He + 2 v
conserved quantities before and after each of the reactions.)
e + 6γ .
39. Integrated Concepts
30. 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
The laser system tested for inertial confinement can produce a 100-kJ
Fusion. Approximately how many kilograms would be required to supply
pulse only 1.00 ns in duration. (a) What is the power output of the laser
the annual energy use in the United States?
system during the brief pulse?
31. Tritium is naturally rare, but can be produced by the reaction
(b) How many photons are in the pulse, given their wavelength is
n + 2H → 3 H + γ
1.06 µm ?
. How much energy in MeV is released in this
neutron capture?
(c) What is the total momentum of all these photons?
32. Two fusion reactions mentioned in the text are
(d) How does the total photon momentum compare with that of a single
1.00 MeV deuterium nucleus?
n + 3He → 4 He + γ
40. Integrated Concepts
and
Find the amount of energy given to the 4 He nucleus and to the γ ray in
n + 1H → 2 H + γ .
the reaction n +3 He →4 He + γ , using the conservation of
Both reactions release energy, but the second also creates more fuel.
momentum principle and taking the reactants to be initially at rest. This
Confirm that the energies produced in the reactions are 20.58 and 2.22
should confirm the contention that most of the energy goes to the γ ray.
MeV, respectively. Comment on which product nuclide is most tightly
41. Integrated Concepts
bound, 4 He or 2 H .
(a) What temperature gas would have atoms moving fast enough to bring
33. (a) Calculate the number of grams of deuterium in an 80,000-L
two 3 He nuclei into contact? Note that, because both are moving, the
swimming pool, given deuterium is 0.0150% of natural hydrogen.
average kinetic energy only needs to be half the electric potential energy
(b) Find the energy released in joules if this deuterium is fused via the
of these doubly charged nuclei when just in contact with one another.
reaction 2 H + 2H → 3 He + n .
(b) Does this high temperature imply practical difficulties for doing this in
controlled fusion?
(c) Could the neutrons be used to create more energy?
CHAPTER 32 | MEDICAL APPLICATIONS OF NUCLEAR PHYSICS 1179
42. Integrated Concepts
(e) Look up the half-life of the final nucleus to see if it lives long enough
(a) Estimate the years that the deuterium fuel in the oceans could supply
to be a useful fuel.
the energy needs of the world. Assume world energy consumption to be
49. The electrical power output of a large nuclear reactor facility is 900
ten times that of the United States which is 8×1019 J/y and that the
MW. It has a 35.0% efficiency in converting nuclear power to electrical.
deuterium in the oceans could be converted to energy with an efficiency
(a) What is the thermal nuclear power output in megawatts?
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
(b) How many 235 U nuclei fission each second, assuming the average
the mass of deuterium available. Note that approximate energy yield of
fission produces 200 MeV?
deuterium is 3.37×1014 J/kg.
(c) What mass of 235 U is fissioned in one year of full-power operation?
(b) Comment on how much time this is by any human measure. (It is not
an unreasonable result, only an impressive one.)
50. 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?
43. (a) Calculate the energy released in the neutron-induced fission
(similar to the spontaneous fission in Example 32.2)
n + 238U → 96 Sr + 140 Xe + 3 n,
51. Find the mass converted into energy by a 12.0-kT bomb.
52. What mass is converted into energy by a 1.00-MT bomb?
given m(96 Sr) = 95.921750 u and m(140 Xe) = 139.92164 . (b)
53. Fusion bombs use neutrons from their fission trigger to create tritium
This result is about 6 MeV greater than the result for spontaneous fission. fuel in the reaction n +6 Li →3 H +4 He . What is the energy released
Why? (c) Confirm that the total number of nucleons and total charge are
by this reaction in MeV?
conserved in this reaction.
54. It is estimated that the total explosive yield of all the nuclear bombs in
44. (a) Calculate the energy released in the neutron-induced fission
existence currently is about 4,000 MT.
reaction
(a) Convert this amount of energy to kilowatt-hours, noting that
n + 235U → 92 Kr + 142 Ba + 2 n,
1 kW ⋅ h = 3.60×106 J .
given m(92 Kr) = 91.926269 u and m(142 Ba) = 141.916361 u .
(b) What would the monetary value of this energy be if it could be
converted to electricity costing 10 cents per kW·h?
(b) Confirm that the total number of nucleons and total charge are
55. A radiation-enhanced nuclear weapon (or neutron bomb) can have a
conserved in this reaction.
smaller total yield and still produce more prompt radiation than a
45. (a) Calculate the energy released in the neutron-induced fission
conventional nuclear bomb. This allows the use of neutron bombs to kill
reaction
nearby advancing enemy forces with radiation without blowing up your
n + 239Pu → 96 Sr + 140Ba + 4 n,
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.
given m(96 Sr) = 95.921750 u and m(140 Ba) = 139.910581 u .
56. (a) How many 239 Pu nuclei must fission to produce a 20.0-kT yield,
(b) Confirm that the total number of nucleons and total charge are
conserved in this reaction.
assuming 200 MeV per fission? (b) What is the mass of this much
239 Pu ?
46. Confirm that each of the reactions listed for plutonium breeding just
following Example 32.4 conserves the total number of nucleons, the total
57. Assume one-fourth of the yield of a typical 320-kT strategic bomb
charge, and electron family number.
comes from fission reactions averaging 200 MeV and the remainder from
47. Breeding plutonium produces energy even before any plutonium is
fusion reactions averaging 20 MeV.
fissioned. (The primary purpose of the four nuclear reactors at Chernobyl
(a) Calculate the number of fissions and the approximate mass of
was breeding plutonium for weapons. Electrical power was a by-product
uranium and plutonium fissioned, taking the average atomic mass to be
used by the civilian population.) Calculate the energy produced in each of 238.
the reactions listed for plutonium breeding just following Example 32.4.
(b) Find the number of fusions and calculate the approximate mass of
The pertinent masses are m(239 U) = 239.054289 u ,
fusion fuel, assuming an average total atomic mass of the two nuclei in
m(239 Np) = 239.052932 u , and m(239 Pu) = 239.052157 u .
each reaction to be