Solved: (II) How much mass of is required to produce the

Natural aluminum is all If it absorbs a neutron, what does it become? Does it decay by or What will be the product nucleus?

Determine whether the reaction requires a threshold energy, and why

Is the reaction possible with slow neutrons? Explain

(a) Complete the following nuclear reaction, (b) What is the Q-value?

The reaction requires an input of energy equal to 2.438 MeV. What is the mass o

(a) Can the reaction occur if the bombarding particles have 18.00 MeV of kinetic energy? (d stands for deuterium, ) (b) If so, how much energy is released? If not, what kinetic energy is needed?

(II) (a) Can the reaction \(p+ ^7 _3 Li\ \rightarrow\ ^4 _2 He +\alpha\) occur if the incident proton has kinetic energy = 3100 keV? (b) If so, what is the total kinetic energy of the products? If not, what kinetic energy is needed?

In the reaction the incident particles have 9.85 MeV of kinetic energy. The mass of is 16.999132 u. (a) Can this reaction occur? (b) If so, what is the total kinetic energy of the products? If not, what kinetic energy is needed?

Calculate the Q-value for the capture reaction

Calculate the total kinetic energy of the products of the reaction if the incoming deuteron

Radioactive is produced in the atmosphere when a neutron is absorbed by Write the reaction and find its Q-value

An example of a stripping nuclear reaction is (a) What is X, the resulting nucleus? (b) Why is it called a stripping reaction? (c) What is the Q-value of this reaction? Is the reaction endothermic or exothermic

An example of a pick-up nuclear reaction is (a) Why is it called a pick-up reaction? (b) What is the resulting nucleus? (c) What is the Q-value of this reaction? Is the reaction endothermic or exothermic?

Does the reaction require energy, or does it release energy? How much energy?

Calculate the energy released (or energy input required) for the reaction

What is the energy released in the fission reaction of Eq. 314? (The masses of and are 140.914411 u and 91.926156 u, respectively.)

Calculate the energy released in the fission reaction Use Appendix B, and assume the initial kinetic energy of the neutron is very small.

How many fissions take place per second in a 240-MW reactor? Assume 200 MeV is released per fission.

(I) The energy produced by a fission reactor is about 200 MeV per fission. What fraction of the mass of a \(^{235} _{92} U\) nucleus is this?

Suppose that the average electric power consumption, day and night, in a typical house is 960 W. What initial mass of would have to undergo fission to supply the electrical needs of such a house for a year? (Assume 200 MeV is released per fission, as well as 100% efficiency.)

Consider the fission reaction (a) How many neutrons are produced in this reaction? (b) Calculate the energy release. The atomic masses for Sb and Nb isotopes are 132.915250 u and 97.910328 u, respectively

How much mass of is required to produce the same amount of energy as burning 1.0 kg of coal (about

What initial mass of is required to operate a 950-MW reactor for 1 yr? Assume 34% efficiency.

If a 1.0-MeV neutron emitted in a fission reaction loses one-half of its kinetic energy in each collision with moderator nuclei, how many collisions must it make to reach thermal energy A 3 2 kT = 0.040 eVB?

Assuming a fission of into two roughly equal fragments, estimate the electric potential energy just as the fragments separate from each other. Assume that the fragments are spherical (see Eq. 301) and compare your calculation to the nuclear fission energy released, about 200 MeV

Suppose that the neutron multiplication factor is 1.0004. If the average time between successive fissions in a chain of reactions is 1.0 ms, by what factor will the reaction rate increase in 1.0 s?

(I) What is the average kinetic energy of protons at the center of a star where the temperature is \(2 \times 10^7\ K\)? [Hint: See Eq. 13-8.]

Show that the energy released in the fusion reaction is 17.59 MeV.

Show that the energy released when two deuterium nuclei fuse to form with the release of a neutron is 3.27 MeV (Eq. 318b)

Verify the Q-value stated for each of the reactions of Eqs. 316. [Hint: Use Appendix B; be careful with electrons (included in mass values except for p, d, t).

(a) Calculate the energy release per gram of fuel for the reactions of Eqs. 318a, b, and c. (b) Calculate the energy release per gram of uranium in fission, and give its ratio to each reaction in (a).

How much energy is released when absorbs a slow neutron and becomes

If a typical house requires 960 W of electric power on average, what minimum amount of deuterium fuel would have to be used in a year to supply these electrical needs? Assume the reaction of Eq. 318b

If is struck by a slow neutron, it can form and another nucleus. (a) What is the second nucleus? (This is a method of generating this isotope.) (b) How much energy is released in the process?

Suppose a fusion reactor ran on dd reactions, Eqs. 318a and b in equal amounts. Estimate how much natural water, for fuel, would be needed per hour to run a 1150-MW reactor, assuming 33% efficiency

Show that the energies carried off by the nucleus and the neutron for the reaction of Eq. 318c are about 3.5 MeV and 14 MeV, respectively. Are these fixed values, independent of the plasma temperature?

How much energy (J) is contained in 1.00 kg of water if its natural deuterium is used in the fusion reaction of Eq. 318a? Compare to the energy obtained from the burning of 1.0 kg of gasoline, about 5 * 107 J.

(a) Give the ratio of the energy needed for the first reaction of the carbon cycle to the energy needed for a deuteriumtritium reaction (Example 319). (b) If a deuteriumtritium reaction actually requires a temperature estimate the temperature needed for the first carbon-cycle reaction.

(I) 350 rads of \(\alpha\)-particle radiation is equivalent to how many rads of X-rays in terms of biological damage?

A dose of 4.0 Sv of rays in a short period would be lethal to about half the people subjected to it. How many grays is this?

How many rads of slow neutrons will do as much biological damage as 72 rads of fast neutrons?

How much energy is deposited in the body of a 65-kg adult exposed to a 2.5-Gy dose?

A cancer patient is undergoing radiation therapy in which protons with an energy of 1.2 MeV are incident on a 0.20-kg tumor. (a) If the patient receives an effective dose of 1.0 rem, what is the absorbed dose? (b) How many protons are absorbed by the tumor? Assume

(II) A \(0.035-\mu Ci\) sample of \(^{32} _{15} P\) is injected into an animal for tracer studies. If a Geiger counter intercepts 35% of the emitted \(\beta\) particles, what will be the counting rate, assumed 85% efficient?

About 35 eV is required to produce one ion pair in air. Show that this is consistent with the two definitions of the roentgen given in the text

A 1.6-mCi source of (in ), a emitter, is implanted in a tumor where it is to administer 32 Gy. The half- life of is 14.3 days, and 1.0 mCi delivers about Approximately how long should the source remain implanted?

What is the mass of a 2.50- source?

(II) \(^{57} _{27} Co\) emits 122-keV \(\gamma\) rays. If a 65-kg person swallowed \(1.55\ \mu Ci\) of \(^{57} _{27} Co\), what would be the close rate (Gy/day) averaged over the whole body? Assume that 50% of the \(\gamma\)-rays energy is deposited in the body. [Hint: Determine the rate of energy deposited in the body and use the definition of the gray.]

Ionizing radiation can be used on meat products to reduce the levels of microbial pathogens. Refrigerated meat is limited to 4.5 kGy. If 1.6-MeV electrons irradiate 5 kg of beef, how many electrons would it take to reach the allowable limit?

Huge amounts of radioactive were released in the accident at Chernobyl in 1986. Chemically, iodine goes to the human thyroid. (It can be used for diagnosis and treatment of thyroid problems.) In a normal thyroid, absorption can cause damage to the thyroid. (a) Write down the reaction for the decay of (b) Its half-life is 8.0 d; how long would it take for ingested to become 5.0% of the initial value? (c) Absorbing 1 mCi of can be harmful; what mass of iodine is this?

Assume a liter of milk typically has an activity of 2000 pCi due to If a person drinks two glasses (0.5 L) per day, estimate the total effective dose (in Sv and in rem) received in a year. As a crude model, assume the milk stays in the stomach 12 hr and is then released. Assume also that roughly 10% of the 1.5 MeV released per decay is absorbed by the body. Compare your result to the normal allowed dose of 100 mrem per year. Make your estimate for (a) a 60-kg adult, and (b) a 6-kg baby

Radon gas, is considered a serious health hazard (see discussion in text). It decays by -emission. (a) What is the daughter nucleus? (b) Is the daughter nucleus stable or radioactive? If the latter, how does it decay, and what is its half-life? (See Fig. 3011.) (c) Is the daughter nucleus also a noble gas, or is it chemically reactive? (d) Suppose 1.4 ng of seeps into a basement. What will be its activity? If the basement is then sealed, what will be the activity 1 month later?

Calculate the wavelength of photons needed to produce NMR transitions in free protons in a 1.000-T field. In what region of the spectrum is this wavelength?

Consider a system of nuclear power plants that produce 2100 MW. (a) What total mass of fuel would be required to operate these plants for 1 yr, assuming that 200 MeV is released per fission? (b) Typically 6% of the nuclei that fission produce strontium90, a emitter with a half-life of 29 yr. What is the total radioactivity of the in curies, produced in 1 yr? (Neglect the fact that some of it decays during the 1-yr period.)

J. Chadwick discovered the neutron by bombarding with the popular projectile of the day, alpha particles. (a) If one of the reaction products was the then unknown neutron, what was the other product? (b) What is the Q-value of this reaction?

Fusion temperatures are often given in keV. Determine the conversion factor from kelvins to keV using, as is common in this field, without the factor

One means of enriching uranium is by diffusion of the gas Calculate the ratio of the speeds of molecules of this gas containing and on which this process depends

. (a) What mass of was actually fissioned in the first atomic bomb, whose energy was the equivalent of about 20 kilotons of TNT (1 kiloton of TNT releases )? (b) What was the actual mass transformed to energy?

The average yearly background radiation in a certain town consists of 32 mrad of X-rays and rays plus 3.4 mrad of particles having a RBE of 10. How many rem will a person receive per year on average?

A shielded -ray source yields a dose rate of at a distance of 1.0 m for an average-sized person. If workers are allowed a maximum dose of 5.0 rem in 1 year, how close to the source may they operate, assuming a 35-h work week? Assume that the intensity of radiation falls off as the square of the distance. (It actually falls off more rapidly than because of absorption in the air, so your answer will give a better-than-permissible value.)

Radon gas, is formed by decay. (a) Write the decay equation. (b) Ignoring the kinetic energy of the daughter nucleus (its so massive), estimate the kinetic energy of the particle produced. (c) Estimate the momentum of the alpha and of the daughter nucleus. (d) Estimate the kinetic energy of the daughter, and show that your approximation in (b) was valid

In the net reaction, Eq. 317, for the protonproton chain in the Sun, the neutrinos escape from the Sun with energy of about 0.5 MeV. The remaining energy, 26.2 MeV, is available to heat the Sun. Use this value to calculate the heat of combustion per kilogram of hydrogen fuel and compare it to the heat of combustion of coal, about

Energy reaches Earth from the Sun at a rate of about Calculate (a) the total power output of the Sun, and (b) the number of protons consumed per second in the reaction of Eq. 317, assuming that this is the source of all the Suns energy. (c) Assuming that the Suns mass of was originally all protons and that all could be involved in nuclear reactions in the Suns core, how long would you expect the Sun to glow at its present rate? See Problem 62. [Hint: Use law.]

Estimate how many solar neutrinos pass through a ceiling of a room, at latitude , for an hour around midnight on midsummer night. [Hint: See Problems 62 and 63.]

Estimate how much total energy would be released via fission if 2.0 kg of uranium were enriched to 5% of the isotope

Some stars, in a later stage of evolution, may begin to fuse two nuclei into one nucleus. (a) How much energy would be released in such a reaction? (b) What kinetic energy must two carbon nuclei each have when far apart, if they can then approach each other to within 6.0 fm, center-to-center? (c) Approximately what temperature would this require?

An average adult body contains about of which comes from food. (a) How many decays occur per second? (b) The potassium decay produces beta particles with energies of around 1.4 MeV. Estimate the dose per year in sieverts for a 65-kg adult. Is this a significant fraction of the background rate?

When the nuclear reactor accident occurred at Chernobyl in 1986, were released into the atmosphere. Assuming that this radiation was distributed uniformly over the surface of the Earth, what was the activity per square meter? (The actual activity was not uniform; even within Europe wet areas received more radioactivity from rainfall.)

A star with a large helium abundance can burn helium in the reaction What is the Q-value for this reaction?

A \(1.2-\mu Ci\ ^{137} _{55} Cs\) source is used for 1.4 hours by a 62-kg worker. Radioactive \(^{137} _{55} Cs\) decays by \(\beta^-\) decay with a half-life of 30 yr. The average energy of the emitted betas is about 190 keV per decay. The \(\beta\) decay is quickly followed by a \(\gamma\) with an energy of 660 keV. Assuming the person absorbs all emitted energy, what effective dose (in rem) is received?

Suppose a future fusion reactor would be able to put out 1000 MW of electrical power continuously. Assume the reactor will produce energy solely through the reaction given in Eq. 318a and will convert this energy to electrical energy with an efficiency of 33%. Estimate the minimum amount of deuterium needed to run this facility per year

If a 65-kg power plant worker has been exposed to the maximum slow-neutron radiation for a given year, how much total energy (in J) has that worker absorbed? What if he were exposed to fast protons?

Consider the fission reaction (a) What is X? (b) If this were part of a chain reaction in a fission power reactor running at barely critical, what would happen on average to the three produced neutrons? (c) (optional) What is the Q-value of this reaction? [Hint: Mass values can be found at www.nist.gov/pml/data/comp.cfm.]

A large amount of was released during the Chernobyl nuclear reactor accident in 1986. The enters the body through the food chain. How long will it take for 85% of the released during the accident to decay? See Appendix B.

Three radioactive sources have the same activity, 35 mCi. Source A emits 1.0-MeV rays, source B emits 2.0-MeV rays, and source C emits 2.0-MeV alphas. What is the relative danger of these sources?

A 55-kg patient is to be given a medical test involving the ingestion of (Section 317) which decays by emitting a 140-keV gamma. The half-life for this decay is 6 hours. Assuming that about half the gamma photons exit the body without interacting with anything, what must be the initial activity of the Tc sample if the whole-body dose cannot exceed 50 mrem? Make the rough approximation that biological elimination of Tc can be ignored.

Problem 1COQ The Sun is powered by (a) nuclear alpha decay. (b) nuclear beta decay. (c) nuclear gamma decay. (d) nuclear fission. (e) nuclear fusion.

Problem 1MCQ In a nuclear reaction, which of the following is not conserved? (a) Energy. (b) Momentum. (c) Electric charge. (d) Nucleon number. (e) None of the above.

\(\text { (I) }\) Natural aluminum is all \(\begin{array}{l}27 \\13\end{array} A l\). If it absorbs a neutron, what does it become? Does it decay by \(\beta^{+} \text {or } \beta^{-}\)? What will be the product nucleus? Equation Transcription: Text Transcription: (I) 13^27 Al \beta^+ or \beta^-

Fill in the missing particles or nuclei: 1. \(n+\frac{232}{90} T h \rightarrow ?+\gamma\) 2. \(\mathrm{n}+{ }_{56}^{137} \mathrm{Ba} \rightarrow{ }_{55}^{137} \mathrm{Cs}+?\) (c) \(d+{ }_{1}^{2} H \rightarrow{ }_{2}^{4} H e+?\) (d) \(\alpha+\frac{197}{79} \mathrm{Au} \rightarrow ?+d\) where d stands for deuterium. Equation Transcription: Text Transcription: N+90 ^ 232Th \rightarrow ?+ n+56^137Ba \rightarrow 55^137Cs+? d+1^2H \rightarrow 2^4He+? \alpha +79^197Au \rightarrow ?+d

Problem 1SL Referring to Section 31–2, (a) state three problems that must be overcome to make a functioning fission nuclear reactor; (b) state three environmental problems or dangers that do or could result from the operation of a nuclear fission reactor; (c) describe an additional problem or danger associated with a breeder reactor.

Problem 2MCQ Fission fragments are typically (a) ?+ emitters. (b) ?- emitters. (c) Both. (d) Neither.

\(\text { (I) }\) Determine whether the reaction \({ }_{1}^{2} H+{ }_{1}^{2} H \rightarrow{ }_{2}^{3} H e+n\) requires a threshold energy, and why. Equation Transcription: Text Transcription: (I) 1^2H + 1^2H 2^3He + n

When \({ }_{11}^{22} N a\) is bombarded by deuterons \(\left({ }_{1}^{2} H\right)\) ,an \(\alpha\) particle is emitted. What is the resulting nuclide? Write down the reaction equation. Equation Transcription: Text Transcription: 11^22 Na (1^2H) \alpha

Problem 2SL Referring to Section 31–3, (a) why can small nuclei combine to form larger ones, releasing energy in the process? (b) Why does the first reaction in the proton–proton chain limit the rate at which the Sun produces energy? (c) What are the heaviest elements for which energy is released if the elements are created by fusion of lighter elements? (d)What keeps the Sun and stars together, allowing them to sustain fusion? (e) What two methods are currently being investigated to contain high-temperature plasmas on the Earth to create fusion in the laboratory?

Which of the following properties would decrease the critical mass needed to sustain a nuclear chain reaction? (a) Low boiling point. (b) High melting point. (c) More neutrons released per fission. (d) Low nuclear density. (e) Filled valence shell. (f) All of the above

\((I)\) Is the reaction \(n+{ }_{92}^{238} U \rightarrow{ }_{92}^{239} U+\gamma\) possible with slow neutrons? Explain. Equation Transcription: Text Transcription: (I) n + 92 ^ 238 U \rightarrow 92 ^ 239 U + \gamma

Problem 3Q Why are neutrons such good projectiles for producing nuclear reactions?

Problem 3SL Deuterium makes up 0.0115% of natural hydrogen on average. Make a rough estimate of the total deuterium in the Earth’s oceans and estimate the total energy released if all of it were used in fusion reactors.

(II) (a) Complete the following nuclear reaction, \(p + ?\ \rightarrow\ ^{32} _{16} S + \gamma\). (b) What is the Q-value?

Problem 4Q What is the Q-value for radioactive decay reactions? (a) Q < 0 (b) Q > 0 (c) (d) The sign of Q depends on the nucleus.

The energy output of massive stars is believed to be due to the carbon cycle (see text). (a) Show that no carbon is consumed in this cycle and that the net effect is the same as for the proton–proton chain. (b) What is the total energy release? (c) Determine the energy output for each reaction and decay. (d) Why might the carbon cycle require a higher temperature \((\approx 2 \times 10^7\ K)\) than the proton-proton chain \((\approx 1.5 \times 10^7\ K)\)?

Problem 5MCQ Why is a moderator needed in a normal uranium fission reactor? (a) To increase the rate of neutron capture by uranium-235. (b) To increase the rate of neutron capture by uranium-238. (c) To increase the rate of production of plutonium-239. (d) To increase the critical mass of the fission fuel. (e) To provide more neutrons for the reaction. (f ) All of the above.

\(\text { (II) }\) The reaction \(p+{ }_{8}^{18} O \rightarrow{ }_{9}^{18} F+n\) requires an input of energy equal to \(2.438 \mathrm{MeV}\). What is the mass of \({ }_{9}^{18} F\)? Equation Transcription: MeV Text Transcription: (II) p+8^18 O \rightarrow 9^18 F + n 2.438MeV 9^18 F

Problem 5Q The energy from nuclear fission appears in the form of thermal energy—but the thermal energy of what?

Problem 5SL Consider the effort by humans to harness nuclear fusion as a viable energy source. (a) What are some advantages of using nuclear fusion rather than nuclear fission? (b) What is the major technological problem with using controlled nuclear fusion as a source of energy? (c) Discuss two different approaches to solving this problem. (d) What fuel is necessary in a nuclear fusion reaction? (e) Write a nuclear reaction using two nucler of the fuel in part (d) to create a third nucleus. (f) Calculate the Q-value of the reaction in part (e).

What is the difference between nuclear fission and nuclear fusion? (a) Nuclear fission is used for bombs; nuclear fusion is used in power plants. (b) There is no difference. Fission and fusion are different names for the same physical phenomenon. (c) Nuclear fission refers to using deuterium to create a nuclear reaction. (d) Nuclear fusion occurs spontaneously, as happens to the \(C^{14}\) used in carbon dating. (e) In nuclear fission, a nucleus splits; in nuclear fusion, nucleons or nuclei and nucleons join to form a new nucleus. Equation Transcription: Text Transcription: C14

\(\text { (II) }\) (a) Can the reaction \(n+{ }_{12}^{24} M g \rightarrow{ }_{11}^{23} N a+d\) occur if the bombarding particles have \(18.00 \mathrm{MeV}\) of kinetic energy? (d stands for deuterium, \({ }_{1}^{2} \mathrm{H}\).) (b) If so, how much energy is released? If not, what kinetic energy is needed? Equation Transcription: Text Transcription: (II) n + 12^24Mg \rightarrow 11^23Na+d 18.00 MeV 1^2H

(a) If \({ }_{92}^{235} \mathrm{U}\) released only 1.5 neutrons per fission on average (instead of 2.5), would a chain reaction be possible? (b) If so, how would the chain reaction be different than if 3 neutrons were released per fission? Equation Transcription: Text Transcription: 92 ^ 235 U

Problem 6SL 1. Explain how each of the following can cause damage to materials: beta particles, alpha particles, energetic neutrons, and gamma rays. (b) How might metals be damaged? (c) How can the damage affect living cells?

Problem 7MCQ A primary difficulty in energy production by fusion is (a) the scarcity of necessary fuel. (b) the disposal of radioactive by-products produced. (c) the high temperatures necessary to overcome the electrical repulsion of protons. (d) the fact that it is possible in volcanic regions only.

\(\text { (II) }\) (a) Can the reaction \(p+L i \rightarrow{ }_{s}^{4} H e+\alpha\) occur if the incident proton has kinetic energy \(=3100 \mathrm{keV}\)? (b) If so, what is the total kinetic energy of the products? If not, what kinetic energy is needed? Equation Transcription: Text Transcription: (II) p + Li \rightarrow s 4 He+ \alpha =3100 keV

Problem 7Q Why can’t uranium be enriched by chemical means?

If two hydrogen nuclei, \({ }_{1}^{2} H\), each of mass \(m_{H}\), fuse together and form a helium nucleus of mass \(m_{\mathrm{He}}\) (a) \(\mathrm{m}_{\mathrm{He}}<2 \mathrm{~m}_{\mathrm{H}}\) (b) \(m_{H e}=2 m_{H}\) (c) \(m_{H e}>2 m_{H}\) (d) All of the above are possible. Equation Transcription: Text Transcription: 1^2H mH mHe mHe < 2mH mHe =2 mH mHe > 2 mH

\((I I)\) In the reaction \(\alpha+{ }_{7}^{14} N \rightarrow{ }_{8}^{17} O+p\), the incident particles have \(9.85 \mathrm{MeV}\) of kinetic energy. The mass of \({ }_{8}^{17} O \text { is } 16.999132 u\) () Can this reaction occur? (b) If so, what is the total kinetic energy of the products? If not, what kinetic energy is needed? Equation Transcription: Text Transcription: (II) \alpha +7^14 N \rightarrow 8^17 O + p 9.85 MeV 8^17 O is 16.999132 u

How can a neutron, with practically no kinetic energy, excite a nucleus to the extent shown in Fig. 31–3?

Problem 9MCQ Which radiation induces the most biological damage for a given amount of energy deposited in tissue? (a) Alpha particles. (b) Gamma radiation. (c) Beta radiation. (d) All do the same damage for the same deposited energy.

(II) Calculate the \(Q-\text { value }\) for the “capture” reaction \(\alpha+{ }_{8}^{16} O \rightarrow{ }_{10}^{20} N e+\gamma\) Equation Transcription: Text Transcription: Q-value \alpha+_8^16 O \rightarrow_10^20 N e+\gamma

Why would a porous block of uranium be more likely to explode if kept under water rather than in air?

Problem 10MCQ Which would produce the most energy in a single reaction? (a) The fission reaction associated with uranium-235. (b) The fusion reaction of the Sun (two hydrogen nuclei fused to one helium nucleus). (c) Both (a) and (b) are about the same. (d) Need more information.

(II) Calculate the total kinetic energy of the products of the reaction \(d+{ }_{6}^{13} C \rightarrow{ }_{7}^{14} N+n\) if the incoming deuteron has kinetic energy \(K E=41.4 \mathrm{MeV} \text {. }\) Equation Transcription: Text Transcription: d+6^13C \rightarrow 7^14N+n KE=41.4MeV

Problem 10Q A reactor that uses highly enriched uranium can use ordinary water (instead of heavy water) as a moderator and still have a self-sustaining chain reaction. Explain.

Problem 11MCQ The fuel necessary for fusion-produced energy could be derived from (a) water. (b) superconductors. (c) uranium. (d) helium. (e) sunlight.

\((I I)\) Radioactive \(\frac{14}{6} C\) is produced in the atmosphere when a neutron is absorbed by { }_{7}^{14} N Write the reaction and find its Q-value. Equation Transcription: Text Transcription: (II) 6^14C 7^14N

Problem 11Q Why must the fission process release neutrons if it is to be useful?

Problem 12MCQ Which of the following is true? (a) Any amount of radiation is harmful to living tissue. (b) Radiation is a natural part of the environment. (c) All forms of radiation will penetrate deep into living tissue. (d) None of the above is true.

\(\text { (II) }\) An example of a stripping nuclear reaction is \(\mathrm{d}+{ }_{3}^{6} \mathrm{Li} \rightarrow \mathrm{X}+\mathrm{p}\) (a) What is X, the resulting nucleus? (b) Why is it called a “stripping” reaction? (c) What is the Q-value of this reaction? Is the reaction endothermic or exothermic? Equation Transcription: Text Transcription: (II) D+3 ^6Li \rightarrow X+p

Problem 12Q Why are neutrons released in a fission reaction?

Problem 13MCQ Which of the following would reduce the cell damage due to radiation for a lab technician who works with radioactive isotopes in a hospital or lab? (a) Increase the worker’s distance from the radiation source. (b) Decrease the time the worker is exposed to the radiation. (c) Use shielding to reduce the amount of radiation that strikes the worker. (d) Have the worker wear a radiation badge when working with the radioactive isotopes. (e) All of the above.

\(\text { (II) }\) An example of a pick-up nuclear reaction is \({ }_{2}^{3} \mathrm{He}+{ }_{6}^{12} \mathrm{C} \rightarrow X+\alpha\) (a) Why is it called a “pick-up” reaction? (b) What is the resulting nucleus? (c) What is the Q-value of this reaction? Is the reaction endothermic or exothermic? Equation Transcription: Text Transcription: (II) 2^3 He + 6^12C \rightarrow X + \alpha

What is the reason for the “secondary system” in a nuclear reactor, Fig. 31–8? That is, why is the water heated by the fuel in a nuclear reactor not used directly to drive the turbines?

Problem 14MCQ If the same dose of each type of radiation was provided over the same amount of time, which type would be most harmful? (a) X-rays. (b) ?- rays. (c) ? -rays. (d) ? -particles.

(II) Does the reaction \(p+{ }_{3}^{7} L i \rightarrow{ }_{2}^{4} H e+\alpha\) require energy, or does it release energy? How much energy? Equation Transcription: Text Transcription: p + 3^7 Li \rightarrow 2^4 He +\alpha

Problem 14Q What is the basic difference between fission and fusion?

\({ }_{92}^{235} \bigcup\) releases an average of 2.5 neutrons per fission compared to 2.9 for \({ }_{94}^{239} \mathrm{Pu}\). Which has the smaller critical mass? (a) \({ }_{92}^{235} \bigcup\) (b) \({ }_{94}^{239} \mathrm{Pu}\). (c) Both the same. Equation Transcription: Text Transcription: 92^235 U 94^239 Pu 92^235 U 94^239 Pu

(II) Calculate the energy released (or energy input required) for the reaction \(\alpha+{ }_{4}^{9} B e \rightarrow{ }_{6}^{12} C+n\) Equation Transcription: Text Transcription: \alpha+_4^9 B e \rightarrow_6^12 C+n

Problem 15Q Discuss the relative merits and disadvantages, including pollution and safety, of power generation by fossil fuels, nuclear fission, and nuclear fusion.

(I) What is the energy released in the fission reaction of Eq. 31–4? (The masses of \({ }_{56}^{141} \mathrm{Ba} \text { and }{ }_{36}^{92} \mathrm{Kr}\) are \(140.914411 \text { u and } 91926156 u\), respectively.) Equation Transcription: Text Transcription: 56 ^ 141Ba and 36 ^ 92Kr 140.914411 u and 91926156 u

Problem 16Q Why do gamma particles penetrate matter more easily than beta particles do?

(I) Calculate the energy released in the fission reaction \(\mathrm n+{ }_{92}^{235} \mathrm U \rightarrow { }_{38}^{88}\mathrm {Sr}+{ }_{54}^{136} \mathrm{Xe}+12 \mathrm n\) Use Appendix B, and assume the initial kinetic energy of the neutron is very small.

Problem 17Q Light energy emitted by the Sun and stars comes from the fusion process. What conditions in the interior of stars make this possible?

Problem 18P (I) How many fissions take place per second in a 240-MW reactor? Assume 200 MeV is released per fission.

Problem 18Q How do stars, and our Sun, maintain confinement of the plasma for fusion?

(I) The energy produced by a fission reactor is about \(200 \mathrm{MeV}\) per fission. What fraction of the mass of a \({ }_{92}^{235} \mathrm{U}\) nucleus is this? Equation Transcription: Text Transcription: 200 MeV 92 ^ 235 U

Problem 19Q People who work around metals that emit alpha particles are trained that there is little danger from proximity or touching the material, but they must take extreme precautions against ingesting it.Why? (Eating and drinking while working are forbidden.)

\(\text { (II) }\) Suppose that the average electric power consumption, day and night, in a typical house is 960 W. What initial mass of \({ }_{92}^{235} U\) would have to undergo fission to supply the electrical needs of such a house for a year? (Assume \(200 \mathrm{MeV}\) is released per fission, as well as \(100 \%\) efficiency.) Equation Transcription: Text Transcription: (II) 92^235 U 200 MeV 100%

Problem 20Q What is the difference between absorbed dose and effective dose? What are the SI units for each?

(II) Consider the fission reaction \({ }_{92}^{235} U+n \rightarrow{ }_{51}^{133} \mathrm{Sb}+{ }_{41}^{98} \mathrm{Nb}+? \mathrm{n}\) (a) How many neutrons are produced in this reaction? (b) Calculate the energy release. The atomic masses for Sb and Nb isotopes are \(132.915250 u \text { and } 97.910328 u\), respectively. Equation Transcription: Text Transcription: 92^235 U+n \rightarrow _51^133nSb+_41^98 Nb+?n 132.915250 u and 97.910328 u

Problem 21Q Radiation is sometimes used to sterilize medical supplies and even food. Explain how it works.

(II) How much mass of \({ }_{92}^{235} \mathrm{U}\) is required to produce the same amount of energy as burning \(1.0 \mathrm{~kg}\) of coal (about \(3 \times 10^{7} \mathrm{~J}\))? Equation Transcription: Text Transcription: 92^235U 1.0 kg 3 x 10^7J

Problem 22Q How might radioactive tracers be used to find a leak in a pipe?

(II) What initial mass of \({ }_{92}^{235} \mathrm{U}\) is required to operate a \(950-M W\) reactor for 1 yr? Assume \(34 \%\) efficiency. Equation Transcription: Text Transcription: 92^235U 950-MW 34%

(II) If a \(1.0-M e V\) neutron emitted in a fission reaction loses one-half of its kinetic energy in each collision with moderator nuclei, how many collisions must it make to reach thermal energy \(\left(\frac{2}{2} k T=0.040 \mathrm{eV}\right)\)? Equation Transcription: Text Transcription: 1.0-MeV (3 over 2kT=0.040 eV)

Problem 26P (III) Suppose that the neutron multiplication factor is1.0004. If the average time between successive fissions in a chain of reactions is 1.0 ms, by what factor will the reaction rate increase in 1.0 s?

(II) Assuming a fission of \({ }_{92}^{236} \mathrm{U}\) into two roughly equal fragments, estimate the electric potential energy just as the fragments separate from each other. Assume that the fragments are spherical (see Eq. 30–1) and compare your calculation to the nuclear fission energy released, about \(200 \mathrm{MeV}\) Equation Transcription: Text Transcription: 92^236U 200 MeV

(I) What is the average kinetic energy of protons at the center of a star where the temperature is \(2 \times 10^{7} K\)? [Hint: See Eq. 13–8.] Equation Transcription: Text Transcription: 2 x 10^7 K

(II) Show that the energy released in the fusion reaction \({ }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \rightarrow{ }_{2}^{4} \mathrm{He}+n \text { is } 17.59 \mathrm{MeV}\) Equation Transcription: Text Transcription: 1 ^ 2 H+1^3H \rightarrow 2^4He+n is 17.59 MeV

(II) Show that the energy released when two deuterium nuclei fuse to form \({ }_{2}^{3} \mathrm{He}\) with the release of a neutron is \(3.27 \mathrm{MeV}\) (Eq. 31–8b). Equation Transcription: Text Transcription: 2^3He 3.27 MeV

(II) Verify the \(Q \text {-value }\) stated for each of the reactions of Eqs. 31–6. [Hint: Use Appendix B; be careful with electrons (included in mass values except for p, d, t).] Equation Transcription: Text Transcription: Q-value

Determine the resulting nucleus in the reaction \(n+{ }_{56}^{137} B a \rightarrow ?+\gamma\). Energy and momentum are also conserved in nuclear reactions, and can be used to determine whether or not a given reaction can occur. For example, if the total mass of the final products is less than the total mass of the initial particles, this decrease in mass (recall \(\Delta E=\Delta m c^{2}\)) is converted to kinetic energy \((K E)\) of the outgoing particles. But if the total mass of the products is greater than the total mass of the initial reactants, the reaction requires energy. The reaction will then not occur unless the bombarding particle has sufficient kinetic energy. Consider a nuclear reaction of the general form \(a+X \rightarrow Y+b\) (31-1) where particle a is a moving projectile particle (or small nucleus) that strikes nucleus X, producing nucleus Y and particle b (typically, \(p, n, \alpha, \gamma\)). We define the reaction energy, or Q-value, in terms of the masses involved, as \(Q=\left(M_{a}+M_{x}-M_{b}-M_{y}\right)c^{2}\) (31-2a) For a \(\gamma\) ray, \(M=0\). If energy is released by the reaction, \(Q>0 \). If energy is required, \(Q<0\) Because energy is conserved, Q has to be equal to the change in kinetic energy (final minus initial): \(Q=K E_{b}+K E_{Y}-K E_{a}-K E_{x}\) (31-2b) If X is a target nucleus at rest (or nearly so) struck by incoming particle a, then \(K E_{x}=0\). For \(Q>0\), the reaction is said to be exothermic or exoergic; energy is released in the reaction, so the total kinetic energy is greater after the reaction than before. If Q is negative, the reaction is said to be endothermic or endoergic: an energy input is required to make the reaction happen. The energy input comes from the kinetic energy of the initial colliding particles (a and X). Equation Transcription: Text Transcription: n+_56^137 B a \rightarrow ?+\gamma \Delta E=\Delta m c^{2} (K E) a+X \rightarrow Y+b p, n, \alpha, \gamma Q=(Ma+Mx-Mb-My)c2 \gamma M=0 Q>0 Q<0 Q=KEb+KEY-KEa-KEx KEx=0 Q>0

In the fission reaction \(n+{ }_{92}^{235} U \rightarrow{ }_{53}^{137} \mid+{ }_{39}^{96} Y+\) neutrons, how many neutrons are produced? Figure 31–4 shows the measured distribution of fission fragments according to mass. Only rarely (about 1 in ) does a fission result in equal mass fragments (arrow in Fig. 31–4). Equation Transcription: Text Transcription: n+_92^235 U \rightarrow _53^137 \mid+_39^96 Y+

A nuclear-powered submarine needs \(6000-k W\) input power. How many \({ }_{92}^{235} U\) fissions is this per second? Equation Transcription: Text Transcription: 6000-kW 92^235 U

Return to the Chapter-Opening Question, page 885, and answer it again now. Try to explain why you may have answered it differently the first time.

Problem 31EE If the Sun is generating a constant amount of energy via fusion, the mass of the Sun must be (a) increasing, (b) decreasing, (c) constant, (d) irregular.

(II) (a) Calculate the energy release per gram of fuel for the reactions of Eqs. 31–8a, b, and c. (b) Calculate the energy release per gram of uranium \({ }_{92}^{235} \mathrm{U}\) in fission, and give its ratio to each reaction in (a). Equation Transcription: Text Transcription: 92^235U

(II) How much energy is released when \({ }_{92}^{238} U\) absorbs a slow neutron (kinetic energy \(\approx 0\)) and becomes \({ }_{92}^{239} U\)? Equation Transcription: Text Transcription: 92^238 U \approx 0 92^239 U

\(\text { (II) }\) If a typical house requires \(960 \mathrm{~W}\) of electric power on average, what minimum amount of deuterium fuel would have to be used in a year to supply these electrical needs? Assume the reaction of Eq. 31–8b. Equation Transcription: Text Transcription: (II) 960 W

\((I I)\) If \({ }_{3}^{6} L i\) is struck by a slow neutron, it can form \({ }_{2}^{4} \mathrm{He}\) and another nucleus. (a) What is the second nucleus? (This is a method of generating this isotope.) (b) How much energy is released in the process? Equation Transcription: Text Transcription: (II) 3^6Li 2^4He

\(\text { (II) }\) Suppose a fusion reactor ran on \(" d-d "\) reactions, Eqs. 31–8a and b in equal amounts. Estimate how much natural water, for fuel, would be needed per hour to run a \text { \(1150-MW }\) reactor, assuming \(33 \%\) efficiency. Equation Transcription: Text Transcription: (II) "d-d" 1150-MW 33%

\(\text { (III) }\) Show that the energies carried off by the \({ }_{2}^{4} \mathrm{He}\) nucleus and the neutron for the reaction of Eq. 31–8c are about \(3.5 \mathrm{MeV} \text { and } 14 \mathrm{MeV}\), respectively. Are these fixed values, independent of the plasma temperature? Equation Transcription: Text Transcription: (III) 2^4He 3.5 MeV and 14 MeV

\(\text { (III) }\) How much energy \((\mathrm{J})\) is contained in \(1.00 \mathrm{~kg}\) of water if its natural deuterium is used in the fusion reaction of Eq. 31–8a? Compare to the energy obtained from the burning of \(1.00 \mathrm{~kg}\) of gasoline, about \(5 X 10^{7} \mathrm{~J}\) Equation Transcription: Text Transcription: (III) (J) 1.00 kg 1.00 kg 5 X 10^7J

\((I I I)\) (a) Give the ratio of the energy needed for the first reaction of the carbon cycle to the energy needed for a deuterium–tritium reaction (Example 31–9). (b) If a deuterium–tritium reaction actually requires a temperature \(T \approx 3 X 10^{8} \mathrm{~K}\), estimate the temperature needed for the first carbon-cycle reaction. Equation Transcription: Text Transcription: (III) T \approx 3 X 10^8~K

Problem 39P (I) 350 rads of ?-particle radiation is equivalent to how many rads of X-rays in terms of biological damage?

\(\text { (I) }\) A dose of \(4.0 S v\) of \(\gamma\) rays in a short period would be lethal to about half the people subjected to it. How many grays is this? Equation Transcription: Text Transcription: (I) 4.0 Sv \gamma

Problem 41P (I) How many rads of slow neutrons will do as much biological damage as 72 rads of fast neutrons?

Problem 42P (II) How much energy is deposited in the body of a 65-kg adult exposed to a 2.5-Gy dose?

\text { (II) }\) A cancer patient is undergoing radiation therapy in which protons with an energy of \(1.2 \mathrm{MeV}\) are incident on a \(0.20-\mathrm{kg}\) tumor. (a) If the patient receives an effective dose of \(1.0 \mathrm{rem}\), what is the absorbed dose? (b) How many protons are absorbed by the tumor? Assume \(R B E \approx 1\) Equation Transcription: Text Transcription: (II) 1.2 MeV 0.20-kg 1.0 rem R B E \approx 1

\(\text { (II) }\) A \(0.035-\mu C i\) sample of \({ }_{15}^{32} P\) is injected into an animal for tracer studies. If a Geiger counter intercepts \(35 \%\) of the emitted \(\beta\) particles, what will be the counting rate, assumed \(\text { 85\% }\) efficient? Equation Transcription: Text Transcription: (II) 0.035-\mu C i 15^32P 35% \beta 85%

Problem 45P (II) About 35 eV is required to produce one ion pair in air. Show that this is consistent with the two definitions of the roentgen given in the text.

\(\text { (II) }\) A \(1.6-m C i\) source of \({ }_{15}^{32} \mathrm{P}\) (in \(\mathrm{NaHPO}_{4}\)), a \(\beta\) emitter, is implanted in a tumor where it is to administer \(32 \text { Gy }\). The half-life of \(\begin{array}{l}32 \\15\end{array} P\) is 14.3 days, and \(1.0 \mathrm{mCi}\) delivers about \(10 \mathrm{mGy} / \mathrm{min}\). Approximately how long should the source remain implanted? Equation Transcription: Text Transcription: (II) 1.6-mCi 15^32P NaHPO4 \beta 32 Gy 15^32P 1.0-mCi 10 mGy/min

\(\text { (II) }\) What is the mass of a \(2.50-\mu C i{ }_{6}^{14} C\) source? Equation Transcription: Text Transcription: (II) 2.50-\mu C i_6^14 C

\(\text { (II) }\) \({ }_{27}^{57} \mathrm{Co}\) emits \(\text { 122-keV } \gamma\) rays. If a \(\text { 65-kg }\) person swallowed \(1.55 \mu C i \text { of }{ }_{27}^{57} C o\), what would be the dose rate (Gy/day) averaged over the whole body? Assume that \(50 \%\) of the \(\gamma\) -ray energy is deposited in the body. [Hint: Determine the rate of energy deposited in the body and use the definition of the gray.] Equation Transcription: Text Transcription: (II) 27^57 Co 122-keV \gamma 65-kg 1.55 Ci of 27^57 Co 50% \gamma

Problem 49P (II) Ionizing radiation can be used on meat products to reduce the levels of microbial pathogens. Refrigerated meat is limited to 4.5 kGy. If 1.6-MeV electrons irradiate 5 kg of beef, how many electrons would it take to reach the allowable limit?

\((I I I)\) Huge amounts of radioactive \({ }_{53}^{131} I\) were released in the accident at Chernobyl in 1986. Chemically, iodine goes to the human thyroid. (It can be used for diagnosis and treatment of thyroid problems.) In a normal thyroid, \({ }_{53}^{131} I\) absorption can cause damage to the thyroid. (a) Write down the reaction for the decay of \({ }_{53}^{131} I\) (b) Its half-life is 8.0 d; how long would it take for ingested \({ }_{53}^{131} I\) to become \(5.0 \%\) of the initial value? (c) Absorbing \(1 \mathrm{mCi}\) of \({ }_{53}^{131} I\) can be harmful; what mass of iodine is this? Equation Transcription: Text Transcription: (III) 53^131 I 53^131 I 53^131 I 53^131 I 5.0% 1 mCi 53^131 I

\(\text { (III) }\) Assume a liter of milk typically has an activity of \(2000 p C i\) due to \({ }_{19}^{40} K\) If a person drinks two glasses \((0.5 L)\) per day, estimate the total effective dose (in Sv and in rem) received in a year. As a crude model, assume the milk stays in the stomach 12 hr and is then released. Assume also that roughly \(10 \%\) of the \(1.5 \mathrm{MeV}\) released per decay is absorbed by the body. Compare your result to the normal allowed dose of 100 mrem per year. Make your estimate for (a) a \(60-\mathrm{kg}\) adult, and (b) a \(\text { 6-kg }\) baby. Equation Transcription: Text Transcription: (III) 2000 pCi 19^40 K (0.5 L) 10% 1.5 MeV 60-kg 6-kg

\((I I I)\) Radon gas, \({ }_{86}^{222} \mathrm{Rn}\), is considered a serious health hazard (see discussion in text). It decays by \(\alpha\) -emission. (a) What is the daughter nucleus? (b) Is the daughter nucleus stable or radioactive? If the latter, how does it decay, and what is its half-life? (See Fig. 30–11.) (c) Is the daughter nucleus also a noble gas, or is it chemically reactive? (d) Suppose 1.4 ng of \({ }_{86}^{222} \mathrm{Rn}\) seeps into a basement. What will be its activity? If the basement is then sealed, what will be the activity 1 month later? Equation Transcription: Text Transcription: (III) 86^222 Rn \alpha 86^222 Rn

Problem 53P (II) Calculate the wavelength of photons needed to produce NMR transitions in free protons in a 1.000-T field. In what region of the spectrum is this wavelength?

Consider a system of nuclear power plants that produce \(2100 M W\) (a) What total mass of \(\begin{array}{l}235 \\92\end{array} U\) fuel would be required to operate these plants for 1 yr, assuming that \(200 \mathrm{MeV}\) is released per fission? (b) Typically \(6 \%\) of the \({ }_{92}^{235} \mathrm{U}\) nuclei that fission produce \(\text { strontium-90, }{ }_{38}^{90} \mathrm{Sr}, \mathrm{a} \beta^{-}\) emitter with a half-life of 29 yr. What is the total radioactivity of the \({ }_{38}^{90} \mathrm{Sr}\), in curies, produced in 1 yr? (Neglect the fact that some of it decays during the 1-yr period.) Equation Transcription: Text Transcription: 2100 MW 92^235 U 200 MeV 6% 92^235U strontium-90, 38^90Sr, a ,\beta^- 38^90Sr

J. Chadwick discovered the neutron by bombarding \({ }_{4}^{9} \mathrm{Be}\) with the popular projectile of the day, alpha particles. (a) If one of the reaction products was the then unknown neutron, what was the other product? (b) What is the \(\text { Q-value }\) of this reaction? Equation Transcription: Text Transcription: 4^9 Be Q-value

Fusion temperatures are often given in keV. Determine the conversion factor from kelvins to keV using, as is common in this field \(\overline{K E}=k T\) without the factor \(\frac{3}{2}\) Equation Transcription: Text Transcription: \overline KE =kT 3 over 2

One means of enriching uranium is by diffusion of the gas \(U F_{6}\). Calculate the ratio of the speeds of molecules of this gas containing \({ }_{92}^{235} \mathrm{U} \text { and }{ }_{92}^{238} \mathrm{U}\) , on which this process depends. Equation Transcription: Text Transcription: UF6 92^235 U and 92^238 U

(a) What mass of \({ }_{92}^{235} \mathrm{U}\) was actually fissioned in the first atomic bomb, whose energy was the equivalent of about 20 kilotons of TNT (1 kiloton of TNT releases \(5 \times 10^{12} \mathrm{~J}\))? (b) What was the actual mass transformed to energy? Equation Transcription: Text Transcription: 92^235 U 5 X 10^12J

The average yearly background radiation in a certain town consists of 32 mrad of X-rays and \(\gamma\) rays plus \(3.4 \mathrm{mrad}\) of particles having a RBE of 10. How many rem will a person receive per year on average? Equation Transcription: Text Transcription: \gamma 3.4 mrad

Problem 60GP A shielded -ray source yields a dose rate of 0.048 rad/h at a distance of 1.0 m for an average-sized person. If workers are allowed a maximum dose of 5.0 rem in 1 year, how close to the source may they operate, assuming a 35-h work week? Assume that the intensity of radiation falls off as the square of the distance. (It actually falls off more rapidly than 1/r2 because of absorption in the air, so your answer will give a better-than-permissible value.)

Radon gas, \({ }_{86}^{222} R n\), is formed by \(\alpha\) decay. (a) Write the decay equation. (b) Ignoring the kinetic energy of the daughter nucleus (it’s so massive), estimate the kinetic energy of the particle produced. (c) Estimate the momentum of the alpha and of the daughter nucleus. (d) Estimate the kinetic energy of the daughter, and show that your approximation in (b) was valid. Equation Transcription: Text Transcription: 86^222 Rn \alpha

In the net reaction, Eq. 31–7, for the proton–proton chain in the Sun, the neutrinos escape from the Sun with energy of about \(0.5 \mathrm{MeV}\) The remaining energy, \(26.2 \mathrm{MeV}\), is available to heat the Sun. Use this value to calculate the “heat of combustion” per kilogram of hydrogen fuel and compare it to the heat of combustion of coal, about \(3 X 10^{7} \mathrm{~J} / \mathrm{kg}\) Equation Transcription: Text Transcription: 0.5 MeV 26.2 MeV 3 X 10^7J/kg

Energy reaches Earth from the Sun at a rate of about \(1300 \mathrm{~W} / \mathrm{m}^{2}\). Calculate (a) the total power output of the Sun, and (b) the number of protons consumed per second in the reaction of Eq. 31–7, assuming that this is the source of all the Sun’s energy. (c) Assuming that the Sun’s mass of \(2.0 X 10^{30} \mathrm{~kg}\) was originally all protons and that all could be involved in nuclear reactions in the Sun’s core, how long would you expect the Sun to “glow” at its present rate? See Problem 62. [Hint: Use law 1/r2 law.] Equation Transcription: Text Transcription: 1300 W/m^2 2.0 X 10^30kg

Estimate how many solar neutrinos pass through a \(180-m^2\) ceiling of a room, at latitude \(44^{\circ}\), for an hour around midnight on midsummer night. [Hint: See Problems 62 and 63.]

Estimate how much total energy would be released via fission if \(2.0 \mathrm{~kg}\) of uranium were enriched to \(5 \%\) of the isotope \({ }_{92}^{235} U\) Equation Transcription: Text Transcription: 2.0 kg 5% 92^235U

Some stars, in a later stage of evolution, may begin to fuse two \(^{12} _6 C\) nuclei into one \(^{24} _{12} Mg\) nucleus. (a) How much energy would be released in such a reaction? (b) What kinetic energy must two carbon nuclei each have when far apart, if they can then approach each other to within 6.0 fm, center-to-center? (c) Approximately what temperature would this require?

An average adult body contains about \(0.10 \mu \text { Ci of }{ }_{19}^{40} K\), which comes from food. (a) How many decays occur per second? (b) The potassium decay produces beta particles with energies of around \(1.4 \mathrm{MeV}\). Estimate the dose per year in sieverts for a \(65-k g\) adult. Is this a significant fraction of the \(3.6-m S v / y r\) background rate? Equation Transcription: Text Transcription: 0.10 \mu Ci of 19^40K 1.4 MeV 65-kg 3.6-mSv/yr

Problem 68GP When the nuclear reactor accident occurred at Chernobyl in 1986, 2.0 * 107 Ci were released into the atmosphere. Assuming that this radiation was distributed uniformly over the surface of the Earth, what was the activity per square meter? (The actual activity was not uniform; even within Europe wet areas received more radioactivity from rainfall.)

A star with a large helium abundance can burn helium in the reaction \({ }_{2}^{4} H e+{ }_{2}^{4} H e+{ }_{2}^{4} H e \rightarrow{ }_{6}^{12} C\) What is the Q-value for this reaction? Equation Transcription: Text Transcription: 2^4 He + 2^4 He + 2^4 He \rightarrow 6^12 C

A \(1.2-\mu C i{ }_{55}^{137} \mathrm{Cs}\) source is used for 1.4 hours by a \(62-k g\) worker. Radioactive \({ }_{55}^{137} \mathrm{Cs}\) decays by \(\beta^{-}\) decay with a halflife of 30 yr. The average energy of the emitted betas is about \(190 \mathrm{keV}\) per decay. The decay \(\beta\) is quickly followed by a \(\gamma\) with an energy of \(660 \mathrm{keV}\). Assuming the person absorbs all emitted energy, what effective dose (in rem) is received? Equation Transcription: Text Transcription: 1.2- \mu Ci 55^137 Cs 62-kg 55^137 Cs \beta^- 190 keV \beta \gamma 660 keV

Suppose a future fusion reactor would be able to put out \(1000 \mathrm{MW}\) of electrical power continuously. Assume the reactor will produce energy solely through the reaction given in Eq. 31–8a and will convert this energy to electrical energy with an efficiency of \(33 \%\). Estimate the minimum amount of deuterium needed to run this facility per year. Equation Transcription: Text Transcription: 1000 MW 33%

Problem 72 GP If a 65-kg power plant worker has been exposed to the maximum slow-neutron radiation for a given year, how much total energy (in J) has that worker absorbed? What if he were exposed to fast protons?

Consider the fission reaction \(n+{ }_{92}^{235} U \rightarrow{ }_{38}^{92} S r+X+3 n\) (a) What is X? (b) If this were part of a chain reaction in a fission power reactor running at “barely critical,” what would happen on average to the three produced neutrons? (c) (optional) What is the Q-value of this reaction? [Hint: Mass values can be found at www.nist.gov/pml/data/comp.cfm.] Equation Transcription: Text Transcription: n + 92 ^ 235 U \rightarrow 38 ^ 92 Sr + X + 3n

A large amount of \({ }_{38}^{90} \mathrm{Sr}\) was released during the Chernobyl nuclear reactor accident in 1986. The\({ }_{38}^{90} \mathrm{Sr}\) enters the body through the food chain. How long will it take for \(85 \%\) of the \({ }_{38}^{90} \mathrm{Sr}\) released during the accident to decay? See Appendix B. Equation Transcription: Text Transcription: 38^90Sr 38^90Sr 85% 38^90Sr

Three radioactive sources have the same activity, \(35 \mathrm{mCi}\) Source A emits \(1.0-M e V \gamma\) rays, source B emits \(2.0-\mathrm{MeV} \gamma\) rays, and source C emits \(2.0-\mathrm{MeV}\) alphas. What is the relative danger of these sources? Equation Transcription: Text Transcription: 35 mCi 1.0-MeV \gamma 2.0-MeV \gamma 2.0-MeV

A \(55-k g\) patient is to be given a medical test involving the ingestion of \({ }_{43}^{99 m} T c\) (Section 31–7) which decays by emitting a \(140-k e V\) gamma. The half-life for this decay is 6 hours. Assuming that about half the gamma photons exit the body without interacting with anything, what must be the initial activity of the Tc sample if the whole-body dose cannot exceed \(50 \text { mrem }\)? Make the rough approximation that biological elimination of Tc can be ignored. Equation Transcription: Text Transcription: 55-kg 4399mTc 140-keV 50 mrem

Natural aluminum is all If it absorbs a neutron, what does it become? Does it decay by or What will be the product nucleus?

Determine whether the reaction requires a threshold energy, and why

Is the reaction possible with slow neutrons? Explain

(a) Complete the following nuclear reaction, (b) What is the Q-value?

The reaction requires an input of energy equal to 2.438 MeV. What is the mass o

(a) Can the reaction occur if the bombarding particles have 18.00 MeV of kinetic energy? (d stands for deuterium, ) (b) If so, how much energy is released? If not, what kinetic energy is needed?

(a) Can the reaction occur if the incident proton has (b) If so, what is the total kinetic energy of the products? If not, what kinetic energy is needed?

In the reaction the incident particles have 9.85 MeV of kinetic energy. The mass of is 16.999132 u. (a) Can this reaction occur? (b) If so, what is the total kinetic energy of the products? If not, what kinetic energy is needed?

Calculate the Q-value for the capture reaction

Calculate the total kinetic energy of the products of the reaction if the incoming deuteron

Radioactive is produced in the atmosphere when a neutron is absorbed by Write the reaction and find its Q-value

An example of a stripping nuclear reaction is (a) What is X, the resulting nucleus? (b) Why is it called a stripping reaction? (c) What is the Q-value of this reaction? Is the reaction endothermic or exothermic

An example of a pick-up nuclear reaction is (a) Why is it called a pick-up reaction? (b) What is the resulting nucleus? (c) What is the Q-value of this reaction? Is the reaction endothermic or exothermic?

Does the reaction require energy, or does it release energy? How much energy?

Calculate the energy released (or energy input required) for the reaction

What is the energy released in the fission reaction of Eq. 314? (The masses of and are 140.914411 u and 91.926156 u, respectively.)

Calculate the energy released in the fission reaction Use Appendix B, and assume the initial kinetic energy of the neutron is very small.

How many fissions take place per second in a 240-MW reactor? Assume 200 MeV is released per fission.

The energy produced by a fission reactor is about 200 MeV per fission. What fraction of the mass of a nucleus is this?

Suppose that the average electric power consumption, day and night, in a typical house is 960 W. What initial mass of would have to undergo fission to supply the electrical needs of such a house for a year? (Assume 200 MeV is released per fission, as well as 100% efficiency.)

Consider the fission reaction (a) How many neutrons are produced in this reaction? (b) Calculate the energy release. The atomic masses for Sb and Nb isotopes are 132.915250 u and 97.910328 u, respectively

How much mass of is required to produce the same amount of energy as burning 1.0 kg of coal (about

What initial mass of is required to operate a 950-MW reactor for 1 yr? Assume 34% efficiency.

If a 1.0-MeV neutron emitted in a fission reaction loses one-half of its kinetic energy in each collision with moderator nuclei, how many collisions must it make to reach thermal energy A 3 2 kT = 0.040 eVB?

Assuming a fission of into two roughly equal fragments, estimate the electric potential energy just as the fragments separate from each other. Assume that the fragments are spherical (see Eq. 301) and compare your calculation to the nuclear fission energy released, about 200 MeV

Suppose that the neutron multiplication factor is 1.0004. If the average time between successive fissions in a chain of reactions is 1.0 ms, by what factor will the reaction rate increase in 1.0 s?

What is the average kinetic energy of protons at the center of a star where the temperature is [Hint: See Eq. 138.]

Show that the energy released in the fusion reaction is 17.59 MeV.

Show that the energy released when two deuterium nuclei fuse to form with the release of a neutron is 3.27 MeV (Eq. 318b)

Verify the Q-value stated for each of the reactions of Eqs. 316. [Hint: Use Appendix B; be careful with electrons (included in mass values except for p, d, t).

(a) Calculate the energy release per gram of fuel for the reactions of Eqs. 318a, b, and c. (b) Calculate the energy release per gram of uranium in fission, and give its ratio to each reaction in (a).

How much energy is released when absorbs a slow neutron and becomes

If a typical house requires 960 W of electric power on average, what minimum amount of deuterium fuel would have to be used in a year to supply these electrical needs? Assume the reaction of Eq. 318b

If is struck by a slow neutron, it can form and another nucleus. (a) What is the second nucleus? (This is a method of generating this isotope.) (b) How much energy is released in the process?

Suppose a fusion reactor ran on dd reactions, Eqs. 318a and b in equal amounts. Estimate how much natural water, for fuel, would be needed per hour to run a 1150-MW reactor, assuming 33% efficiency

(III) Show that the energies carried off by the \(^4 _2 He\) nucleus and neutron for the reaction of Eq. 31-8c are about 3.5 MeV and 14 MeV, respectively. Are these fixed values, independent of the plasma temperature?

How much energy (J) is contained in 1.00 kg of water if its natural deuterium is used in the fusion reaction of Eq. 318a? Compare to the energy obtained from the burning of 1.0 kg of gasoline, about 5 * 107 J.

(a) Give the ratio of the energy needed for the first reaction of the carbon cycle to the energy needed for a deuteriumtritium reaction (Example 319). (b) If a deuteriumtritium reaction actually requires a temperature estimate the temperature needed for the first carbon-cycle reaction.

350 rads of -particle radiation is equivalent to how many rads of X-rays in terms of biological damage?

(I) A dose of 4.0 Sv of \(\gamma\) rays in a short period would be lethal to about half the people subjected to it. How many grays is this?

How many rads of slow neutrons will do as much biological damage as 72 rads of fast neutrons?

How much energy is deposited in the body of a 65-kg adult exposed to a 2.5-Gy dose?

A cancer patient is undergoing radiation therapy in which protons with an energy of 1.2 MeV are incident on a 0.20-kg tumor. (a) If the patient receives an effective dose of 1.0 rem, what is the absorbed dose? (b) How many protons are absorbed by the tumor? Assume

A 0.035- sample of is injected into an animal for tracer studies. If a Geiger counter intercepts 35% of the emitted particles, what will be the counting rate, assumed 85% efficient?

About 35 eV is required to produce one ion pair in air. Show that this is consistent with the two definitions of the roentgen given in the text

A 1.6-mCi source of (in ), a emitter, is implanted in a tumor where it is to administer 32 Gy. The half-life of is 14.3 days, and 1.0 mCi delivers about Approximately how long should the source remain implanted?

What is the mass of a 2.50- source?

(II) \(^{57} _{27} Co\) emits 122-keV \(\gamma\) rays. If a 65-kg person swallowed \(1.55\ \mu Ci\) of \(^{57} _{27} Co\), what would be the dose rate (Gy/day) averaged over the whole body? Assume that 50% of the \(\gamma\)-ray energy is deposited in the body. [Hint: Determine the rate of energy deposited in the body and use the definition of the gray.]

Ionizing radiation can be used on meat products to reduce the levels of microbial pathogens. Refrigerated meat is limited to 4.5 kGy. If 1.6-MeV electrons irradiate 5 kg of beef, how many electrons would it take to reach the allowable limit?

Huge amounts of radioactive were released in the accident at Chernobyl in 1986. Chemically, iodine goes to the human thyroid. (It can be used for diagnosis and treatment of thyroid problems.) In a normal thyroid, absorption can cause damage to the thyroid. (a) Write down the reaction for the decay of (b) Its half-life is 8.0 d; how long would it take for ingested to become 5.0% of the initial value? (c) Absorbing 1 mCi of can be harmful; what mass of iodine is this?

Assume a liter of milk typically has an activity of 2000 pCi due to If a person drinks two glasses (0.5 L) per day, estimate the total effective dose (in Sv and in rem) received in a year. As a crude model, assume the milk stays in the stomach 12 hr and is then released. Assume also that roughly 10% of the 1.5 MeV released per decay is absorbed by the body. Compare your result to the normal allowed dose of 100 mrem per year. Make your estimate for (a) a 60-kg adult, and (b) a 6-kg baby

Radon gas, is considered a serious health hazard (see discussion in text). It decays by -emission. (a) What is the daughter nucleus? (b) Is the daughter nucleus stable or radioactive? If the latter, how does it decay, and what is its half-life? (See Fig. 3011.) (c) Is the daughter nucleus also a noble gas, or is it chemically reactive? (d) Suppose 1.4 ng of seeps into a basement. What will be its activity? If the basement is then sealed, what will be the activity 1 month later?

Calculate the wavelength of photons needed to produce NMR transitions in free protons in a 1.000-T field. In what region of the spectrum is this wavelength?

Consider a system of nuclear power plants that produce 2100 MW. (a) What total mass of fuel would be required to operate these plants for 1 yr, assuming that 200 MeV is released per fission? (b) Typically 6% of the nuclei that fission produce strontium90, a emitter with a half-life of 29 yr. What is the total radioactivity of the in curies, produced in 1 yr? (Neglect the fact that some of it decays during the 1-yr period.)

J. Chadwick discovered the neutron by bombarding with the popular projectile of the day, alpha particles. (a) If one of the reaction products was the then unknown neutron, what was the other product? (b) What is the Q-value of this reaction?

Fusion temperatures are often given in keV. Determine the conversion factor from kelvins to keV using, as is common in this field, without the factor

One means of enriching uranium is by diffusion of the gas Calculate the ratio of the speeds of molecules of this gas containing and on which this process depends

. (a) What mass of was actually fissioned in the first atomic bomb, whose energy was the equivalent of about 20 kilotons of TNT (1 kiloton of TNT releases )? (b) What was the actual mass transformed to energy?

The average yearly background radiation in a certain town consists of 32 mrad of X-rays and rays plus 3.4 mrad of particles having a RBE of 10. How many rem will a person receive per year on average?

A shielded -ray source yields a dose rate of at a distance of 1.0 m for an average-sized person. If workers are allowed a maximum dose of 5.0 rem in 1 year, how close to the source may they operate, assuming a 35-h work week? Assume that the intensity of radiation falls off as the square of the distance. (It actually falls off more rapidly than because of absorption in the air, so your answer will give a better-than-permissible value.)

Radon gas, is formed by decay. (a) Write the decay equation. (b) Ignoring the kinetic energy of the daughter nucleus (its so massive), estimate the kinetic energy of the particle produced. (c) Estimate the momentum of the alpha and of the daughter nucleus. (d) Estimate the kinetic energy of the daughter, and show that your approximation in (b) was valid

In the net reaction, Eq. 317, for the protonproton chain in the Sun, the neutrinos escape from the Sun with energy of about 0.5 MeV. The remaining energy, 26.2 MeV, is available to heat the Sun. Use this value to calculate the heat of combustion per kilogram of hydrogen fuel and compare it to the heat of combustion of coal, about

Energy reaches Earth from the Sun at a rate of about Calculate (a) the total power output of the Sun, and (b) the number of protons consumed per second in the reaction of Eq. 317, assuming that this is the source of all the Suns energy. (c) Assuming that the Suns mass of was originally all protons and that all could be involved in nuclear reactions in the Suns core, how long would you expect the Sun to glow at its present rate? See Problem 62. [Hint: Use law.]

Estimate how many solar neutrinos pass through a ceiling of a room, at latitude , for an hour around midnight on midsummer night. [Hint: See Problems 62 and 63.]

Estimate how much total energy would be released via fission if 2.0 kg of uranium were enriched to 5% of the isotope

Some stars, in a later stage of evolution, may begin to fuse two nuclei into one nucleus. (a) How much energy would be released in such a reaction? (b) What kinetic energy must two carbon nuclei each have when far apart, if they can then approach each other to within 6.0 fm, center-to-center? (c) Approximately what temperature would this require?

An average adult body contains about of which comes from food. (a) How many decays occur per second? (b) The potassium decay produces beta particles with energies of around 1.4 MeV. Estimate the dose per year in sieverts for a 65-kg adult. Is this a significant fraction of the background rate?

When the nuclear reactor accident occurred at Chernobyl in 1986, were released into the atmosphere. Assuming that this radiation was distributed uniformly over the surface of the Earth, what was the activity per square meter? (The actual activity was not uniform; even within Europe wet areas received more radioactivity from rainfall.)

A star with a large helium abundance can burn helium in the reaction What is the Q-value for this reaction?

A source is used for 1.4 hours by a 62-kg worker. Radioactive decays by decay with a halflife of 30 yr. The average energy of the emitted betas is about 190 keV per decay. The decay is quickly followed by a with an energy of 660 keV. Assuming the person absorbs all emitted energy, what effective dose (in rem) is received?

Suppose a future fusion reactor would be able to put out 1000 MW of electrical power continuously. Assume the reactor will produce energy solely through the reaction given in Eq. 31–8a and will convert this energy to electrical energy with an efficiency of 33%. Estimate the minimum amount of deuterium needed to run this facility per year.

If a 65-kg power plant worker has been exposed to the maximum slow-neutron radiation for a given year, how much total energy (in J) has that worker absorbed? What if he were exposed to fast protons?

Consider the fission reaction (a) What is X? (b) If this were part of a chain reaction in a fission power reactor running at barely critical, what would happen on average to the three produced neutrons? (c) (optional) What is the Q-value of this reaction? [Hint: Mass values can be found at www.nist.gov/pml/data/comp.cfm.]

A large amount of was released during the Chernobyl nuclear reactor accident in 1986. The enters the body through the food chain. How long will it take for 85% of the released during the accident to decay? See Appendix B.

Three radioactive sources have the same activity, 35 mCi. Source A emits 1.0-MeV rays, source B emits 2.0-MeV rays, and source C emits 2.0-MeV alphas. What is the relative danger of these sources?

A 55-kg patient is to be given a medical test involving the ingestion of (Section 317) which decays by emitting a 140-keV gamma. The half-life for this decay is 6 hours. Assuming that about half the gamma photons exit the body without interacting with anything, what must be the initial activity of the Tc sample if the whole-body dose cannot exceed 50 mrem? Make the rough approximation that biological elimination of Tc can be ignored.