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Silberberg Chemistry Molecular Nature Of Matter And Change 4e Copy2

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  • 1. Fusing nuclei The Z machine of Sandia National Laboratory, the most powerful x-ray generator on Earth, helps scientists understand phe- nomena from the origin of the universe to nuclear fusion. It is rou- tinely used to fuse hydrogen nuclei at temperatures exceeding those within the Sun. In this chapter, we explore both the fundamental nature of atomic nuclei and their remark- able practical applications. Nuclear Reactions and Their Applications 24.1 Radioactive Decay and Nuclear Stability 24.3 Nuclear Transmutation: Induced 24.5 Applications of Radioisotopes Components of the Nucleus Changes in Nuclei Radioactive Tracers Types of Radioactive Emissions Early Transmutation Experiments Applications of Ionizing Radiation Types of Radioactive Decay; Particle Accelerators 24.6 The Interconversion of Mass and Energy Nuclear Equations 24.4 The Effects of Nuclear Radiation The MassDefect The Mode of Decay on Matter Nuclear Binding Energy 24.2 The Kinetics of Radioactive Decay Excitation and Ionization 24.7 Applications of Fission and Fusion Rateof Radioactive Decay Ionizing Radiation and Living Matter Nuclear Fission Radioisotopic Dating Nuclear Fusion
  • 2. ar below the outer fringes of the cloud of electrons l~€s the atom's F tiny, dense core, held together by the strongest force/in the universe. For nearly the entire text so far, we have focused on an atom's elec- trons, treating the nucleus as little more than their electrostatic anchor, examining the effect of its positive charge on atomic properties and, ulti- mately, chemical behavior. But, for the scientists probing the structure and behavior of the nucleus itself, there is the scene of real action, one that holds enormous potential benefit and great mystery and wonder. Society is ambivalent about the applications of nuclear research, however. The • discoveryof the atomic nucleus(Section promise of abundant energy and treatments for disease comes hand-in-hand with 2.4) the threat of nuclear waste contamination, reactor accidents, and unimaginable • protons, neutrons,massnumber,and the destruction from nuclear war or terrorism. Can the power of the nucleus be har- ~X notation (Section2.S) nessed for our benefit, or are the risks too great? In this chapter, we discuss the • half-life and first-order reaction rate principles that can help you answer this vital question. (Section16.4) The changes that occur in atomic nuclei are strikingly different from chemi- cal changes. In the reactions you've studied so far, electrons are shared or trans- ferred to form compounds, while nuclei sit by passively, never changing their identities. In nuclear reactions, the roles are reversed: electrons in their orbitals are usually bystanders as the nuclei undergo changes that, in nearly every case, form different elements. Nuclear reactions are often accompanied by energy changes a million times greater than those in chemical reactions, energy changes so great that changes in mass are detectable. Moreover, nuclear reaction yields and rates are typically not subject to the effects of pressure, temperature, and catalysis that so clearly influence chemical reactions. Table 24.1 summarizes the general differences between chemical and nuclear reactions. I1mIID Comparison of Chemical and Nuclear Reactions Chemical Reactions Nuclear Reactions 1. One substance is converted into another, but atoms never 1. Atoms of one element typically are converted into atoms of change identity. another element. 2. Orbital electrons are involved as bonds break and form; 2. Protons, neutrons, and other particles are involved; orbital nuclear particles do not take part. electrons rarely take part. 3. Reactions are accompanied by relatively small changes in 3. Reactions are accompanied by relatively large changes in energy and no measurable changes in mass. energy and measurable changes in mass. 4. Reaction rates are influenced by temperature, 4. Reaction rates are affected by number of nuclei, but not by concentration, catalysts, and the compound in which an temperature, catalysts, or, normally, the compound in element occurs. which an element occurs. IN THIS CHAPTER ... We survey the field of nuclear chemistry, beginning with an investigation of nuclear stability-why some nuclei are stable, whereas oth- ers are unstable and undergo radioactive decay. You'll see how radioactivity is detected and how the kinetics of decay is applied. We explore how nuclei syn- thesized in particle accelerators have extended the periodic table beyond ura- nium, the last naturally occurring element. Then, we consider the effects of radioactive emissions on matter, especially living matter, focusing on some major applications in science, technology, and medicine. A major focus is to calculate the energy released in nuclear fission and fusion and discuss current and future attempts to harness this energy. Finally, we end with a look at the nuclear processes that create the chemical elements in the stars. 1045
  • 3. 1046 Chapter 24 Nuclear Reactions and Their Applications 24.1 RADIOACTIVE DECAY AND NUCLEAR STABILITY A stable nucleus remains intact indefinitely, but the great majority of nuclei are unstable. An unstable nucleus exhibits radioactivity: it spontaneously disinte- grates, or decays, by emitting radiation. In the next section, you'll see that each type of unstable nucleus has its own characteristic rate of radioactive decay, which can range from a fraction of a second to billions of years. In this section, we con- sider important terms and notation for nuclei, discuss some of the key events in the discovery of radioactivity, and describe the various types of radioactive decay and how to predict which type occurs for a given nucleus. The Components of the Nucleus: Terms and Notation Recall from Chapter 2 that the nucleus contains essentially all the atom's mass but is only about 10-4 times its diameter (or 10-12 times its volume). Obviously, The Tiny, Massive Nucleus If you the nucleus is incredibly dense: about 1014 g/ml., Protons and neutrons, the could strip the electrons from the atoms elementary particles that make up the nucleus, are collectively called nucleons. in an object and compress the nuclei to- The term nuclide refers to a nucleus with a particular composition, that is, with gether, the object would lose only a frac- specific numbers of the two types of nucleons. Most elements occur in nature as tion of a percent of its mass, but it would a mixture of isotopes, atoms with the characteristic number of protons of the ele- shrink to 0.0000000001 % (10-1°%) of its ment but different numbers of neutrons. Therefore, each isotope of an element volume. An atom the size of the Houston has a particular nuclide that we identify by the numbers of protons and neutrons Astrodome would have a nucleus the size of a grapefruit, which would contain vir- it contains. The nuclide of the most abundant isotope of oxygen, for example, tually all the atom's mass. contains eight protons and eight neutrons, whereas the nuclide of the least abun- dant isotope contains eight protons and ten neutrons. The relative mass and charge of a particle-a nucleon, another elementary particle, or a nuclide-is described by the notation ~X, where X is the symbol for the particle, A is the mass number, or the total number of nucleons, and Z is the charge of the particle; for nuclides, A is the sum of protons and neutrons and Z is the number of protons (atomic number). Using this notation, we write the three subatomic elementary particles as follows: _?e (electron), jp (proton), and bn (neutron) (In nuclear notation, the element symbol refers to the nucleus only, so a proton is also sometimes represented as lH.) The number of neutrons (N) in a nucleus is the mass number (A) minus the atomic number (Z): N = A - Z. The two nat- urally occurring isotopes of chlorine, for example, have 17 protons (Z = 17), but one has 18 neutrons mCl, also written 35Cl) and the other has 20 mCl, or 37Cl). Nuclides can also be designated with the element name followed by the mass number, for example, chlorine-35 and chlorine-37. Despite some small variations, in naturally occurring samples of an element or its compounds, the isotopes of the element are present in particular, fixed proportions. Thus, in a sample of sodium chloride (or any Cl-containing substance), 75.77% of the Cl atoms are chlorine-35 and the remaining 24.23% are chlorine-37. To understand this chapter, it's very important for you to be comfortable with nuclear notations, so please take a moment to review Sample Problem 2.2 on p. 51 and Problems 2.37 to 2.44 at the end of Chapter 2. The Discovery of Radioactivity and the Types of Emissions In 1896, the French physicist Antoine-Henri Becquerel discovered, quite by acci- dent, that uranium minerals, even when wrapped in paper and stored in the dark, emit a penetrating radiation that can produce bright images on a photographic plate. Becquerel also found that the radiation creates an electric discharge in air,
  • 4. 24.1 Radioactive Decay and Nuclear Stability 1047 thus providing a means for measuring its intensity. Two years later, a young doctoral student named Marie Sklodowska Curie began a search for other miner- als that behaved like uranium in this way. She found that thorium minerals also emit radiation and discovered that the intensity of the radiation is directly pro- portional to the concentration of the element in the mineral, not to the nature of the mineral or compound in which the element occurs. Curie named the emis- sions radioactivity and showed that they are unaffected by temperature, pressure, or other physical and chemical conditions. To her surprise, Curie found that certain uranium minerals were even more radioactive than pure uranium, which implied that they contained traces of one or more as yet unknown, highly radioactive elements. She and her husband, the physicist Pierre Curie, set out to isolate all the radioactive components in pitch- blende, the principal ore of uranium. After months of painstaking chemical work, they isolated two extremely small, highly radioactive fractions, one that precipi- Her Brilliant Career Marie Curie tated with bismuth compounds and another that precipitated with alkaline earth (1867-1934) is the only person to be compounds. Through chemical and spectroscopic analysis, Marie Curie was able awarded Nobel Prizes in two different sci- to show that these fractions contained two new elements, which she named polo- ences, one in physics in 1903 for her re- nium (after her native Poland) and radium. Polonium (Po; Z = 84), the most search into radioactivity and the other in metallic member of Group 6A(l6), lies to the right of bismuth in Period 6. chemistry in 1911 for the discovery of Radium (Ra; Z = 88), which is the heaviest alkaline earth metal, lies under bar- polonium and the discovery, isolation, and study of radium and its compounds. ium in Group 2A(2). Purifying radium proved to be another arduous task. Starting with several tons of pitchblende residues from which the uranium had been extracted, Curie pre- pared compounds of the larger Group 2A(2) elements, continually separating minuscule amounts of radium compounds from enormously larger amounts of chemically similar barium compounds. It took her four years to isolate 0.1 g of radium chloride, which she melted and electrolyzed to obtain pure metallic ZnS-coated screen (or photographic plate) radium. During the next few years, Henri Becquerel, the Curies, and P. Villard in France and Emest Rutherford and his coworkers in England studied the nature of radioactive emissions. Rutherford and his colleague Frederick Soddy observed that elements other than radium were formed when radium decayed. In 1902, they proposed that radioactive emission results in the change of one element into another. To their contemporaries, this idea sounded like a resurrection of alchemy and was met with disbelief and ridicule. We now know it to be true: under most circumstances, when a nuclide of one element decays, it changes into a nuclide of a different element. These studies led to an understanding of the three most common types of radioactive emission: Lead Radioactive block material • Alpha particles (symbolized a or iHe) are dense, positively charged particles identical to helium nuclei. • Beta particles (symbolized r3, r3-, or more usually - ?r3) are negatively charged Voltage particles identified as high-speed electrons. (The emission of electrons from the source nucleus may seem strange, but as you'll see shortly, r3 particles arise as a result of a nuclear reaction.) mmDI Three types of radioactive • Gamma rays (symbolized as 'Y, or sometimes 8'Y) are very high-energy pho- emissions in an electric field. Positively charged ex particles bend toward the neg- tons, about 105 times as energetic as visible light. ative plate; negatively charged 13 particles bend toward the positive plate. The cur- The behavior of these three emissions in an electric field is shown in Figure 24.1. vature is greater for 13 particles because Note that a particles bend to a small extent toward the negative plate, r3 particles they have much lower mass. The 'I rays, bend to a great extent toward the positive plate, and 'Y rays are not affected by uncharged high-energy photons, are un- the electric field. We'll discuss the effects of these emissions on matter later. affected by the field.
  • 5. 1048 Chapter 24 Nuclear Reactions and Their Applications Types of Radioactive Decay; Balancing Nuclear Equations When a nuclide decays, it forms a nuclide of lower energy, and the excess energy is carried off by the emitted radiation. The decaying, or reactant, nuclide is called the parent; the product nuclide is called the daughter. Nuclides can decay in several ways. As we discuss the major types of decay, which are summarized in Table 24.2, note the principle used to balance nuclear reactions: the total Z (charge, number of protons) and the total A (sum of protons and neutrons) of the reactants equal those of the products: ~~~~: Reactants ~ = ~~:~l ~Products (24.1) 1. Alpha decay involves the loss of an et particle (iHe) from a nucleus. For each et particle emitted by the parent nucleus, A decreases by 4 and Z decreases by 2. Every element that is heavier than lead (Pb; Z = 82), as well as a few lighter ones, exhibits et decay. In Rutherford's classic experiment that established the existence of the atomic nucleus (Section 2.4, pp. 47-48), radium was the source of the et particles that were used as projectiles. Radium undergoes ex decay to yield radon (Rn; Z = 86): emED Modes of Radioactive Decay* Change in Mode Emission Decay Process A Z N et Decay et CiHe) + -4 -2 -2 Reactant (parent) Product (daughter) a expelled f3 Decay" o 1n 1p• 1 + O~ () -1 o +1 -1 .. in nucleus in nucleus ~ expelled Positron emission t hv high-energy photon + " %'~,p' nucleus with xp+ and ynO nucleus with (x- 1)p+ and (y+ 1)nO + O~O 1 positron expelled o -1 +1 Electron capture t x-ray photon -1 °e + 1p 1 1n o o -1 +1 absorbed from in nucleus in nucleus low-energy orbital 'Y Emission + o o o excited stable y photon nucleus nucleus radiated "Neutrinos (v) are involved in several of these processes but are not shown. "Nuclear chemists consider [3 decay to be a more general process that includes three decay modes: negatron emission (which the text calls "[3 decay"), positron emission, and electron capture.
  • 6. 24.1 Radioactive Decay and Nuclear Stability 1049 Note that the A value for Ra equals the sum of the A values for Rn and He (226 = 222 + 4), and that the Z value for Ra equals the sum of the Z values for Rn and He (88 = 86 + 2). 2. Beta decay involves the ejection of a 13particle (-?13) from the nucleus. * This change does not involve the expulsion of a 13particle that was actually in the nucleus, but rather the conversion of a neutron into a proton, which remains in the nucleus, and a f3 particle, which is expelled immediately: The Little Neutral One A neutral par- ticle called a neutrino (v) is also emitted bn -+ ip + -?f3 in many nuclear reactions, including the As always, the totals of the A and the Z values for reactant and products are equal. change of a neutron to a proton: Radioactive nickel-63 becomes stable copper-63 through 13decay: 6n -+ ip + -?f3 + v ~~Ni -+ ~§Cu + -?f3 Theory suggests that neutrinos have a Another example is the 13decay of carbon-14, applied in radiocarbon dating: mass much less than 10-4 times that of an I~C -+ IjN + -?f3 electron, and that at least 109 neutrinos Note that f3 decay results in a product nuclide with the same A but with Zone exist in the universe for every proton. Neutrinos interact with matter so slightly higher (one more proton) than in the reactant nuclide. In other words, an atom that it would take a piece of lead 1 light- of the element with the next higher atomic number is formed. year thick to absorb them. We will not dis- 3. Positron decay involves the emission of a positron from the nucleus. A cuss them further, except to mention that key idea of modem physics is that every fundamental particle has a correspond- experiments in Japan in the 1990s de- ing antiparticle, another particle with the same mass but opposite charge. The tected neutrinos and obtained evidence positron (symbolized ?13;note the positive Z) is the antiparticle of the electron. that they have mass. Using a cathedral- Positron decay occurs through a process in which a proton in the nucleus is con- sized pool containing 50,000 tons of ultra- verted into a neutron, and a positron is expelled.' Positron decay has the oppo- pure water buried 1 mile underground site effect of f3 decay, resulting in a daughter nuclide with the same A but with Z in a zinc mine, an international team of one lower (one fewer proton) than the parent; thus, an atom of the element with scientists obtained results that suggest the next lower atomic number forms. Carbon-l I , a synthetic radioisotope, decays that neutrinos may account for a signifi- cant portion of the "missing" matter in the to a stable boron isotope through emission of a positron: universe and may provide enough mass l~C -+ l~B + ?f3 (and, thus, gravitational attraction) to pre- 4. Electron capture occurs when the nucleus of an atom draws in an elec- vent the universe from expanding forever. tron from an orbital of the lowest energy level. The net effect is that a nuclear proton is transformed into a neutron: ip + _?e -+ 6n (We use the symbol _?e to distinguish an orbital electron from a beta particle, symbol _?13.)The orbital vacancy is quickly filled by an electron that moves down from a higher energy level, and that energy difference appears as an x-ray photon. Radioactive iron forms stable manganese through electron capture: ~~Fe + _?e -+ ~~Mn + hv (x-ray) Electron capture has the same net effect as positron decay (Z lower by 1, A unchanged), even though the processes are entirely different. 5. Gamma emission involves the radiation of high-energy photons from "I an excited nucleus. Recall that an atom in an excited electronic state reduces its energy by emitting photons, usually in the DV and visible ranges. Similarly, a nucleus in an excited state lowers its energy by emitting photons, which are of "I much higher energy (much shorter wavelength) than DV photons. Many nuclear processes leave the nucleus in an excited state, so 'Yemission accompanies most other types of decay. Several "I photons ("I rays) of different frequencies can be *In formal nuclear chemistry terminology, {3 decay indicates a more general phenomenon that also includes positron emission and electron capture (see footnote to Table 24.2). tThe process, called pair production, involves a transformation of energy into matter. A high- energy (>1.63x10-13 J) photon becomes an electron and a positron simultaneously. The elec- tron and a proton in the nucleus form a neutron, while the positron is expelled.
  • 7. 1050 Chapter 24 Nuclear Reactions and Their Applications emitted from an excited nucleus as it returns to the ground state. Many of Marie Curie's experiments involved the release of v rays, such as 2~~U ---->- 2~riTh + ~He + 28-y Because 'Y rays have no mass or charge, 'Y emission does not change A or Z. Gamma rays also result when a particle and an antiparticle annihilate each other, as when an emitted positron meets an orbital electron: ?[3 (from nucleus) + _?e (outside nucleus) ---->- 28-y SAMPLE PROBLEM 24.1 Writing Equations for Nuclear Reactions Problem Write balanced equations for the following nuclear reactions: (a) Naturally occurring thorium-232 undergoes ex decay. (b) Chlorine-36 undergoes electron capture. Plan We first write a skeleton equation that includes the mass numbers, atomic numbers, and symbols of all the particles, showing the unknown particles as 1x. Then, because the total of mass numbers and the total of charges on the left side and the right side must be equal, we solve for A and Z, and use Z to determine X from the periodic table. Solution (a) Writing the skeleton equation: 2~6Th ---->- 1x + ~He Solving for A and Z and balancing the equation: For A, 232 = A + 4, so A = 228. For Z, 90 = Z + 2, so Z = 88. From the periodic table, we see that the element with Z = 88 is radium (Ra). Thus, the balanced equation is 2§6Th - 2~~Ra + ~He (b) Writing the skeleton equation: f~Cl + _?e ---->- ~X Solving for A and Z and balancing the equation: For A, 36 + 0 = A, so A = 36. For Z, 17 + (-1) = Z, so Z = 16. The element with Z = 16 is sulfur (S), so we have 1~Cl_?e -1~S + Check Always read across superscripts and then across subscripts, with the yield arrow as an equal sign, to check your arithmetic. In part (a), for example, 232 = 228 + 4, and 90 = 88 + 2. FOLLOW-UP PROBLEM 24.1 Write a balanced equation for the reaction in which a nuclide undergoes [3 decay and produces cesium-133. Nuclear Stability and the Mode of Decay There are several ways that an unstable nuclide might decay, but can we predict how it will decay? Indeed, can we predict if a given nuclide will decay at all? Our knowledge of the nucleus is much less than that of the atom as a whole, but some patterns emerge from observation of the naturally occurring nuclides. The Band of Stability and the Neutron-to-Proton (N/Z) Ratio A key factor that determines the stability of a nuclide is the ratio of the number of neutrons to the number of protons, the N/Z ratio, which we calculate from (A - Z}/Z. For lighter nuclides, one neutron for each proton (N/Z = 1) is enough to provide stability. However, for heavier nuclides to be stable, the number of neutrons must exceed the number of protons, and often by quite a lot. But, if the N/Z ratio is either too high or not high enough, the nuclide is unstable and decays. Figure 24.2A is a plot of number of neutrons vs. number of protons for the stable nuclides. The nuclides form a narrow band of stability that gradually increases from an N/Z ratio of 1, near Z = 10, to an N/Z ratio slightly greater than 1.5, near Z = 83 for 209Bi. Several key points are as follows:
  • 8. 24.1 Radioactive Decay and Nuclear Stability 1051 140 Cl. decay 209 130 Bi 83 • stable • a emitter N ~ ('Z = 1.52) .. :: • ~ emitter o e- capture and/or positron emitter 120 . ... ... . WJ 110 ••••000 100 •••••00 •••••000 90 80 Region shown in 8 Cl) c 2 -S Q) 85 :H~:8~0 ••••~Q!00 <: ..., z Cl) 107A 47 g~ ••• ••!. r •••• ~~O c 2 -S 70 ( t::' = 1 .28 ) :.r: . "<. _ •••••• O~ Q) z 60 z • :.: ..: . ~ ••• OOOOU .:.: . 80 I I I I I I ::i. 55 60 Protons (Z) 65 70 50 ....I·: . 8 :.:-: 40 ~~Fe~ ;.!': ~ A plot of number of neutrons vs. number of protons (t::'=1.15) ;:. for the stable nuclides. A, A plot of N vs. Z for all stable nuclides Z .i:: gives rise to a narrow band that veers above N/Z = 1 shortly beyond 30 :-: .. Positron emission and/or Z = 10. The N/Z values for several stable nuclides are given. The .... ..J• i electron capture most common modes of decay for unstable nuclides in a particular region are shown: nuclides with a high N/Z ratio often undergo 20 13 decay; those with a low ratio undergo e- capture or positron emis- sion; heavy nuclei beyond the stable band (and a few lighter ones) 10 undergo Cl. decay. B, The blue box in part A is expanded to show the stable and many of the unstable nuclides in that area. Note the modes of decay: Cl. decay decreases both Nand Z by 2; 13 decay de- o 10 20 30 40 50 60 70 80 90 creases N and increases Z by 1; positron emission and e - capture Protons (Z) increase N and decrease Z by 1. A • Very few stable nuclides exist with N/Z < 1; the only two are ~H and ~He. For lighter nuclides, N/Z = 1: for example, 'iHe, l~C, l~O, and are partic- T8Ne ularly stable. • The N/Z ratio of stable nuclides gradually increases as Z increases. No stable nuclide exists with N/Z = 1 for Z > 20. Thus, for ~~Fe, N/Z = 1.15; for l~;Ag, N/Z = 1.28; and for l~~W, N/Z = 1.49. • All nuclides with Z > 83 are unstable. Bismuth-209 is the heaviest stable nuclide. Therefore, the largest members of Groups lA(l), 2A(2), 4A(l4), 6A(l6), 7A(l7), and 8A(l8) are radioactive, as are all the actinides and the elements of the fourth transition series (Period 7). Stability and Nuclear Structure Given that protons are positively charged and neutrons uncharged, what holds the nucleus together? Nuclear scientists answer this question and explain the importance of the N/Z ratio in terms of two oppos- ing forces. Electrostatic repulsive forces between protons would break the nucleus apart if not for the presence of an attractive force that exists between all nucle- ons (protons and neutrons) called the strong force. This force is about 1000 times stronger than the repulsive force but operates only over the short distances within the nucleus. Competition between the attractive strong force and the repulsive electrostatic force determines nuclear stability.
  • 9. 1052 Chapter 24 Nuclear Reactions and Their Applications I11mIm Number of Stable Curiously, the oddness or evenness of Nand Z values is related to some important patterns of nuclear stability. Two interesting points become apparent Nuclides for Elements 48 to 54* when we classify the known stable nuclides: Atomic No. of Element No. Nudides • Elements with an even Z (number of protons) usually have a larger number of Cd 48 8 stable nuclides than elements with an odd Z. Table 24.3 demonstrates this point In 49 2 for cadmium (Z = 48) through xenon (Z = 54). So 50 10 • Well over half the stable nuclides have both even N and even Z (Table 24.4). Sb 51 2 (Only seven nuclides with odd N and odd Z are either stable-s-jl-l, ~Li, l~B, Te 52 8 I:jN-or decay so slowly that their amounts have changed little since Earth I 53 1 formed-~~V, 1~~La, and 1~7Lu.) Xe 54 9 One model of nuclear structure that attempts to explain these findings postu- *EvenZ shown in boldface. lates that protons and neutrons lie in nucleon shells, or energy levels, and that stability results from the pairing of like nucleons. This arrangement leads to the stability of even values of Nand Z. (The analogy to electron energy levels and I.mlIm An Even-Odd the stability that arises from electron pairing is striking.) Just as noble gases-the elements with 2, 10, 18, 36, 54, and 86 electrons- Breakdown of the Stable Nuclides are exceptionally stable because of their filled electron shells, nuclides with N No. of or Z values of 2, 8, 20, 28, 50, 82 (and N = 126) are exceptionally stable. Z N Nuclides These so-called magic numbers are thought to correspond to the numbers of protons Even Even 157 or neutrons in filled nucleon shells. A few examples are ~gTi (N = 28), Even Odd 53 ~~Sr (N = 50), and the ten stable nuclides of tin (Z = 50). Some extremely sta- Odd Even 50 ble nuclides have double magic numbers: iHe, l~O, i8Ca, and 2~~Pb (N = 126). Odd Odd 7 TOTAL 267 SAMPJE PROBLEM 24.2 Predicting Nuclear Stability Problem Which of the following nuclides would you predict to be stable and which radioactive: (a) i~Ne; (b) i~s;(c) 2§8Th; (d) l~~Ba? Explain. Plan In order to evaluate the stability of each nuclide, we determine the N/2 ratio from (A - 2)/2, the value of 2, stable N/2 ratios (from Figure 24.2), and whether 2 and N are even or odd. 18 - 10 Solution (a) Radioactive. The ratio N/2 ;= 10 ;= 0.8. The minimum ratio for sta- bility is 1.0; so, despite even Nand Z, this nuclide has too few neutrons to be stable. (b) Stable. This nuclide has N/Z ;= 1.0 and Z < 20, with even Nand Z. Thus, it is most likely stable. (c) Radioactive. Every nuclide with Z > 83 is radioactive. (d) Radioactive. The ratio N/Z ;=1.20. For Z from 55 to 60, Figure 24.2A shows N/Z 2: 1.3, so this nuclide probably has too few neutrons to be stable. Check By consulting a table of isotopes, such as the one in the CRC Handbook of Chem- istry and Physics, we find that our predictions are correct. FOLLOW-UP PROBLEM 24.2 Why is i1p stable but igp unstable? Predicting the Mode of Decay An unstable nuclide generally decays in a mode that shifts its N/Z ratio toward the band of stability. This fact is illustrated in Fig- ure 24.2B on the preceding page, which expands a small region of Figure 24.2A to show all of the stable and many of the radioactive nuclides in that region, as well as their modes of decay. Note the following points, and then we'll apply them in a sample problem: 1. Neutron-rich nuclides. Nuclides with too many neutrons for stability (a high NIZ) lie above the band of stability. They undergo f3 decay, which converts a neutron into a proton, thus reducing the value of NIZ.
  • 10. 24.1 Radioactive Decay and Nuclear Stability 1053 2. Neutron-poor nuclides. Nuclides with too few neutrons for stability (a low N/Z) lie below the band. They undergo positron decay or electron capture, both of which convert a proton into a neutron, thus increasing the value of N/Z. 3. Heavy nuclides. Nuclides with Z > 83 are too heavy to lie within the band and undergo Cl' decay, which reduces their Z and N values by two units per emission. (Several lighter nuclides also exhibit Cl' decay.) ~A"'~P~.EPROBLEM 24.3 Predicting the Mode of Nuclear Decay Problem Predict the nature of the nuclear change(s) each of the following radioactive nuclides is likely to undergo: (a) l~B; (b) 2§j:U; (c) ~~As;(d) l~~La. Plan We use the NjZ ratio to decide where the nuclide lies relative to the band of stabil- ity and how its ratio compares with others in the nearby region of the band. Then, we pre~ diet which of the decay modes just discussed will yield a product nuclide that is closer to the band. Solution (a) This nuclide has an NjZ ratio of 1.4, which is too high for this region of the band. It will probably undergo f?> decay, increasing Z to 6 and lowering the NjZ ratio to 1. (b) This nuclide is heavier than those close to it in the band of stability. It will probably undergo ex decay and decrease its total mass. (c) This nuclide, with an NjZ ratio of 1.24, lies in the band of stability, so it will proba- bly undergo either f?> decay or positron emission. (d) This nuclide has an NjZ ratio of 1.23, which is too low for this region of the band, so it will decrease Z by either positron emission or electron capture. Comment Both possible modes of decay are observed for the nuclides in parts (c) and (d). FOLLOW·UP PROBLEM 24.3 What mode of decay would you expect for (a) ~~Fe; (b) 2~~Am? Decay Series A parent nuclide may undergo a series of decay steps before a sta- 148 ble daughter nuclide forms. The succession of steps is called a decay series, or 146 disintegration series, and is typically depicted on a gridlike display. Figure 24.3 /adeCay 144 shows the decay series from uranium-238 to lead-206. Numbers of neutrons (N) " ~ decay are plotted against numbers of protons (Z) to form the grid, which displays a series 142 of QC and f3 decays. The zigzag pattern is typical and occurs because QC decay 140 decreases both Nand Z, whereas f3 decay decreases N but increases Z. Note that 138 it is quite common for a given nuclide to undergo both types of decay. (Gamma decay accompanies many of these steps, but it does not affect the mass or type g 136 Cf! of the nuclide.) This decay series is one of three that occur in nature. All end with c 134 e isotopes of lead whose nuclides all have one (Z = 82) or two (N = 126, Z = 82) :J ill 132 magic numbers. A second series begins with uranium-235 and ends with lead-207, Z and a third begins with thorium-232 and ends with lead-208. (Neptunium-237 130 began a fourth series, but its half-life is so much less than the age of Earth that 128 - only traces of it remain today.) 126 124 Nuclear reactions are not affected by reaction conditions or chemical composition and 122 release much more energy than chemical reactions. A radioactive nuclide is unstable 78 80 82 84 86 88 90 92 and may emit ex particles (~He nuclei), f3 particles (-~f3; high-speed electrons), Protons (Z) positrons (~f3), or "/ rays (8,,/; high-energy photons) or may capture an orbital electron Figure 14.3 The 238 U decay series. (_~e). A narrow band of neutron-to-proton ratios (N/Z) includes those of all the sta- Uranium-238 (top right) decays through a ble nuclides. Radioactive decay allows an unstable nuclide to achieve a more stable series of emissions of ex or [3 particles to N/Z ratio. Certain "magic numbers" of neutrons and protons are associated with very lead-206 (bottom left) in 14 steps. stable nuclides. By comparing a nuclide's N/Z ratio with those in the band of stabil- ity, we can predict that, in general, heavy nuclides undergo ex decay, neutron-rich nuclides undergo f3 decay, and proton-rich nuclides undergo positron emission or electron capture. Three naturally occurring decay series all end in isotopes of lead.
  • 11. 1054 Chapter 24 Nuclear Reactions and Their Applications 24.2 THE KINETICS OF RADIOACTIVE DECAY Chemical and nuclear systems both tend toward maximum stability. Just as the concentrations in a chemical system change in a predictable direction to give a stable equilibrium ratio, the type and number of nucleons in an unstable nucleus change in a predictable direction to give a stable N/Z ratio. As you know, how- ever, the tendency of a chemical system to become more stable tells nothing about how long that process will take, and the same holds true for nuclear systems. In this section, we examine the kinetics of nuclear change; later, we'll examine the energetics of such change. To begin, a Tools of the Laboratory essay on the oppo- site page describes how radioactivity is detected and measured. The Rate of Radioactive Decay ~ Animation: Radioactive Decay Radioactive nuclei decay at a characteristic rate, regardless of the chemical sub- ~ Online Learning Center stance in which they occur. The decay rate, or activity (.stl), of a radioactive sam- ple is the change in number of nuclei (H) divided by the change in time (r). As we saw with chemical reaction rates, because the number of nuclei is decreasing, a minus sign precedes the expression for the decay rate: i1N Decay rate (.511) = -& The SI unit of radioactivity is the becquerel (Bq); it is defined as one disinte- gration per second (d/s): 1 Bq = 1 d/s. A much larger and more common unit of radioactivity is the curie (Ci): 1 curie equals the number of nuclei disintegrating each second in 1 g of radium-226: 1 Ci = 3.70X 1010 d/s (24.2) Because the curie is so large, the millicurie (mCi) and microcurie (/-LCi)are com- monly used. We often express the radioactivity of a sample in terms of specific activity, the decay rate per gram. An activity is meaningful only when we consider the large number of nuclei in a macroscopic sample. Suppose there are 1 X 1015 radioactive nuclei of a par- ticular type in a sample and they decay at a rate of 10% per hour. Although any particular nucleus in the sample might decay in a microsecond or in a million hours, the average of all decays results in 10% of the entire collection of nuclei disintegrating each hour. During the first hour, 10% of the original number, or 1X 1014 nuclei, will decay. During the next hour, 10% of the remaining 9X 1014 nuclei, or 9 X 1013 nuclei, will decay. During the next hour, 10% of those remain- ing will decay, and so forth. Thus, for a large collection of radioactive nuclei, the number decaying per unit time is proportional to the number present: Decay rate (.511) ex N or .511 = kN where k is called the decay constant and is characteristic of each type of nuclide. The larger the value of k, the higher is the decay rate. Combining the two rate expressions just given, we obtain i1N .511 = -- = kN (24.3) I1t Note that the activity depends only on H raised to the first power (and on the constant value of k). Therefore, radioactive decay is a first-order process (see Section 16.4). The only difference in the case of nuclear decay is that we con- sider the number of nuclei rather than their concentration. ~ Animation: Half-Life Half-Life of Radioactive Decay Decay rates are also commonly expressed in terms ~ Online Learning Center of the fraction of nuclei that decay over a given time interval. The half-life (t1/2) of a nuclide is the time it takes for half the nuclei present in a sample to decay. The number of nuclei remaining is halved after each half-life. Thus, half-life has the same meaning for a nuclear change as for a chemical change (Section 16.4).
  • 12. Counters for the Detection of Radioactive Emissions R adioactive emissions interact with atoms in surrounding ma- emits photons. Each photon, in turn, strikes a cathode, releasing terials. To determine the rate of nuclear decay, we measure an electron through the photoelectric effect (Section 7.1). This the radioactivity of a sample by observing the effects of these electron hits other portions of the tube that release increasing interactions over time. Because these effects can be electrically numbers of electrons, and the resulting current is recorded. Liquid amplified billions of times, it is even possible to detect the decay scintillation counters employ an organic mixture that contains a of a single nucleus. Ionization counters and scintillation counters phosphor and a solvent (Figure B24.2). This "cocktail" dissolves are two devices used to measure radioactive emissions. the sample and emits light when excited by the emission. These An ionization counter detects radioactive emissions as they counters are often used to measure emissions from dissolved ra- ionize a gas. Ionization produces free electrons and gaseous dioactive biological samples. cations, which are attracted to electrodes that conduct a current to a recording device. The most common type of ionization counter is a Geiger-Miiller counter (Figure B24.1). It consists of a tube filled with argon gas; the tube housing acts as the cathode, and a thin wire in the center of the tube acts as the anode. Emissions from the sample enter the tube through a thin window and strike argon atoms, producing free electrons that are accelerated toward the anode. These electrons collide with other argon atoms and free more electrons in an avalanche effect. The current created is am- plified and appears as a meter reading and/or an audible click. The initial release of 1 electron can release 1010 electrons in a micro- second, giving the Geiger-Muller counter great sensitivity. In a scintillation counter, radioactive emissions too weak to ionize surrounding atoms are detected by their ability to excite atoms and cause them to emit light. The light-emitting substance Figure 824.2 Vials of a scintillation "cocktail" emitting light. in the counter, called a phosphor, is coated onto part of a photo- A radioactive substance dissolved in an organic mixture (cocktail) multiplier tube, a device that increases the original electrical sig- emits particles that excite the phosphor component to emit light. Light nal. Incoming radioactive particles strike the phosphor, which intensity is proportional to the concentration of the substance. e /~ I Emitted particle Sample ~ // / . l /- / r~--- . Argon gas (+) e Toward cathode H Figure 824.1 Detection of radioactivity by an ionization counter.When an Ar atom absorbs the energy of a radioactive particle (red), it is ionized to an Ar+ ion (purple) and an electron (yellow). The free electron collides with and ionizes another Ar atom. As the process continues, the Ar+ ions migrate to the negative electrode, and the electrons migrate to the positive electrode, resulting in a current. 1055
  • 13. 1056 Chapter 24 Nuclear Reactions and Their Applications 'l{o ~ Decrease in number of 14C Number Initial Number of nuclei over time. A plot of number of 14C number half-lives of nuclei nuclei vs. time gives a decreasing curve. i at time t of nuclei / In each half-life (5730 years), half the i4C nuclei present undergo decay. A plot of U ID ::l N..t = N..o xn W C mass of i4C vs. time is identical. After 1st U 1 ;0 "2 'l{o half-life (5730 yr) '0 : After 2nd Q; I half-life (11,460 yr) -----i------ .0 1 E "4 'l{o After 3rd Z ::l 1 "8 'l{o _____ l ~ half-life (17,190 yr) t I Y 0 10,000 20,000 Time (yr) Figure 24.4 shows the decay of carbon-14, which has a half-life of 5730 years, in terms of number of 14C nuclei remaining: I~C - 'iN + -?f3 We can also consider the half-life in terms of mass of substance. As 14C decays to the product 14N, its mass decreases. If we start with 1.0 g of carbon-14, half that mass of 14C (0.50 g) will be left after 5730 years, half of that mass (0.25 g) after another 5730 years, and so on. The activity depends on the number of nuclei present, so the activity is halved after each succeeding half-life as well. We determine the half-life of a nuclear reaction from its rate constant. Re- arranging Equation 24.3 and integrating over time gives HI Ho In - -kt or In - = kt (24.4) Ho Ht where X 0 is the number of nuclei at t = 0, and Xt is the number of nuclei remain- Il.mrIm Decay Constants (k) ing at any time t. (Note the similarity to Equation 16.4, p. 686.) To calculate the and Half-Lives (t,/2) half-life (tI/2), we set Nt equal to 1N 0 and solve for t1/2: of Beryllium Isotopes Ho ~2 Nuclide k tV2 ln 1.'r = kt1/2 so t1/2 = -k (24.5) 2J' 0 ~Be l.30X 1O~2/day 53.3 days Exactly analogous to the half-life of a first-order chemical change, this half-life ~Be l.OX 1016/s 6.7X 1O~17 s is not dependent on the number of nuclei and is inversely related to the decay ~Be Stable constant: I~Be 4.3XlO-7/yr large k =? short tl/2 and small k =? long t1/2 IlBe 5.02X 1O~2/s The decay constants and half-lives of radioactive nuclides vary over a very wide range, even those for the nuclides of a given element (Table 24.5). SAMPLE PROBLEM 24.4Finding the Number of Radioactive Nuclei Problem Strontium-90 is a radioactive by-product of nuclear reactors that behaves bio- logically like calcium, the element above it in Group 2A(2). When 90Sr is ingested by mammals, it is found in their milk and eventually in the bones of those drinking the milk. If a sample of 90Sr has an activity of 1.2XIOl2 d/s, what are the activity and the fraction of nuclei that have decayed after 59 yr (tl/2 of 90Sr = 29 yr)? Plan The fraction of nuclei that have decayed is the change in number of nuclei, expressed as a fraction of the starting number. The activity of the sample (s1.) is proportional to the number of nuclei (H), so we know that Ho - Ht s1.-0 s1.t Fraction decayed = Ho s1. 0 We are given s1.0 (1.2X 1012 d/s), so we find s1.t from the integrated form of the first-order rate equation (Equation 24.4), in which t is 59 yr. To solve that equation, we first need k, which we can calculate from the given t1/2 (29 yr).
  • 14. 24.2 The Kinetics of Radioactive Decay 1057 Solution Calculating the decay constant k: In 2 In 2 0.693 tl/2 = k so k = - tl/2 = -- 29 yr = 0.024 yr-I Applying Equation 24.4 to calculate sat, the activity remaining at time t: Ho In-=ln-=kt sao or In sao - In sal = kt Ht sa, So, In sa, = -kt + In sao = -(0.024 yr-1 X 59 yr) + In (1.2XlO12 d/s) In sat = -1.4 + 27.81 = 26.4 sat = 2.9X1011 d/s (All the data contain two significant figures, so we retained two in the answer.) Calculat- ing the fraction decayed: sao - sa, 1.2X 1012d/s - 2.9X 1011d/s Fraction decayed = ,.// 0 0.76 ,)CJ-o 1.2X 1 12 d/s Check The answer is reasonable: t is about 2 half-lives, so sa, should be about ~sao, or about 0.3XlO'2; therefore, the activity should have decreased by about j. Comment An alternative approach is to use the number of half-lives (t/tl/2) to find the fraction of activity (or nuclei) remaining. By combining Equations 24.4 and 24.5 and sub- stituting (In 2)/tl/2 for k, we obtain In No = (In 2)t = _t_In 2 = In 2t/II/2 N, tl/2 tl/2 Thus, H, In - = In (I)'/' - 1 /2 Ho 2 Taking the antilog gives Fraction remaining = H~ = N (1)'/1 2" 12 / = (1)59/29 2" = 0.24 So, Fraction decayed = 1.00 - 0.24 = 0.76 FOLLOW-UP PROBLEM 24.4Sodium-24 (t1/2 = 15 h) is used to study blood cir- culation. If a patient is injected with a 24NaCI solution whose activity is 2.5 X 109 d/s, how much of the activity is present in the patient's body and excreted fluids after 4.0 days? Radioisotopic Dating The historical record fades rapidly with time and virtually disappears for events of more than a few thousand years ago. Much of our understanding of prehistory comes from a technique called radioisotopic dating, which uses radioisotopes to determine the age of an object. The method supplies data about the ages of objects in fields as diverse as art history, archeology, geology, and paleontology. The technique of radiocarbon dating, for which the American chemist Willard F. Libby won the Nobel Prize in chemistry in 1960, is based on measuring the amounts of 14C and 12C in materials of biological origin. The accuracy of the method falls off after about six half-lives of 14C (t1/2 = 5730 yr), so it is used to date objects up to about 36,000 years old. Here is how the method works. High-energy neutrons resulting from cosmic ray collisions reach Earth continually from outer space. They enter the atmo- sphere and cause the slow formation of 14C by bombarding ordinary 14N atoms: ljN + 6n ---+ I~C + jp Through the processes of formation and radioactive decay, the amount of 14C in the atmosphere has remained nearly constant. * 'Cosmic ray intensity does vary slightly with time, which affects the amount of atmospheric 14C. From 14C activity in ancient trees, we know the amount fell slightly about 3000 years ago to cur- rent levels. Recently, nuclear testing and fossil fuel combustion have aiso altered the fraction of 14C slightly. Taking these factors into account improves the accuracy of the dating method.
  • 15. 1058 Chapter 24 Nuclear Reactions and Their Applications The 14C atoms combine with 02, diffuse throughout the lower atmosphere, and enter the total carbon pool as gaseous 14C02 and aqueous H14C03 -. They mix with ordinary l2C02 and H12C03 -, reaching a constant 12C:14C ratio of about 1012:1. The CO2 is taken up by plants during photosynthesis, and then taken up and excreted by animals that eat the plants. Thus, the l2C: 14C ratio of a living organism has the same constant value as the environment. When an organism dies, however, it no longer takes in 14C, so the l2C:14C ratio steadily increases because the amount of 14C decreases as it decays: l~C _ ljN + -?13 The difference between the l2e:14C ratio in a dead organism and the ratio in liv- ing organisms reflects the time elapsed since the organism died. As you saw in Sample Problem 24.4, the first-order rate equation can be expressed in terms of a ratio of activities: The Case of the Shroud of TurinOne No .wo of the holiest Christian relics is the famed In-=ln-=kt Shroud of Turin. It is a piece of linen that Nt .wt bears a faint image of a man's body and We use this expression in radiocarbon dating, where stlo is the activity in a liv- was thought to be the burial cloth used to ing organism and sl, is the activity in the object whose age is unknown. Solving wrap the body of Jesus Christ. In 1988, for t gives the age of the object: the Vatican allowed scientific testing of the cloth by radiocarbon dating. Three t =- 1 In - .wo (24.6) labs in Europe and the United States inde- k .wt pendently measured the 12C:14Cratio of a A useful graphical method in radioisotopic dating shows a plot of the natu- SO-mg piece of the linen and determined ral logarithm of the specific activity vs. time, which gives a straight line with a that the flax from which the cloth was slope of -k, the negative of the decay constant. Using such a plot and measur- made was grown between 1260 AD and ing the 14C specific activity of an object, we can determine its age; several exam- 1390 AD. Despite this evidence, the ples appear in Figure 24.5. To determine the ages of more ancient objects or of shroud lost none of its fascination: 10 years later, in 1998, when the shroud was objects that do not contain carbon, different radioisotopes are measured. (See the again put on display, about 2 million peo- margin note on the opposite page.) ple lined up to view it. 3.00 ~~ Charcoai from earliest Polynesian culture in H~waii pp .i .'.~., Linen, wra ...•.•. s from Book of Isaia,~; Deq~ s~~.Scrolls ...ng...... i . H ' ':!',., Chhrcoal fr~m earliest settlement in JapaQ 2.00 Bur.ASdtree from eruption that created Crater"Lake, Oregon Burned bones ofsloth in - Ct:1ilEiancave. Earlies,! Burned bison bones associated with trace of human presence Folsom Man, found at Lubbock, Texas at tip of South America Me~6Iithic-Neolithic transition site.Belt Cave, Iran Figure 24.5 Radiocarbon dating for de- Charcoal from Lascaux termining the age of artifacts. The natural Caves, France, site of . logarithms of the specific activities of 14C extensive cavepalntinqs ~ • (see background) (activity/g 14C) for various artifacts are projected onto a line whose slope equals -k, the negative of the 14C decay con- 16,000 stant. The age (in years) of an artifact is determined from the horizontal axis.
  • 16. 24_3 Nuclear Transmutation: Induced Changes in Nuclei 1059 SAMPLE PROBLEM 24.5 Applying Radiocarbon Dating Problem The charred bones of a sloth in a cave in Chile represent the earliest evidence of human presence at the southern tip of South America. A sample of the bone has a spe- cific activity of 5.22 disintegrations per minute per gram of carbon (d/min-g). If the ratio of 12C:14C in living organisms results in a specific activity of 15.3 d/min-g, how old are the bones (tl/2 of 14C = 5730 yr)? Plan We first calculate k from the given t1/2 (5730 yr). Then we apply Equation 24.6 to find the age (t) of the bones, using the given activities of the bones (.wt = 5.22 d/min-g) and of a living organism (.wo = 15.3 d/min-g), Solution Calculating k for 14Cdecay: k= In2 = 0.693 = 1.21XlO-4yr-1 t1/2 5730 yr Calculating the age (t) of the bones: l.wo 1 (15.3 d/min-g) t = -In - = ------In 4 1 ----- = 8.89x103 yr k .wt 1.21XlO- yr- 5.22d/min-g The bones are about 8900 years old. Check The activity of the bones is between !and ± the activity of a living organism, so the age should be between one and two half-lives (5730 to 11,460 yr). FOLLOW·UP PROBLEM 24.5A sample of wood from an Egyptian mummy case has a specific activity of 9.41 d/min-g. How old is the case? Ionization and scintillation counters measure the number of emissions from a radioac- tive sample. The decay rate (activity) of a sample is proportional to the number of radioactive nuclei. Nuclear decay is a first-order process, so the half-life does not depend on the number of nuclei. Radioisotopic methods, such as 14C dating, deter- mine the ages of objects by measuring the ratio of specific isotopes in the sample. 24.3 NUCLEAR TRANSMUTATION: INDUCED CHANGES IN NUCLEI The alchemists' dream of changing base metals into gold was never realized, but in the early 20th century, atomic physicists found that they could change one ele- How Old Is the Solar System? ment into another. Research into nuclear transmutation, the induced conversion By comparing the ratio of 238Uto its final of one nucleus into another, was closely linked with research into atomic struc- decay product, 206pb,geochemists found ture and led to the discovery of the neutron and to the production of artificial that the oldest known surface rocks on radioisotopes. Later, high-energy bombardment of nuclei in particle accelerators Earth-granite in western Greenland- began a scientific endeavor, which continues to this day, of creating many new are about 3.7 billion years old. The ratio of 238U:206Pb meteorites gives 4.65 bil- in nuclides and a growing number of new elements. lion years for the age of the Solar System, and therefore Earth. From this and other Early Transmutation Experiments; Discovery of the Neutron isotope ratios, such as 4°K:40 (tl/2 of Ar The first recognized transmutation occurred in 1919, when Emest Rutherford 40K = 1.3XIQ9 yr) as well as 87Rb:87Sr showed that Q' particles emitted from radium bombarded atmospheric nitrogen to (t1/2 of 87Rb = 4.9X 1010 yr), Moon rocks form a proton and oxygen-17: collected by Apollo astronauts have been shown to be 4.2 billion years old, and they 'jN + j:He _ iH + I~O provide evidence for volcanic activity on By 1926, experimenters had found that Q' bombardment transmuted most elements the Moon's surface about 3.3 billion years with low atomic numbers to the next higher element, with ejection of a proton. ago. That was about the time that, accord- A notation for nuclear bombardment reactions shows the reactant (target) ing to these methods, the first organisms nucleus to the left and the product nucleus to the right of a set of parentheses, were evolving on Earth. within which a comma separates the projectile particle from the ejected particle(s): reactant nucleus (particle in, particlets) out) product nucleus 17 Using this notation, the previous reaction is 14N (o.p) 0.
  • 17. 1060 Chapter 24 Nuclear Reactions and Their Applications An unexpected finding in a transmutation experiment led to the discovery of the neutron. When lithium, beryllium, and. boron were bombarded with a parti- cles, they emitted highly penetrating radiation that could not be deflected by a magnetic or electric field. Unlike "y radiation, these emissions were massive enough to eject protons from the substances they penetrated. In 1932, James Chadwick, a student of Rutherford, proposed that these emissions consisted of neutral particles with a mass similar to that of a proton, and he named them neu- trons. Chadwick received the Nobel Prize in physics in 1935 for his discovery. In 1933, Irene and Frederic Joliot-Curie (see photo), daughter and son-in-law of Marie and Pierre Curie, created the first artificial radioisotope, phosphorus-30. When they bombarded aluminum foil with a particles, phosphorus-30 and neu- trons were formed: gAl + iHe - bD + f~P or 27 Al (o..n) 30p Since then, other techniques for producing artificial radioisotopes have been developed. In fact, the majority of the nearly 1000 known radionuclides have been produced artificially. The Joliot-Curies in their laboratory. Particle Accelerators and the Transuranium Elements During the 1930s and 1940s, researchers probing the nucleus bombarded elements with neutrons, a particles, protons, and deuterons (nuclei of the stable hydrogen isotope deuterium, 2H). Neutrons are especially useful as projectiles because they have no charge and thus are not repelled as they approach a target nucleus. The other particles are all positive, so early researchers found it difficult to give them enough energy to overcome their repulsion by the target nuclei. Beginning in the 1930s, however, particle accelerators were invented to impart high kinetic ener- gies to particles by placing them in an electric field, usually in combination with a magnetic field. In the simplest and earliest design, protons are introduced at one end of a tube and attracted to the other end by a potential difference. A major advance was the linear accelerator, a series of separated tubes of increasing length that, through a source of alternating voltage, change their charge from positive to negative in synchrony with the movement of the particle through them (Figure 24.6A). A proton, for example, exits the first tube just when that tube becomes positive and the next tube negative. Repelled by the first tube and attracted by the second, the proton accelerates across the gap between them. A 40-ft linear accelerator with 46 tubes, built in California after World War Il, accel- erated protons to speeds several million times faster than the early accelerators. Later designs, such as the Stanford Linear Accelerator (Figure 24.6B), accelerate Alternating To vacuum voltage sources +/- t 6 Proton source A Figure 24.6 A linear accelerator. A, The voltage of each tubular section is alter- nated, so that the positively charged particle (a proton here) is repelled from the section it is leaving and attracted to the section it is entering. As a result, the parti- cle's speed is continually increased. B, The linear accelerator operated by Stanford University in California. B
  • 18. 24.3 Nuclear Transmutation: Induced Changes in Nuclei 1061 Alternating voltage source Path of proton beam L Evacuated chamber Proton source Target "Dees" Figure 24.7 The cyclotron accelerator. When the positively charged particle reaches the gap be- tween the two D-shaped electrodes ("dees"), it is repelled by one dee and attracted by the other. The particles move in a spiral path, so the cyclotron can be much smaller than a linear accelerator. heavier particles, such as B, C, 0, and Ne nuclei, several hundred million times faster, with correspondingly greater kinetic energies. The cyclotron (Figure 24.7), invented by E. O. Lawrence in 1930, applies the principle of the linear accelerator but uses electromagnets to give the particle a spiral path, thus saving space. The magnets lie within an evacuated chamber above The Powerful Bevatron The bevatron, and below two "dees," open, D-shaped electrodes that function like the tubes in used to study the physics of high-energy the linear design. The particle is accelerated as it passes from one dee, which is particle collisions, includes a linear momentarily positive, to the other, which is momentarily negative. Its speed and section and a synchrotron section. The in- radius increase until it is deflected toward the target nucleus. The synchrotron uses strument at the Lawrence Berkeley Labo- a synchronously increasing magnetic field to make the particle's path circular ratory in California increases the kinetic rather than spiral. 0 energy of the particles by a factor of more Accelerators have many applications, from producing radioisotopes used in than 6 billion. A beam of 1010 protons medical applications to studying the fundamental nature of matter. Perhaps their makes more than 4 million revolutions, a distance of 300,000 miles, in 1.8 s, attain- most specific application for chemists is the synthesis of transuranium elements, ing a final speed about 90% of the speed those with atomic numbers higher than uranium, which is the heaviest naturally of light! Even more powerful bevatrons occurring element. Some reactions that were used to form several of these ele- are in use at the Brookhaven National ments appear in Table 24.6. The transuranium elements include the remaining Laboratory in New York and at CERN, actinides (Z = 93 to 103), in which the Sf sub level is being filled, and the ele- outside Geneva, Switzerland. ments in the fourth transition series (Z = 104 to 112), in which the 6d sublevel Im'm:DI Formation of Some Transuranium Nuclides Reaction Half-life of Product 2~9pu + ~He ~ 2~~Am + lH + 26n 50.9 h 2~£pU + iHe ~ 2~gCm + 6n 163 days 2~tCm + ~He ~ 2~~Bk + lH + 26n 4.94 days 2§~U + l~C ~ 2~~Cf + 46n 36 h 2§~Es + ~He ~ Ig?Md + 6n 76min 2§§Cf + l~B ~ Ig~Lr + 66n 28 s
  • 19. 1062 Chapter 24 Nuclear Reactions and Their Applications is being filled. (In 1999, one research group reported the synthesis of elements Naming the Transuranium Elements 114, 116, and 118, but later retracted the data for elements 116 and 118. Another The last naturally occurring element was group, using different reactant nuclides, has since synthesized and confirmed the named after Uranus, thought at the time to be the outermost planet; then, the first two artificial elements were named after the more recently discovered Neptune and Pluto. The next few elements were named after famous scientists, as in curium, and places, as in americium. But conflicting _11 existence of element 116. Very recently, data for elements 113 and 115 have been . reported, but they have not been confirmed as of mid-2004.) . "~~ One nucleus can be transmuted to another through bombardment with high-energy particles. Accelerators increase the kinetic energy of particles in nuclear bombard- claims of discovery by scientists in differ- ment experiments and are used to produce transuranium elements. ent countries led to controversies about names for elements 104 and higher. To provide interim names until the disputes 24.4 THE EFFECTSOF NUCLEAR RADIATION could be settled, the International Union of Pure and Applied Chemistry (IUPAC) ON MATTER adopted a system that uses the atomic In 1986, an accident at the Chernobyl nuclear facility in the former Soviet Union number as the basis for a Latin name. released radioactivity that is estimated to have already caused thousands of can- Thus, for example, element 104 was cer deaths. In the same year, isotopes used in medical treatment emitted radioac- named unnilquadium (un = 1, nil = 0, quad = 4, ium = element suffix), with the tivity that prevented thousands of cancer deaths. In this section and the next, we symbol Unq. After much compromise, the examine the harmful and beneficial effects of radioactivity. IUPAC has finalized these names: 104, The key to both of these outcomes is that nuclear changes cause chemical rutherfordium (Rf); 105, dubnium (Db); changes in surrounding matter. In other words, even though the nucleus of an 106, seaborgium (Sg); 107, bohrium (Bh); atom undergoes a reaction with little or no involvement of the atom's electrons, 108, hassium (Hs); 109, meitnerium (Mt); the emissions do affect the electrons of nearby atoms. and 110, darmstadtium (Ds). Elements with atomic numbers 111 and higher have The Effects of Radioactive Emissions: Excitation and Ionization not yet been named. Radioactive emissions interact with matter in two ways, depending on their energies: • Excitation. In the process of excitation, radiation of relatively low energy inter- acts with an atom of a substance, which absorbs some of the energy and then re-emits it. Because electrons are not lost from the atom, the radiation that causes excitation is called nonionizing radiation. If the absorbed energy causes the atoms to move, vibrate, or rotate more rapidly, the material becomes hotter. Concentrated aqueous solutions of plutonium salts boil because the emissions excite the surrounding water molecules. (Polonium has therefore been suggested as a lightweight heat source, with no moving parts, for use on space stations.) Particles of somewhat higher energy excite electrons in other atoms to higher energy levels. As the atoms return to their ground state, they emit photons, often in the blue or UV region (see the description of scintilla- tion counters in the Tools of the Laboratory essay, p. 1055). • Ionization. In the process of ionization, radiation collides with an atom ener- getically enough to dislodge an electron: Atom ionizing radiation) ion + +e A cation and a free electron result, and the number of such cation-electron pairs that are produced is directly related to the energy of the incoming radi- ation. The high-energy radiation that gives rise to this effect is called ionizing radiation. The free electron of the pair often collides with another atom and ejects a second electron (see the description of Geiger-Muller counters in the Tools of the Laboratory essay, p. 1055). Effects of Ionizing Radiation on Living Matter Whereas nonionizing radiation is relatively harmless, ionizing radiation has a destructive effect on living tissue. When the atom that was ionized is part of a bio- logical macromolecule or membrane component, the results can be devastating.
  • 20. 24.4 The Effects of Nuclear Radiation on Matter 1063 Units of Radiation Dose and Its Effects To measure the effects of ionizing radia- a (-0.03 mm) tion, we need a unit for radiation dose. Units of radioactive decay, such as the becquerel and curie, measure the number of decay events in a given time but not their energy or absorption by matter. The number of cation-electron pairs produced in a given amount of living tissue is a measure of the energy absorbed by the tis- sue. The SI unit for such energy absorption is the gray (Gy); it is equal to 1 joule I I P (-2 mm) of energy absorbed per kilogram of body tissue: 1 Gy = 1 J/kg. A more widely used unit is the rad (radiation-absorbed dose), which is equal to 0.01 Gy: 1 rad = 0.01 J/kg = 0.01 Gy To measure actual tissue damage, we must account for differences in the strength of the radiation, the exposure time, and the type of tissue. To do this, we multiply the number of rads by a relative biological effectiveness (RBE) factor, which depends on the effect of a given type of radiation on a given tissue or body part. The product is the rem (roentgen equivalent for man), the unit of radia- tion dosage equivalent to a given amount of tissue damage in a human: no. of rems = no. of rads X RBE Doses are often expressed in millirems (10-3 rem). The SI unit for dosage equiv- alent is the sievert (Sv). It is defined in the same way as the rem but with absorbed dose in grays; thus, 1 rem = 0.01 Sv. Penetrating Power of Emissions The effect on living tissue of a radiation dose depends on the penetrating power and ionizing ability of the radiation. Fig- ure 24.8 depicts the differences in penetrating power of the three common emis- sions. Note, in general, that penetrating power is inversely related to the mass and charge of the emission. In other words, if a particle interacts strongly with matter, it penetrates only slightly, and vice versa: • a Particles. Alpha particles are massive and highly charged, which means that they interact with matter most strongly of the three common types of emis- Figure 24.8 Penetrating power of radio- sions. As a result, they penetrate so little that a piece of paper, light clothing, active emissions. Penetrating power is of- or the outer layer of skin can stop a radiation from an external source. How- ten measured in terms of the depth of ever, if ingested, an a emitter such as plutonium-239 causes grave localized water that stops 50% of the incoming ra- damage through extensive ionization. . diation. (Water is the main component of living tissue.) Alpha particles, with the • f3Particles and positrons. Beta particles and positrons have less charge and highest mass and charge, have the low- much less mass than a particles, so they interact less strongly with matter. Even est penetrating power, and -y rays have though a given particle has less chance of causing ionization, a [3 (or positron) the highest. (Average values of actual emitter is a more destructive external source because the particles penetrate penetrating distances are shown.) deeper. Specialized heavy clothing or a thick (0.5 cm) piece of metal is required to stop these particles. • Rays. Neutral, massless rays interact least with matter and, thus, penetrate 'Y "I most. A block of lead several inches thick is needed to stop them. Therefore, an external ray source is the most dangerous because the energy can ionize "I many layers of living tissue. A Tragic Way to Tell Time in the Dark In the early 20th century,wristwatchand Molecular Interactions How does the damage take place on the molecular level? clock dials were painted by hand with When ionizing radiation interacts with a molecule, it causes the loss of an elec- paint containingradium so they would tron from a bond or a lone pair. The resulting charged species go on to form glow in the dark. To write numbers free radicals, molecular or atomic species with one or more unpaired electrons. clearly,the youngwomenhired to apply As we've seen several times already, species with lone electrons are very reac- thepaint"tipped"finebrushesrepeatedly tive and tend to form electron pairs by bonding to other species. To do this, they betweentheir lips. Smallamountsof in- attack bonds in other molecules, sometimes forming more free radicals. gested226Ra2+ ereincorporated w intothe When radiation strikes biological tissue, for instance, the most likely mol- "I bonesof the women,along with normal ecule to absorb it is water, which forms an electron and a water ion-radical: ea2+, which led to numerouscases of bonefractureandjaw cancer. H20 +"y ----+ H20'+ + e- --......,...•
  • 21. 1064 Chapter 24 Nuclear Reactions and Their Applications The H20. + and e - collide with other water molecules to form free radicals: H20'+ + H20 --+ H30+ + 'OH and e" + H20 --+ H· + OH- These free radicals go on to attack more water molecules and surrounding bio- molecules, whose bonding and structure, as you know (Section 15.6), are inti- mately connected with their function. The double bonds in membrane lipids are particularly susceptible to free- radical attack: H· + RCH=CHR' --+ RCH2-CHR' In this reaction, one electron of the 'IT bond forms a C - H bond between one of the double-bonded carbons and the H', and the other electron resides on the other carbon to form a free radical. Changes to lipid structure cause changes in mem- brane fluidity and other damage that, in turn, cause leakage of the cell and destruc- tion of the protective fatty tissue around organs. Changes to critical bonds in enzymes lead to their malfunction as catalysts of metabolic reactions. Changes in the nucleic acids and proteins that govern the rate of cell division cause cancer. Genetic damage and mutations may occur when bonds in the DNA of sperm and egg cells are altered by free radicals. Sources of Ionizing Radiation It is essential to keep the molecular effects of ion- izing radiation in perspective. After all, we are continuously exposed to ionizing radiation from natural and artificial sources (Table 24.7). Indeed, life evolved in the presence of natural ionizing radiation, called background radiation. The mmIJ Ty'pical Radiation Doses from Natural and Artificial Sources Source of Radiation Adult [>q:lo!uue Natural Cosmic radiation 30-50 mrem/yr Radiation from the ground From clay soil and rocks ~25-170 mrem/yr In wooden houses 10-20 mrem/yr In brick houses 60- 70 mrem/yr In concrete (cinder block) houses 60-160 mrem/yr Radiation from the air (mainly radon) Outdoors, average value 20 mrem/yr In wooden houses 70 mrem/yr In brick houses 130 mrem/yr In concrete (cinder block) houses 260 mrem/yr Internal radiation from minerals in tap water and daily intake of food (4oK, 14C, Ra) ~40 mrem/yr Artificial Diagnostic x-ray methods Lung (local) 0.04-0.2 rad/film Kidney (local) 1.5-3 rad/film Dental (dose to the skin) :s 1 rad/film Therapeutic radiation treatment Locally :s 10,000rad Other sources Jet flight (4 h) ~1 mrem Nuclear testing <4 mrem/yr Nuclear power industry <1 mrem/yr TOTAL AVERAGE VALUE 100-200 mrem/yr
  • 22. 24.4 The Effects of Nuclear Radiation on Matter 1065 same radiation that causes harmful mutations also causes beneficial mutations that, over time, allow organisms to adapt and species to change. Background radiation has several sources. One source is cosmic radiation, which increases with altitude because of decreased absorption by the atmosphere. Thus, people in Denver absorb twice as much cosmic radiation as people in Los Angeles; even a jet flight involves measurable absorption. The sources of most background radiation are thorium and uranium minerals present in rocks and soil. Radon, the heaviest noble gas [Group 8A(l8)], is a radioactive product of ura- pCi/L .2.00 nium and thorium decay, and its concentration in the air we breathe varies with .0.00 liiIJ 2.50 .' 3.00 type of local soil and rocks. About 150 g of K+ ions is dissolved in the water .0.50 ~ 1.00 .3.50 Predicted county median in the tissues of an average adult, and 0.0118% of that amount is radioactive 4oK. n 1.50 III 4.00 concentration The presence of these substances and of atmospheric 14C02 means that all food, water, clothing, and building materials are slightly radioactive. o Risk of Radon Radon (Rn; Z = 86), the largest noble gas, is a natural decay The largest artificial source of radiation, and the easiest to control, is associ- product of uranium. Therefore, the ura- ated with medical diagnostic techniques, especially x-rays. The radiation dosage nium content of the local soil and rocks is from nuclear testing and radioactive waste disposal is miniscule for most people, a critical factor in the extent of the threat, but exposures for those living near test sites, nuclear energy facilities, or disposal but radon occurs everywhere in varying areas may be many times higher. concentrations. Radon itself decays to ra- dioactive nuclides of Po, Pb, and Bi, Assessing the Risk from Ionizing Radiation How much radiation is too much? To through a, 13, and "y emission. These approach this question, we must ask several others: How strong is the exposure? processes occur inside the body when How long is the exposure? Which tissue is exposed? Are offspring affected? One radon is inhaled and pose a serious poten- reason we lack clear data to answer these questions is that scientific ethical stan- tial hazard. The emissions damage lung dards forbid the intentional exposure of humans in an experimental setting. How- tissue, and the heavy-metal atoms formed ever, accidentally exposed radiation workers and Japanese atomic bomb survivors aggravate the problem. The latest EPA es- have been studied extensively. Table 24.8 summarizes the immediate tissue effects timates indicate that radon contributes to 15% of annual lung cancer deaths. on humans of an acute single dose of ionizing radiation to the whole body. The ~ severity of the effects increases with dose; a dose of 500 rem will kill about 50% of the exposed population within a month. Most data come from laboratory animals, whose biological systems may dif- fer greatly from ours. Nevertheless, studies with mice and dogs show that lesions ,I . Acute Effects of a Single Dose of Whole-Body Irradiation Lethal Dose Dose (rem) Effect Population (%) No. of Days 5-20 Possible late effect; possible chromosomal aberrations 20-100 Temporary reduction in white blood cells 50+ Temporary sterility in men (100+ rem = 1 yr duration) 100-200 "Mild radiation sickness": vomiting, diarrhea, tiredness in a few hours Reduction in infection resistance Possible bone growth retardation in children 300+ Permanent sterility in women 500 "Serious radiation sickness": 50-70 30 marrow/intestine destruction 400-1000 Acute illness, early deaths 60-95 30 3000+ Acute illness, death in hours 100 2 to days
  • 23. 1066 Chapter 24 Nuclear Reactions and Their Applications and cancers appear after massive whole-body exposure, with rapidly dividing cells affected first. In an adult animal, these are cells of the bone marrow, organ lin- ings, and reproductive organs, but many other tissues are affected in an immature animal or fetus. Studies in both animals and humans show an increase in the inci- dence of cancer from either a high, single exposure or a low, chronic exposure. Reliable data on genetic effects are few. Pioneering studies on fruit flies show a linear increase in genetic defects with both dose and exposure time. However, in the mouse, whose genetic system is obviously much more similar to ours than is the fruit fly's, a total dose given over a long period created one-third as many genetic defects as the same dose given over a short period. Therefore, rate of exposure is a key factor. The children of atomic bomb survivors show higher- than-normal childhood cancer rates, implying that their parents' reproductive sys- Dose tems were affected. Modeling Radiation Risk There are two current models of effect vs. dose. The linear response model proposes that radi- • Relatively low-energy emissions cause excitation of atoms in surrounding matter, ation effects, such as cancer risks, accu- whereas high-energy emissions cause ionization. The effect of ionizing radiation on mulate over time regardless of dose and living matter depends on the quantity of energy absorbed and the extent of ioniza- that populations should not be exposed to tion in a given type of tissue. Radiation dose for the human body is measured in rem. any radiation above background levels. Ionization forms free radicals, some of which proliferate and destroy biomolecular The S-shaped response model assumes an function. All organisms are exposed to varying quantities of natural ionizing radiation. extremely low risk at low doses and advo- Studies show that a large acute dose and a chronic small dose are both harmful. cates concern only at higher doses. If the linear model is more accurate, we should limit all excess exposure, but this would severely restrict medical diagnosis and re- 24.5 APPLICATIONS OF RADIOISOTOPES search, military testing, and nuclear en- Our ability to detect minute amounts of radioisotopes makes them powerful tools ergy production. for studying processes in biochemistry, medicine, materials science, environmen- tal studies, and many other scientific and industrial fields. Such uses depend on the fact that isotopes of an element exhibit very similar chemical and physical behavior. In other words, except for having a less stable nucleus, a radioisotope has nearly the same chemical properties as a nonradioactive isotope of that ele- ment. * For example, the fact that 14C02 is utilized by a plant in the same way as 12C02 forms the basis of radiocarbon dating. Radioactive Tracers: Applications of Nonionizing Radiation Just think how useful it could be to follow a substance through a complex process or from one region of a system to another. A tiny amount of a radioisotope mixed with a large amount of the stable isotope can act as a tracer, a chemical "bea- con" emitting nonionizing radiation that signals the presence of the substance. Reaction Pathways Tracers help us choose from among possible reaction path- ways. One well-studied example is the formation of an organic ester and water from a carboxylic acid and alcohol. Which portions of the reactants end up in the ester and which in the water? Figure 24.9 shows how ISO-tracers answer the ques- tion: an ISO-alcohol gives an ISO-ester, but an ISO-acid gives ISO-water. As another example, consider the reaction between periodate and iodide ions: 104 -(aq) + 21-(aq) + H20(l) - 12(s) + 103 -(aq) + 20H-(aq) Is 103- the result of 1°4- reduction or 1- oxidation? When we add "cold" (non- radioactive) 104- to a solution of 1- that contains some "hot" (radioactive, indi- *Although this statement is generally correct, differences in isotopic mass can influence bond strengths and therefore reaction rates. Such behavior is called a kinetic isotope effect and is particularly important for isotopes of hydroqen-c--'H, 2H, and 3H-because their masses differ by such large proportions. Section 22.4 discussed how the kinetic isotope effect is employed in the industrial production of heavy water, D20.
  • 24. 24.5 Applications of Radioisotopes 1067 Figure 24.9 Which reactant contributes :0: :0: 11 •• which group to the ester? An ester forms I1 .. 18" A R-C-OH + R'- OH R-C-.1§Q-R' + H-Q-H when a carboxylic acid reacts with an ~. alcohol. To determine which reactant sup- plies the 0 atom in the -OR' part of the :0: :0: ester group, acid and alcohol were la- 1I 18" •. 11 •• beled with the 180 and used as tracers. B R-C-OH + R'-OH R-C-Q-R' + A, When R180H reacts with the unlabeled ~. acid, the ester contains 180 but the water doesn't. S, When RC0180H reacts with the unlabeled alcohol, the water contains 18 0. Thus, the alcohol supplies the -OR' part of the ester, and the acid supplies cated in red) 1311-, we find that the 12 is radioactive, not the 103 -: the RC~O part. 104 -(aq) + zI311-(aq) + H20(I) - 131Iz(s) + 103-(aq) + 20H-(aq) These results show that 103- forms through the reduction of 104-, and that 12 forms through the oxidation of 1-. To confirm this pathway, we add 1°4- con- taining some hot 131104- to a solution of cold C. As we expected, the 103- is radioactive, not the 12: 131 104 -(aq) + 21-(aq) + H20(l) - Iz(s) + 131 103 -(aq) + 20H-(aq) Thus, tracers act like "handles" we can "hold" to follow the changing reactants. Far more complex pathways can be followed with tracers as well. The pho- tosynthetic pathway, the most essential and widespread metabolic process on Earth, in which energy from sunlight is used to form the chemical bonds of glu- cose, has an overall reaction that looks quite simple: light 6C02(g) + 6H20(l) chlorophyll ) C6H1206(s) + 602(g) However, the actual process is extremely complex, requiring 13 enzyme-catalyzed steps for each C atom from CO2 incorporated; thus these steps must occur six times for each molecule of C6H1206 that forms. Melvin Calvin and his coworkers took seven years to determine the pathway, using 14C in CO2 as the tracer and paper chromatography as the means of separating the products formed after dif- ferent times of light exposure. Calvin won the Nobel Prize in chemistry in 1961 for this remarkable achievement. Tracers are used in many studies of biological function. Most recently, life in space has required answers to new questions. In an animal study of red blood cell loss during extended space flight, blood plasma volume was measured with 12sI-Iabeled albumin (a blood protein), and slCr-labeled red blood cells were used to assess survival of blood cells. In another study, blood flow in skin under long periods of micro gravity was monitored using injected 133Xe. Material Flow Tracers are used in studies of solid surfaces and the flow of mate- rials. Metal atoms hundreds of layers deep within a solid have been shown to exchange with metal ions from the surrounding solution within a matter of min- utes. Chemists and engineers use tracers to study material movement in semi- conductor chips, paint, and metal plating, in detergent action, and in the process of corrosion, to mention just a few of many applications. Hydrologic engineers use tracers to study the volume and flow of large bod- ies of water. By following radionuclides formed during atmospheric nuclear bomb tests eH in H20, 90Sr2+, and 137 +), scientists have mapped the flow of water Cs from land to lakes and streams to oceans. Surface and deep ocean currents that circulate around the globe are also studied, as are the mechanisms of hurricane formation and the mixing of the troposphere and stratosphere. Industries employ tracers to study material flow during the manufacturing process, such as the flow of ore pellets in smelting kilns, the paths of wood chips and bleach in paper mills, the diffusion of fungicide into lumber, and in a particularly important appli- cation, the porosity and leakage of oil and gas wells in geological formations.
  • 25. 1068 Chapter 24 Nuclear Reactions and Their Applications Activation Analysis A somewhat different use of tracers occurs in neutron acti- vation analysis (NAA). In this method, neutrons bombard a nonradioactive sam- ple, converting a small fraction of its atoms to radioisotopes, which exhibit characteristic decay patterns, such as v-ray spectra, that reveal the elements pres- ent. Unlike chemical analysis, NAA leaves the sample virtually intact, so the method can be used to determine the composition of a valuable object or a very small sample. For example, a painting thought to be a 16th-century Dutch master- piece was shown through NAA to be a 20th-century forgery, because a microgram- sized sample of its pigment contained much less silver and antimony than the pigments used by the Dutch masters. Forensic chemists use NAA to detect traces of ammunition on a suspect's hand or traces of arsenic in the hair of a victim of Spirit on the surface of Mars. poisoning. In 2004, space scientists used NAA instrumentation in the Spirit and Opportunity robot vehicles to analyze the composition of Martian soils and rocks (see photo). Automotive engineers employ NAA and v-ray detectors to measure friction and wear of moving parts without having to take the engine apart. For example, when a steel surface that has been neutron-activated to form some radioactive 59Fe moves against a second steel surface, the amount of radioactivity on the sec- ond surface indicates the amount of material rubbing off. The radioactivity appear- ing in a lubricant placed between the surfaces can demonstrate the lubricant's ability to reduce wear. mlIID Some Radioisotopes Medical Diagnosis The largest use of radioisotopes is in medical science. In fact, over 25% of D.S. hospital admissions are for diagnoses based on data from Used as Medical Tracers radioisotopes. Tracers with half-lives of a few minutes to a few days are employed Body Part to observe specific organs and body parts. For example, a healthy thyroid gland Isotope or Process incorporates dietary 1- into iodine-containing hormones at a known rate. To lIC,18p, PET studies of assess thyroid function, the patient drinks a solution containing a trace amount 13N,150 brain, heart of Na131I, and a scanning monitor follows the uptake of 1311- into the thyroid 6OCO,1921r Cancer therapy (Figure 24. lOA). Technetium-99 (Z = 43) is also used for imaging the thyroid 64Cu Metabolism of (Figure 24. lOB), as well as the heart, lungs, and liver. Technetium does not occur copper naturally, so the radioisotope (actually a metastable form, 99mTc) is prepared just 59Pe Blood flow, spleen before use from radioactive molybdenum: 670a Tumor imaging 1231,1311 ~~Mo -----+ 994~Tc+ -?f3 Thyroid 1111n Brain, colon Tracers are also used to measure physiological processes, such as blood flow. 42 K Blood flow The rate at which the heart pumps blood, for example, can be observed by inject- 81mKr Lung ing 59Fe, which concentrates in the hemoglobin of blood cells. Several radioiso- 99Tc Heart, thyroid, topes used in medical diagnosis are listed in Table 24.9. liver, lung, bone 201Tl Heart muscle 90y Cancer, arthritis Animation: Nuclear Medicine A B Online Learning Center Figure 24.10 The use of radioisotopes to image the thyroid gland.Thyroid scanning is used to assess nutritional deficiencies, inflammation, tumor growth, and other thyroid-related ailments. 131 A, In 1 scanning, the thyroid gland absorbs 1311- ions whose ~ emissions expose a photographic film. The asymmetric image indicates disease. B, A 99Tc scan of a healthy thyroid.
  • 26. 24.5 Applications of Radioisotopes 1069 Figure 24.11 PETand brain activity. These PET scans show brain activity in a normal person (left) and in a patient with Alzheimer's disease (right). Red and yellow indicate relatively high activity within a region. Positron-emission tomography (PET) is a powerful imaging method for observing brain structure and function. A biological substance is synthesized with one of its atoms replaced by an isotope that emits positrons. The substance is injected into a patient's bloodstream, from which it is taken up into the brain. The isotope emits positrons, each of which annihilates a nearby electron. In the anni- hilation process, two 'Y photons are emitted simultaneously 180 from each other: 0 ?13 + _?e -- 22'Y An array of detectors around the patient's head pinpoints the sites of 'Y emission, and the image is analyzed by computer. Two of the isotopes used are 150, injected as H2150 to measure blood flow, and 18Fbonded to a glucose analog to measure glucose uptake, which is a marker for energy metabolism. Among many fasci- nating PET findings are those that show how changes in blood flow and glucose uptake accompany normal or abnormal brain activity (Figure 24.11). In a recent nonmedical development, substances incorporating IIC and 150 are being inves- tigated by PET to learn how molecules interact with and move along the surface of a catalyst. Applications of Ionizing Radiation To be used as a tracer, a radioisotope need emit only low-energy detectable radi- ation. Many other uses of radioisotopes, however, depend on the effects of high- energy, ionizing radiation. The interaction between radiation and matter that causes cancer can also be used to eliminate it. Cancer cells divide more rapidly than normal cells, so radioisotopes that interfere with the cell-division process kill more cancer cells than normal ones. Implants of 198 or of a mixture of 90Sr and 90y have been Au used to destroy pituitary and breast tumor cells, and 'Y rays from 60Co have been used to destroy brain tumors. Irradiation of food increases shelf life by killing microorganisms that cause food to rot (Figure 24.12), but the practice is quite controversial. Advocates point to the benefits of preserving fresh foods, grains, and seeds for long periods, whereas opponents suggest that irradiation might lower the food's nutritional con- tent or produce harmful by-products. The increased use of antibiotics in animal feed has brought about an increased incidence of illness from newer, more resis- Nonirradiated Irradiated tant bacterial strains, providing a stronger argument for the use of irradiation. The United Nations has approved irradiation for potatoes, wheat, chicken, and straw- Figure 24.12 The increased shelf life of berries, and the United States allows irradiation of chicken. irradiated food.
  • 27. 1070 Chapter 24 Nuclear Reactions and Their Applications Ionizing radiation has been used to control harmful insects. Captured males are sterilized by radiation and released to mate, thereby reducing the number of offspring. This method has been used to control the Mediterranean fruit fly in Cal- ifornia and disease-causing insects, such as the tsetse fly and malarial mosquito, in other parts of the world. Radioisotopic tracers emit non ionizing radiation and have been used to study reac- tion mechanisms, material flow, elemental composition, and medical conditions. Ion- izing radiation has been used to destroy cancerous tissue, kill organisms that spoil food, and control insect populations. 24.6 THE INTERCONVERSION OF MASS AND ENERGY Most of the nuclear processes we've considered so far have involved radioactive decay, in which a nucleus emits one or a few small particles or photons to become a slightly lighter nucleus. Two other nuclear processes cause much greater changes. In nuclear fission, a heavy nucleus splits into two much lighter nuclei, emitting several small particles at the same time. In nuclear fusion, the opposite process occurs as two lighter nuclei combine to form a heavier one. Both fission and fusion release enormous quantities of energy. Let's take a look at the origins of this energy by first examining the change in mass that accompanies the breakup of a nucleus into its nucleons and then considering the energy that is equivalent to this mass change. The Mass Defect We have known for most of the 20th century that mass and energy are intercon- vertible. The traditional mass and energy conservation laws have been combined to state that the total quantity of mass-energy in the universe is constant. There- fore, when any reacting system releases or absorbs energy, there must be an accompanying loss or gain in mass. This relation between mass and energy did not concern us earlier because the energy changes involved in breaking or forming chemical bonds are so small that the mass changes are negligible. When 1 mol of water breaks up into its atoms, for example, heat is absorbed: H20(g) - 2H(g) + O(g) f1H?xn = 2 x BE of O-H = 934 kJ We find the mass that is equivalent to this energy from Einstein's equation: or so (24.7) where !:lm is the change in mass between the reactants and the products. Substi- tuting the heat of reaction (in Jzmcl) for f1E and the numerical value for c (2.9979X 108 m/s), we obtain 9.34X 105 J/mol f1m = 8 2 = 1.04 X 10-11 kg/mol = 1.04 X 10-8 g/mol (2.9979XIO m/s) (Units of kg/mol are obtained because the joule includes the kilogram: I J = 1 kg·m2/s2.) The mass of 1 mol of H20 (reactant) is about 10 ng less than the combined masses of 2 mol of Hand 1 mol of 0 (products), a change too small to measure with even the most sophisticated balance. Such minute mass changes when bonds break or form allow us to assume that mass is conserved in chemi- cal reactions.
  • 28. 24.6 The Interconversion of Mass and Energy 1071 The much larger mass change that accompanies a nuclear process is related to the enormous energy required to bind the nucleus together or break it apart. Consider, for example, the change in mass that occurs when one 12e nucleus breaks up into its nucleons: six protons and six neutrons. We calculate this change in mass by combining the mass of six H atoms and six neutrons and then sub- tracting the mass of one 12e atom. This procedure cancels the masses of the elec- trons [six e - (in six 1 H atoms) cancel six e - (in one 12C atom)]. The mass of one IH atom is 1.007825 arnu, and the mass of one neutron is 1.008665 amu, so Mass of six IH atoms = 6.046950 amu Mass of six neutrons = 6.051990 amu Total mass = 12.098940 amu The mass of one 12e atom is 12 amu (exactly). The difference in mass (I1m) is the total mass of the nucleons minus the mass of the nucleus: Sm = 12.098940 amu - 12.000000 amu = 0.098940 amu/2C = 0.098940 g/mol 12C Note that the mass of the nucleus is less than the combined masses of its nucleons. The mass decrease that occurs when nucleons are united into a nucleus is called the mass defect. The size of this mass change (9.89X 10-2 g/mol) is nearly 10 million times that of the previous bond breakage (lOAX 10-9 g/mol) and is easily observed on any laboratory balance. Nuclear Binding Energy Einstein's equation for the relation between mass and energy also allows us to find the energy equivalent of a mass defect. For 12e, after converting grams to kilograms, we have tiE = timc2 = (9.8940X 10-5 kg/mol)(2.9979X 108 m/s)2 = 8.8921XlOJ2 J/mol = 8.8921X109 kl/mol This quantity of energy is called the nuclear binding energy for carbon-l2. In general, the nuclear binding energy is the quantity of energy required to break up 1 mol of nuclei into their individual nucleons: Nucleus + nuclear binding energy ~ nucleons Thus, qualitatively, the nuclear binding energy is analogous to the sum of bond ener- gies of a covalent compound or the lattice energy of an ionic compound. But, quan- titatively, nuclear binding energies are typically several million times greater. e The Force That Binds UsAccording to current theory, the nuclear binding energy We use joules to express the binding energy per mole of nuclei, but the joule is related to the strong force, which holds is an impractically large unit to express the binding energy of a single nucleus. nucleons together in a nucleus. There are Instead, nuclear scientists use the electron volt (e V), the energy an electron three other fundamental forces: (I) the acquires when it moves through a potential difference of 1 volt: weak nuclear force, which is important in 1 eV = 1.602XlO-J9 J f3 decay, (2) the electrostatic force that we observe between charged particles, and Binding energies are commonly expressed in millions of electron volts, that is, in (3) the gravitational force. Toward the end mega-electron volts (MeV): of his life, Albert Einstein tried unsuc- 1 MeV = 106 eV = 1.602X 10-13 J cessfully to develop a theory to explain A particularly useful factor converts a given mass defect in atomic mass units to how the four forces were really different aspects of one unified force that governs its energy equivalent in electron volts: all nature. The 2004 Nobel Prize in 1 amu = 931.5 X 106 eV = 931.5 MeV (24.8) physics was awarded to David J. Gross, Earlier we found the mass defect of the J2e nucleus to be 0.098940 amu. H. David Politzer, and Frank Wilczek for Therefore, the binding energy per 12e nucleus, expressed in MeV, is their explanation of the strong force who, with others, may one day realize Ein- Binding energy 931.5 MeV stein's dream. 12 = 0.098940 amu X ---- = 92.16 MeV C nucleus 1 amu
  • 29. 1072 Chapter 24 Nuclear Reactions and Their Applications We can compare the stability of nuclides of different elements by determining the binding energy per nucleon. For 12C, we have binding energy 92.16 MeV Binding energy per nucleon = ------ ---- = 7.680 MeV/nucleon no. of nucleons 12 nucleons SAMPLE PROBLEM 24.6 Calculating the Binding Energy per Nucleon Problem Iron-56 is an extremely stable nuclide. Compute the binding energy per nucleon for 56Pe and compare it with that for 12C(mass of 56Pe atom = 55.934939 amu; mass of IH atom = 1.007825 amu; mass of neutron = 1.008665 amu). Plan Iron-56 has 26 protons and 30 neutrons in its nucleus. We calculate the mass defect by finding the sum of the masses of 26 IH atoms and 30 neutrons and subtracting the given mass of I 56Pe atom. Then we multiply Ism by the equivalent in Me V (931.5 MeV/amu) and divide by 56 (no. of nucleons) to obtain the binding energy per nucleon. Solution Calculating the mass defect: Mass defect = [(26 X mass lH atom) + (30 X mass neutron)] - mass 56Pe atom = [(26)(1.007825 amu) + (30)(1.008665 amu)] - 55.934939 amu = 0.52846 amu Calculating the binding energy per nucleon: 0.52846 amu X 931.5 Me'V/amu Binding energy per nucleon = ------------ 8.790 MeV/nucleon 56 nucleons An 56Pe nucleus would require more energy to break up into its nucleons than would 12C (7.680 MeV/nucleon), so 56Pe is more stable than 12c. Check The answer is consistent with the great stability of 56Pe. Given the number of dec- imal places in the values, rounding to check the math is useful only to find a major error. The number of nucleons (56) is an exact number, so we retain four significant figures. F0 LL 0 W - U P PRO B L EM 24.6Uranium- 235 is the essential component of the fuel in nuclear power plants. Calculate the binding energy per nucleon for 235U.Is this nuclide more or less stable than 12C (mass of 235U atom = 235.043924 amu)? Fission or Fusion: Means of Increasing the Binding Energy Per Nucleon Calcula- tions similar to Sample Problem 24.6 for other nuclides show that the binding energy per nucleon varies considerably. The essential point is that the greater the binding energy per nucleon, the more stable the nuclide. Figure 24.13 shows a plot of the binding energy per nucleon vs. mass num- ber. It provides information about nuclide stability and the two possible processes nuclides can undergo to form more stable nuclides. Nuclides with fewer than 10 nucleons have a relatively small binding energy per nucleon. The 4He nucleus has an exceptionally large value, however, which is why it is emitted intact as an C' particle. Above A = 12, the binding energy per nucleon varies from about 7.6 to 8.8 MeY. The most important observation is that the binding energy per nucleon peaks for elements with A = 60. In other words, nuclides become more stable with increasing mass number up to around 60 nucleons and then become less stable with higher numbers of nucleons. The existence of a peak of stability suggests that there are two ways nuclides can increase their binding energy per nucleon: • Fission. A heavier nucleus can split into lighter ones (closer to A = 60) by undergoing fission. The product nuclei have greater binding energy per nucleon (are more stable) than the reactant nucleus, and the difference in energy is released. Nuclear power plants generate energy through fission, as do atomic bombs (Section 24.7).
  • 30. 24.7 Applications of Fission and Fusion 1073 348 5BFe 84Kr 1198n 9 205TI 235U sQ) 8 Region of very stable nuclides 6 7 238U c 0 Q) U 6 ::J C 0; 5 BLi 0- >, Fusion Fission E' 4 Q) ~ ~ c Q) DJ 3 3H c; is 3He c 2 m 2H 0 20 40 60 80 100 120 140 160 180 200 220 240 260 Mass number (A) IilmDiI The variation in binding energy per nucleon. A plot of the binding energy per nucleon vs. mass number shows that nuclear stability is greatest in the region near 56Fe. Lighter nuclei may undergo fusion to become more stable; heavier ones may undergo fission. Note the ex- ceptional stability of 4He among extremely light nuclei. • Fusion. Lighter nuclei, on the other hand, can combine to form a heavier one (closer to A = 60) by undergoing fusion. Once again, the product is more sta- ble than the reactants, and energy is released. The Sun and other stars gener- ate energy through fusion, as do hydrogen bombs. In these examples and in all current research efforts for developing fusion as a useful energy source, hydro- gen nuclei fuse to form the very stable helium-4 nucleus. In the next section, we examine fission and fusion and the industrial energy facil- ities designed to utilize them. The mass of a nucleus is less than the sum of the masses of its nucleons by an amount called the mass defect. The energy equivalent to the mass defect is the nuclear binding energy, usually expressed in units of MeV. The binding energy per nucleon is a measure of nuclide stability and varies with the number of nucleons in a nuclide. Nuclides with A = 60 are most stable. Lighter nuclides can join (fusion) or heavier nuclides can split (fission) to become more stable. 24.7 APPLICATIONS OF FISSION AND FUSION Of the many beneficial applications of nuclear reactions, the greatest is the poten- tial for almost limitless amounts of energy, which is based on the multimillion- fold increase in energy yield of nuclear reactions over chemical reactions. Our experience with nuclear energy from power plants in the late 20th century, how- ever, has forced a realization that we must strive to improve ways to tap this energy source safely and economically. In this section, we discuss how fission and fusion occur and how we are applying them. The Process of Nuclear Fission During the mid-1930s, Enrico Fermi and coworkers bombarded uranium (Z = 92) with neutrons in an attempt to synthesize transuranium elements. Many of the
  • 31. 1074 Chapter 24 Nuclear Reactions and Their Applications Figure 24.14 Induced fission ofmU. A neutron bombarding a 235Unucleus results in an extremely unstable 236U nucleus, which becomes distorted in the act of splitting. In this case, which shows one of many possible splitting patterns, the products are 92Kr and 141 Ba. Three neutrons and a great deal of energy are released also. unstable nuclides produced were tentatively identified as having Z > 92, but other scientists were skeptical. Four years later, the German chemist Otto Hahn and his associate F. Strassmann showed that one of these unstable nuclides was an iso- tope of barium (Z = 56). The Austrian physicist Lise Meitner, a coworker of Hahn, and her nephew Otto Frisch proposed that barium resulted from the split- ting of the uranium nucleus into smaller nuclei, a process that they called fission because of its similarity to the fission a biological cell undergoes during re- production. Q The 235U nucleus can split in many different ways, giving rise to various daughter nuclei, but all routes have the same general features. Figure 24.14 depicts one of these fission patterns. Neutron bombardment results in a highly excited 14 236U nucleus, which splits apart in 10- s. The products are two nuclei of unequal mass, two or three neutrons (average of 2.4), and a large quantity of energy. A single 23SU nucleus releases 3.5XlO-lJ J when it splits; 1 mol of 23SU (about Use Meitner (1878-1968) Until very ~ Ib) releases 2.1 X 1013 J -a billion times as much energy as burning ~ lb of coal recently, this extraordinary physicist re- (about 2X 104 J)! ceived little of the acclaim she deserved. Meitner worked in the laboratory of the We harness the energy of nuclear fission, much of which appears as heat, by chemist Otto Hahn, and she was responsi- means of a chain reaction, illustrated in Figure 24.15: the two to three neutrons ble for the discovery of protactinium (Pa; that are released by the fission of one nucleus collide with other fissionable nuclei Z = 91) and numerous radioisotopes. Af- and cause them to split, releasing more neutrons, which then collide with other ter leaving Germany in advance of the nuclei, and so on, in a self-sustaining process. In this manner, the energy released Nazi domination, Meitner proposed the increases rapidly because each fission event in a chain reaction releases two to correct explanation of nuclear fission. In three times as much energy as the preceding one. 1944 Hahn received the Nobel Prize in Whether a chain reaction occurs depends on the mass (and thus the volume) chemistry, but he did not even acknowl- of the fissionable sample. If the piece of uranium is large enough, the product edge Meitner in his acceptance speech. neutrons strike another fissionable nucleus before flying out of the sample, and a Today, most physicists believe Meitner should have received the prize. Despite chain reaction takes place. The mass required to achieve a chain reaction is called controversy over names for elements 104 the critical mass. If the sample has less than the critical mass (called a subcrit- to 109, it was widely agreed that element ical mass), most of the product neutrons leave the sample before they have the 109 should be named meitnerium. opportunity to collide with and cause the fission of another 23SU nucleus, and thus a chain reaction does not occur.
  • 32. 24.7 Applications of Fission and Fusion 1075 Figure 24.15 A chain reaction ofmU. If a sample exceeds the critical mass, neutrons produced by the first fission event collide with other nuclei, causing their fission and the production of more neu- trons to continue the process. Note that various product nuclei form. The vertical dashed lines identify succeeding "generations" of neutrons. Uncontrolled Fission: The Atomic Bomb An uncontrolled chain reaction can be adapted to make an extremely powerful explosive, as several of the world's lead- ing atomic physicists suspected just prior to the beginning of World War n. In August 1939, Albert Einstein wrote the president of the United States, Franklin Delano Roosevelt, to this effect, warning of the danger of allowing the Nazi gov- ernment to develop this power first. It was this concern that led to the Manhat- tan Project, an enormous scientific effort to develop a bomb based on nuclear fission, which was initiated in 1941.* In August 1945, the United States detonated two atomic bombs over Japan, and the horrible destructive power of these bombs was a major factor in the surrender of the Japanese a few days later. Separated In an atomic bomb, small explosions of trinitrotoluene (TNT) bring subcrit- subcritical masses ical masses of fissionable material together to exceed the critical mass, and the ensuing chain reaction brings about the explosion (Figure 24.16). The prolifera- tion of nuclear power plants, which use fissionable materials to generate energy TNT for electricity, has increased concern that more countries (and unscrupulous indi- explosive viduals) may have access to such material for making bombs. Since the devas- tating terrorist attacks of September 11, 2001 in the United States, this concern has been heightened. After all, only 1 kg of fissionable uranium was used in the Figure 24.16 Diagram of an atomic bomb. bomb dropped on Hiroshima, Japan. Small TNT explosions bring subcritical masses together, and the chain reaction occurs. *For an excellent scientific and historical account of the development of the atomic bomb, see R. Rhodes, The Making of the Atomic Bomb, New York, Simon and Schuster, 1986.
  • 33. 1076 Chapter 24 Nuclear Reactions and Their Applications Controlled Fission: Nuclear Energy Reactors Controlled fission can produce elec- tric power more cleanly than can the combustion of coal. Like a coal-fired power plant, a nuclear power plant generates heat to produce steam, which turns a tur- bine attached to an electric generator. In a coal plant, the heat is produced by burning coal; in a nuclear plant, it is produced by splitting uranium. Heat generation takes place in the reactor core of a nuclear plant (Fig- ure 24.17). The core contains thefuel rods, which consist of fuel enclosed in tubes of a corrosion-resistant zirconium alloy. The fuel is uranium(IV) oxide (U02) that has been enriched from 0.7% 235U, the natural abundance of this fissionable iso- tope, to the 3% to 4% 235U required to sustain a chain reaction. (Enrichment of nuclear fuel is the most important application of Graham's law; see the margin note, p. 205.) Sandwiched between the fuel rods are movable control rods made of cadmium or boron (or, in nuclear submarines, hafnium), substances that absorb neutrons very efficiently. When the control rods are moved between the fuel rods, the chain reaction slows because fewer neutrons are available to bombard ura- nium atoms; when they are removed, the chain reaction speeds up. Neutrons that leave the fuel-rod assembly collide with a reflector, usually made of a beryllium Figure 24.17 A light-water nuclearreac- tor. A, Photo of a facility showing the concrete containment shell and nearby water source. B, Schematic of a Iight- water reactor. A -: @Steamproducedoperates »< turbine-generator Contalnrnent shell ( ~Electric power Reactor core 11 @Control rods regulate rate of chain reaction Moderator 11 (J)Enriched uranium in fuel rods releases energy from fission Coolant water out B
  • 34. 24.7 Applications of Fission and Fusion 1077 alloy, which absorbs very few neutrons. Reflecting the neutrons back to the fuel rods speeds the chain reaction. Flowing around the fuel and control rods in the reactor core is the modera- tor, a substance that slows the neutrons, making them much better at causing fis- sion than the fast ones emerging directly from the fission event. In most modem reactors, the moderator also acts as the coolant, the fluid that transfers the released heat to the steam-producing region. Because lH absorbs neutrons, light-water reactors use H20 as the moderator; in heavy-water reactors, D20 is used. The advantage of D20 is that it absorbs very few neutrons, leaving more available for fission, so heavy-water reactors can use unenriched uranium. As the coolant flows around the encased fuel, pumps circulate it through coils that transfer its heat to the water reservoir. Steam formed in the reservoir turns the turbine that runs the generator. The steam is then condensed in large cooling towers (see Figure 13.22, p. 509) using water from a lake or river and returned to the water reservoir. "Breeding" Nuclear Fuel Uranium- Some major accidents at nuclear plants have caused decidedly negative pub- 235 is not an abundant isotope. One solu- lic reactions. In 1979, malfunctions of coolant pumps and valves at the Three- tion to a potential fuel shortage is a Mile Island facility in Pennsylvania led to melting of some of the fuel, serious breeder reactor, designed to consume one type of nuclear fuel as it produces another. damage to the reactor core, and the release of radioactive gases into the atmo- Fuel rods are surrounded by natural U30g, sphere. In 1986, a million times as much radioactivity was released when a cool- which contains 99.3% nonfissionable ing system failure at the Chernobyl plant in Ukraine caused a much greater 238U atoms. As fast neutrons, formed dur- melting of fuel and an uncontrolled reaction. High-pressure steam and ignited ing 235U fission, escape the fuel rod, they graphite moderator rods caused the reactor building to explode and expel radioac- collide with 238U, transmuting it into tive debris. Carried by prevailing winds, the radioactive particles contaminated 239pU,another fissionable nucleus: vegetables and milk in much of Europe. Health officials have evidence that thou- sands of people living near the accident have already or may eventually develop 6 2§~U + n ---+ 2§~U (tl/2 of 2§~U = 23.5 min) cancer from radiation exposure. The design of the Chernobyl plant was particu- larly unsafe because, unlike reactors in the United States and western Europe, the 2§~U ---+ 2§~Np + -?f3 reactor was not enclosed in a massive, concrete containment building. (tl/2 of 2§~Np = 2.35 days) Despite potential safety problems, nuclear power remains an important source 2§~Np ---+ 2§~PU+ -?f3 of electricity. In the late 1990s, nearly every European country employed nuclear (tl/2 of 2§~pu = 2AX 104 yr) power, and it is the major power source in some countries-Sweden creates 50% Although breeder reactors can make fuel of its electricity this way and France almost 80%. Currently, the United States as they operate, they are difficult and ex- obtains about 20% of its electricity from nuclear power, and Canada slightly less. pensive to build, and 239pU is extremely As our need for energy grows, safer reactors will be designed. toxic and long lived. Breeder reactors are However, even a smoothly operating plant has certain inherent problems. The not used in the United States, although problem of thermal pollution is common to all power plants. Water used to con- several are operating in Europe and Japan. dense the steam is several degrees warmer when returned to its source, which can harm aquatic organisms (Section 13.4). A more serious problem is nuclear waste disposal. Many of the fission products formed in nuclear reactors have long half- lives, and no satisfactory plan for their permanent disposal has yet been devised. Proposals to place the waste in containers and bury them in deep bedrock cannot possibly be field-tested for the thousands of years the material will remain harm- ful. Leakage of radioactive material into groundwater is a danger, and earthquakes can occur even in geologically stable regions. Despite studies indicating the pro- posed disposal site at Yucca Mountain, Nevada, may be too geologically active, the U.S. government recently approved the site. It remains to be seen whether we can operate fission reactors and dispose of the waste safely and economically. The Promise of Nuclear Fusion Nuclear fusion is the ultimate source of nearly all the energy on Earth because nearly all other sources depend, directly or indirectly, on the energy produced by nuclear fusion in the Sun. But the Sun and other stars generate more than energy; in fact, all the elements larger than hydrogen were formed in fusion and decay processes within stars, as the upcoming Chemical Connections essay describes.
  • 35. ,,~m""Cosmology Origin of the Elements in the Stars OW did the universe begin? Where did matter come from? Absorption of a particles forms nuclei up to 40Ca: H How were the elements formed? Every culture has creation myths that address such questions, but only recently have as- tronomers, physicists, and chemists begun to offer a scientific 12C ~ a a 160 ~ a 20Ne ~ a a 24Mg ~ a a explanation. The most accepted current model proposes that 28Si --"----t 32S ~ 36Ar ~ 40Ca a sphere of unimaginable properties-diameter of 10-28 cm, den- sity of 10 96 g/mL (density of a nucleus = 1014 g/ml.), and tem- Further contraction and heating to a temperature of 3 X 109 K al- perature of 1032K-exploded in a "Big Bang," for reasons not yet low reactions in which nuclei release neutrons, protons, and a par- even guessed, and distributed its contents through the void of ticles and then recapture them. As a result, nuclei with lower space. Cosmologists consider this moment the beginning of time. binding energies supply nucleons to create those with higher bind- One second later, the universe was an expanding mixture of ing energies. This process, which takes only a few minutes, stops neutrons, protons, and electrons, denser than rock and hotter than at iron (A = 56) and nickel CA = 58), the nuclei with the highest an exploding hydrogen bomb (about 1010 K). During the next few binding energies. minutes, it became a gigantic fusion reactor creating the first 4. Heavier elements form. In very massive stars, the next atomic nuclei: 2H, 3He, and 4He. After 10 minutes, more than 25% stage is the most spectacular. With all the fuel consumed, the core of the mass of the universe existed as 4He, and only about 0.025% collapses within a second. Many Fe and Ni nuclei break down into as 2H. About 100 million years later, or about 15 billion years ago, neutrons and protons. Protons capture electrons to form neutrons, gravitational forces pulled this cosmic mixture into primitive, and the entire core forms an incredibly dense neutron star. (An contracting stars. Earth-sized star that became a neutron star would fit in the Hous- This account of the origin of the universe is based on the ob- ton Astrodome!) As the core implodes, the outer layers explode servation of spectra from the Sun, other stars, nearby galaxies, and in a supernova, which expels material throughout space. A super- cosmic (interstellar) dust. Spectral analysis of planets and chemi- nova occurs an average of every few hundred years in each cal analysis of Earth and Moon rocks, meteorites, and cosmic-ray galaxy; the one shown in Figure B24.4 was observed from the particles furnish data about isotope abundance. From these, a southern hemisphere in 1987, about 160,000 years after the event model has been developed for stellar nucleogenesis, the origin of occurred. The heavier elements are formed during supernova the elements in the stars. The overall process occurs in several events and are found in second-generation stars, those that coa- stages during a star's evolution, and the entire sequence of steps lesce from interstellar 'n and 4He and the debris of exploded first- occurs only in very massive stars, having 10 to 100 times the mass generation stars. of the Sun. Each step involves a contraction of the star that pro- Heavier elements form through neutron-capture processes. In duces higher temperature and heavier nuclei. Such events are the s-process, a nucleus captures a neutron and emits a -y ray. forming elements in stars today. The key stages in the process are Days, months, or even thousands of years after this event, the nu- shown in Figure B24.3 and described below: cleus emits a f3particle to form the next element, as in this con- 1. Hydrogen burning produces He. The initial contraction of version of 68Zn to 700e: a star heats its core to about 107 K, at which point a fusion process called hydrogen burning begins, which produces helium from the abundant protons: 4lH --+ iHe + 2?f3 + 2-y + energy The stable isotopes of most heavy elements form by the s-process. 2. Helium burning produces C, 0, Ne, and Mg. After several Less stable isotopes and those with A greater than 230 cannot billion years of hydrogen burning, about 10% of the IH is con- form by the s-process because their half-lives are too short. These sumed, and the star contracts further. The 4He forms a dense core, form by the r-process during the fury of the supernova. Multiple hot enough (2X 108 K) to fuse 4He. The energy released during he- neutron captures, followed by multiple f3decays, occur in a sec- lium burning expands the remaining IH into a vast envelope: the ond, as when 56Fe is converted to 79Br: star becomes a red giant, more than 100 times its original diame- ter. Within its core, pairs of 4He nuclei (a particles) fuse into un- ~~Fe + 23bn --+ i~Fe --+ ~§Br + 9-?f3 stable 8Be nuclei (tl/2 = 7 X 10-17 s). These collide with another 4He to form stable 12C.Then, further fusion with 4He creates nu- We know from the heavy elements present in the Sun that it is at clei up to 24Mg: least a second-generation star presently undergoing hydrogen a a a burning. Together with its planets, it was formed from the dust of 12C ~ 160 ~ 20Ne ~ 24Mg exploded stars about 4.6X 109 years ago. This means that many of the atoms on Earth, including some within you, came from ex- 3. Elements through Fe and Ni form. For another 10 million ploded stars and are older than the Solar System itself! years, 4He is consumed, and the heavier nuclei created form a Any theory of element formation must be consistent with the core. This core contracts and heats, expanding the star into a element abundances we observe (Section 22.1). Although local supergiant. Within the hot core (7X 108 K), carbon and oxygen compositions, such as those of Earth and Sun, differ, large regions burning occur: of the universe have, on average, similar compositions. Therefore, 12C + 12C --+ 23Na + IH scientists believe that element forming reaches a dynamic equilib- 12C + 160 --+ 28Si + -y rium, which leads to relatively constant amounts of the isotopes. 1078
  • 36. Figure 824.3 Element synthesis in the life cycle of a star. Figure 824.4 A view of Supernova 1987 A.
  • 37. 1080 Chapter 24 Nuclear Reactions and Their Applications Much research is being devoted to making nuclear fusion a practical, direct source of energy on Earth. To understand the advantages of fusion, let's consider one of the most discussed fusion reactions, in which deuterium and tritium react: fH + fH - iHe bn + This reaction produces 1.7 X 109 kJ/mol, an enormous quantity of energy with no radioactive by-products. Moreover, the reactant nuclei are relatively easy to come by. We obtain deuterium from the electrolysis of water (Section 22.4). In nature, tritium forms through the cosmic (neutron) irradiation of 14N: ljN + bn - fH + l~C However, this process results in a natural abundance of only 10-7% 3H. More practically, tritium can be produced in nuclear accelerators by bombarding lithium-6 or by surrounding the fusion reactor itself with material containing lithium-6: ~Li + bn - fH + iHe Thus, fusion seems very promising, at least in principle. However, some extremely difficult problems remain. Fusion requires enormous energy in the form of heat to give the positively charged nuclei enough kinetic energy to force them- selves together. The fusion of deuterium and tritium, for example, occurs at prac- tical rates at about 108 K, hotter than the Sun's core! How can such temperatures be achieved? The reaction that forms the basis of a hydrogen, or thermonuclear, bomb fuses lithium-6 and deuterium, with an atomic bomb inside the device pro- viding the heat. Obviously, a power plant cannot begin operation by detonating atomic bombs. Two research approaches are being used to achieve the necessary heat. In one, atoms are stripped of their electrons at high temperatures, which results in a gaseous plasma, a neutral mixture of positive nuclei and electrons. Because of the extreme temperatures needed for fusion, no material can contain the plasma. The most successful approach to date has been to enclose the plasma within a magnetic field. The tokamak design has a donut-shaped container in which a heli- cal magnetic field confines the plasma and prevents it from contacting the walls (Figure 24.18). Scientists at the Princeton University Plasma Physics facility have achieved some success in generating energy from fusion this way. In another approach, the high temperature is reached by using many focused lasers to com- press and heat the fusion reactants. In any event, as a practical, everyday source Figure 24.18 The tokamak design for -- of energy, fusion still seems to be a long way off. In nuclear fission, neutron bombardment causes a nucleus to split, releasing neutrons that split other nuclei to produce a chain reaction. A nuclear power plant controls the rate of the chain reaction to produce heat that creates steam, which is used to gen- erate electricity. Potential hazards, such as radiation leaks, thermal pollution, and dis- magnetic containment of a fusion plasma. The don ut-shaped chamber of the toka- posal of nuclear waste, remain current concerns. Nuclear fusion holds great promise mak (photo, top; schematic, bottom) con- as a source of clean abundant energy, but it requires extremely high temperatures tains the plasma within a helical magnetic and is not yet practical. The elements were formed through a complex series of field. nuclear reactions in evolving stars. Chapter Perspective With this chapter, our earlier picture of the nucleus as a static point of positive mass at the atom's core has changed radically. Now we picture a dynamic body, capable of a host of changes that involve incredible quantities of energy. Our attempts to apply
  • 38. For Review and Reference 1081 the behavior of this minute system to benefit society have created some of the most fascinating and challenging fields in science today. We began our investigation of chemistry 24 chapters ago, by seeing how the chemical elements and the products we make from them influence nearly every aspect of our material existence. Now we have come full circle to learn that these elements, whose patterns of behavior we have become familiar with yet still marvel at, are continually being born in the countless infernos twinkling in the night sky. For you, the end of this course is a beginning-a chance to apply your new abilities to visualize molecular events and solve problems in whatever field you choose. For the science of chemistry, future challenges are great: What greener energy sources can satisfy our needs while sustaining our environment? What new products can feed, clothe, and house the world's people and maintain precious resources? How can we apply our new genetic insight to defend against cancer, AIDS, and other dreaded diseases? What new materials and technologies can make life more productive and meaningful? The questions are many, but the science of chemistry will always be one of our most powerful means of answering them. (Numbers in parentheses refer to pages, unless noted otherwise.) Learning Objectives Relevant section and/or sample problem (SP)numbers appear 15. How radioisotopes are used in research, analysis, and diagno- in parentheses. sis (Section 24.5) 16. Why the mass of a nuclide is less than the sum of its nucleons' Understand These Concepts masses (mass defect) and how this mass difference is related to the 1. How nuclear changes differ, in general, from chemical changes nuclear binding energy (Section 24.6) (Introduction) 17. How nuclear stability is related to binding energy per nucleon 2. The meanings of radioactivity, nucleon, nuclide, and isotope (Section 24.6) (Section 24.1) 18. How unstable nuclides undergo either fission or fusion to in- 3. Characteristics of three types of radioactive emissions: ex, [3, crease their binding energy per nucleon (Section 24.6) and "y (Section 24.1) 19. The current application of fission and potential application of 4. The various forms of radioactive decay and how each changes fusion to produce energy (Section 24.7) the values of A and Z (Section 24.1) 5. How the N /Z ratio and the even-odd nature of Nand Z correlate Master These Skills with nuclear stability (Section 24.1) 1. Expressing the mass and charge of a particle with the ~X nota- 6. How the N/Z ratio correlates with the mode of decay of an un- tion (Section 24.1; see also Section 2.5) stable nuclide (Section 24.1) 2. Using changes in the values of A and Z to write and balance nu- 7. How a decay series combines numerous decay steps and ends clear equations (SP 24.1) with a stable nuclide (Section 24.1) 3. Using the N/Z ratio and the even-odd nature of Nand Z to pre- 8. Why radioactive decay is a first-order process; the meanings of dict nuclear stability (SP 24.2) decay rate and specific activity (Section 24.2) 4. Using the N/Z ratio to predict the mode of nuclear decay 9. The meaning of half-life in the context of radioactive decay (SP 24.3) (Section 24.2) 5. Converting units of radioactivity (Section 24.2) 10. How the specific activity of an isotope in an object is used to 6. Calculating specific activity, decay constant, half-life, and determine the object's age (Section 24.2) number of nuclei (Section 24.2 and SP 24.4) 11. How particle accelerators are used to synthesize new nuclides 7. Estimating the age of an object from the specific activity and (Section 24.3) half-life of carbon-14 (SP 24.5) 12. The distinction between excitation and ionization and the ex- 8. Writing and balancing equations for nuclear transmutation tent of their effects on matter (Section 24.4) (Section 24.3) 13. The units ofradiation dose; the effects on living tissue of var- 9. Calculating radiation dose and converting units (Section 24.4) ious dosage levels; the inverse relationship between the mass and 10. Calculating the mass defect and its energy equivalent in J and charge of an emission and its penetrating power (Section 24.4) eV (Section 24.6) 14. How ionizing radiation creates free radicals that damage tis- 11. Calculating the binding energy per nucleon and using it to sue; sources and risks of ionizing radiation (Section 24.4) compare stabilities of nuclides (SP 24.6)
  • 39. 1082 Chapter 24 Nuclear Reactions and Their Applications Section 24.1 band of stability (1050) Section 24.3 free radical (1063) radioactivity (1046) strong force (1051) nuclear transmutation (1059) background radiation (1064) nucleon (1046) decay (disintegration) series deuteron (1060) Section 24.5 nuclide (1046) (1053) particle accelerator (1060) tracer (1066) isotope (1046) Section 24.2 transuranium element (1061) Section 24.6 alpha (a) particle (1047) activity (31) (1054) Section 24.4 fission (1070) beta (f3) particle (1047) becquerel (Bq) (1054) excitation (1062) fusion (1070) gamma ("'/)ray (1047) curie (Ci) (1054) nonionizing radiation (1062) mass defect (1071) alpha decay (1048) decay constant (1054) ionization (1062) nuclear binding energy (1071) beta decay (1049) half-life (t1/2) (1054) ionizing radiation (1062) electron volt (eV) (1071) positron decay (1049) Geiger-Muller counter (1055) gray (Gy) (1063) Section 24.7 positron (1049) scintillation counter (1055) rad (radiation-absorbed dose) chain reaction (1074) electron capture (1049) radioisotopic dating (1057) (1063) critical mass (1074) gamma emission (1049) radioisotope (1057) rem (roentgen equivalent for reactor core (1076) N/2 ratio (1050) man) (1063) stellar nucleogenesis (1078) sievert (Sv) (1063) Key Equations and Relationships 24.1 Balancing a nuclear equation (1048): 24.5 Finding the half-life of a radioactive nuclide (1056): ~~:~[1Reactants = ~~:~[1 Products In 2 24.2 Defining the unit of radioactivity (curie, Ci) (1054): tl/2=1:: 1 Ci = 3.70X 1010 disintegrations per second (d/s) 24.6 Calculating the time to reach a given specific activity (age 24.3 Expressing the decay rate (activity) for radioactive nuclei of an object in radioisotopic dating) (1058): (1054): 1 .silo t= -In- 6.N k slt Decay rate (.sil) = -----s:r = kN 24.7 Using Einstein's equation and the mass defect to calculate 24.4 Finding the number of nuclei remaining after a given time, the nuclear binding energy (1070): Nt (1056): 6.E = 6.mc2 24.8 Relating the atomic mass unit to its energy equivalent in MeV (1071): 1 amu = 931.5X 106 eV = 931.5 MeV ~ ~ and Tables These figures (F) and tables (T) provide a review of key ideas. T24.2 Modes ofradioactive decay (1048) F24.2 N vs. Z for the stable nuclides (1051) T24.1 Chemical vs. nuclear reactions (1045) F24.4 Decrease in number of 14Cnuclei over time (1056) F24.1Radioactive emissions in an electric field (1047) F24.13The variation in binding energy per nucleon (1073) Br·ief Solutions to follow-up Problems 24.1 1~~Xe --- l~~CS + -?f3 1 .silo 5730 yr (15.3 d/min.g) 3 24.5 t = -In - = ---In ----- = 4.02X 10 yr 24.2 Phosphorus-31 has a slightly higher N/2 ratio and an even N k slt In 2 9.41 d/rnin-g (16). The mummy case is about 4000 years old. 24.3 (a) N/Z = 1.35; too high for this region of band: f3 decay 24.6 235Uhas 92 [p and 143 6n. (b) Mass too high for stability: a decay Sm = [(92 X 1.007825 amu) + (143 X 1.008665 amu)] 24.41n slt = -kt + In.silo - 235.043924 amu = 1.9151 amu In 2 24 h) 931.5 MeV = - -. - ( X 4.0 days X -- + In (2.5 X 109) 1.9151 amu X ---- 15 h 1 day Binding energy 1 amu = 17.20 nucleon 235 nucleons .silt = 3.0X 107 d/s = 7.591 MeV/nucleon Therefore, 23SU is less stable than 12C.
  • 40. Problems 1083 Problems with colored numbers are answered in Appendix E. (b) Formation of silver-l 07 through electron capture Sections match the text and provide the numbers of relevant Cc) Formation ofpolonium-206 through a decay sample problems. Most offer Concept Review Questions, 24.13 Write balanced nuclear equations for the following: Skill-Building Exercises (grouped in pairs covering the same (a) Production of 2~~Am through 13 decay concept), and Problems in Context. Comprehensive Problems (b) Formation of 2~~Ac through [3 decay are based on material from any section or previous chapter. Cc) Formation of2g~Bi through a decay Radioactive Decay and Nuclear Stability 24.14 Write balanced nuclear equations for the following: (Sample Problems 24.1 to 24.3) (a) Formation of 186Ir through electron capture •• Concept Review Questions (b) Formation of francium-221 through a decay 24.1 How do chemical and nuclear reactions differ in (c) Formation of iodine-129 through [3 decay (a) Magnitude of the energy change? 24.15 Write balanced nuclear equations for the following: (b) Effect on rate of increasing temperature? (a) Formation of 52Mn through positron emission (c) Effect on rate of higher reactant concentration? (b) Formation ofpolonium-215 through a decay (d) Effect on yield of higher reactant concentration? (c) Formation of 81 Kr through electron capture 24.2 Sulfur has four naturally occurring isotopes. The one with the 24.16 Which nuclide(s) would you predict to be stable? Why? lowest mass number is sulfur-32, which is also the most abun- (a) 2g0 Cb) ~~Co (c) ~Li dant (95.02%). 24.17 Which nuclide(s) would you predict to be stable? Why? (a) What percentage of the S atoms in a matchhead are 32S? (a) 1~8Nd (b) Il~Cd Cc) ~~Mo .......... _._._ __ ._._._ . (b) The isotopic mass of 32S is 31.972070 amu. Is the atomic mass of S larger, smaller, or equal to this mass? Explain. 24.18 Which nuclide(s) would you predict to be stable? Why? 24.3 What led Marie Curie to draw the following conclusions? Ca) 1271 (b)tin-106 (c) 68As (a) Radioactivity is a property of the element and not the com- 24.19 Which nuclidets) would you predict to be stable? Why? (a) 48K Cb) 79Br (c) argon-32 pound in which it is found. (b) A highly radioactive element, aside from uranium, occurs in 24.20 What is the most likely mode of decay for each? pitchblende. (a) 2§~U Cb) i~Cr Cc) ~~Mn 24.4 Which of the following types of radioactive decay produce 24.21 What is the most likely mode of decay for each? an atom of a different element: (a) alpha; (b) beta; (c) gamma; (a) ~~Fe (b) i~Cl (c) I~Ru ------ (d) positron; (e) electron capture? Show how Z and N change, if 24.22 What is the most likely mode of decay for each? at all, with each type. (a) 15C (b) 120Xe (c) 224Th 24.5 Why is ~He stable but ~He so unstable that it has never been 24.23 What is the most likely mode of decay for each? detected? (a) 234Th (b) 141Eu (c) 241Am 24.6 How do the modes of decay differ for a neutron-rich nuclide and a proton-rich nuclide? 24.24 Why is ~~Cr the most stable isotope of chromium? 24.7 Why can't you use the position of a nuclide's NjZ ratio rela- 24.25 Why is i8Ca the most stable isotope of calcium? tive to the band of stability to predict whether it is more likely to _ Problems in Context decay by positron emission or by electron capture? 24.26 Neptunium-237 is the parent nuclide of a decay series that EJ Skill-Building Exercises (grouped in similar pairs) starts with a emission, followed by [3 emission, and then two 24.8 Write balanced nuclear equations for the following: more a emissions. Write a balanced nuclear equation for each (a) Alpha decay of 2§iu step. (b) Electron capture by neptunium-232 24.27 Why is helium found in deposits of uranium and thorium (c) Positron emission by l~N ores? What kind of radioactive emission produces it? 24.9 Write balanced nuclear equations for the following: 24.28 In the natural decay series that starts with uranium-235, a (a) Beta decay of sodium-26 sequence of a and [3emissions ends with lead-207. How many a (b) Beta decay offrancium-223 and 13 particles are emitted per atom of uranium-235 to result in (c) Alpha decay of 2gBi an atom of lead-20?? 24.10 Write balanced nuclear equations for the following: The Kinetics of Radioactive Decay (a) Beta emission by magnesium-27 (Sample Problems 24.4 and 24.5) (b) Neutron emission by ~Li Concept Review Questions (c) Electron capture by 1~~Pd 24.29 What electronic process is the basis for detecting radioac- 24.11 Write balanced nuclear equations for the following: tivity in (a) a scintillation counter; (b) a Geiger-Muller counter? (a) Simultaneous 13 and neutron emission by helium-S 24.30 What is the reaction order of radioactive decay? Explain. (b) Alpha decay of polonium-21S 24.31 After 1 minute, half the radioactive nuclei remain from an (c) Electron capture by l~gIn original sample of six nuclei. Is it valid to conclude that tl/2 24.12 Write balanced nuclear equations for the following: equals 1 minute? Would this conclusion be valid if the original (a) Formation of i~Ti through positron emission sample contained 6X 1012 nuclei? Explain.
  • 41. 1084 Chapter 24 Nuclear Reactions and Their Applications 24.32 Radioisotopic dating depends on the constant rate of decay 24.52 Why does bombardment with protons usually require and formation of various nuclides in a sample. How is the pro- higher energies than bombardment with neutrons? portion of 14Ckept relatively constant in living organisms? IB!i'!i Skill-Building Exercises (grouped in similar pairs) Skill-Building Exercises (grouped in similar pairs) 24.53 Determine the missing species in these transmutations, and 24.33 What is the specific activity (in Ci/g) if 1.55 mg of an write a full nuclear equation from the shorthand notation: isotope emits 1.66 Xl 06 ex particles per second? (a) lOB (o.,n) _ 24.34 What is the specific activity (in Ci/g) if 2.6 g of an isotope (b) 28Si (d,_) 29p (the deuteron, d, is 2H) emits 4.13 X 108 13 particles per hour? (c) _ (o..Zn) 244Cf 24.54 Determine the missing species in these transmutations, and 24.35 What is the specific activity (in Bq/g) if 8.58 Jl-g of an express each process in shorthand notation: isotope emits 7 A Xl 04 ex particles per minute? (a) Bombardment of a nuclide with a "I photon yields a proton, a 24.36 What is the specific activity (in Bq/g) if 1.07 kg of an neutron, and 29Si. isotope emits 3.77X 10713 particles per minute? (b) Bombardment of 252Cf with lOByields five neutrons and a 24.37 If one-trillionth of the atoms of a radioactive isotope disin- nuclide. tegrate each hour, what is the decay constant of the process? (c) Bombardment of 238Uwith a particle yields three neutrons 24.38 If 2.8X 10-10% of the atoms of a radioactive isotope disin- and 239pU. tegrate in 1.0 yr, what is the decay constant of the process? r:::1I Problem in Context 24.39 If 1.00X 10-12 mol of l35Cs emits 1.39XlO5 13 particles in 24.55 Names for elements 104, 105, and 106 have been approved 1.00 yr, what is the decay constant? as rutherfordium (Rf), dubnium (Db), and seaborgium (Sg), re- 24.40 If 6AOXlO-9 mol of 176Wemits 1.07 X 1015 positrons in spectively. These elements are synthesized from californium- 1.00 h, what is the decay constant? 249 by bombarding with carbon-12, nitrogen-IS, and oxygen-I 8 nuclei, respectively. Four neutrons are formed in each reaction 24.41 The isotope 2gBi has a half-life of 1.01 yr. What mass (in as well. (a) Write balanced nuclear equations for the formation mg) of a 2.00-mg sample will not decay after 3.75 X 103 h? of these elements. (b) Write the equations in shorthand notation. 24.42 The half-life of radium-226 is 1.60X 103 yr. How many hours will it take for a 2.50-g sample to decay to the point where The Effects of Nuclear Radiation on Matter 0.185 g of the isotope remains? Concept Review Questions 24.43 A rock contains 270 urnol oe38U (tl/2 = 4.5 X 109 yr) and 24.56 Gamma radiation and UV radiation cause different 110 u.mol of 206Pb. Assuming that all the 206Pb comes from processes in matter. What are they and how do they differ? decay of the 238U,estimate the rock's age. 24.57 What is a cation-electron pair, and how does it form? 24.44 A fabric remnant from a burial site has a 14CYC ratio of 24.58 Why is ionizing radiation more dangerous to children than 0.735 of the original value. How old is the fabric? to adults? 24.59 Why is ·OH more dangerous in an organism than OH-? Problems in Context 24.45 Due to decay of 40K, cow's milk has a specific activity of ••• Skill-Building Exercises (grouped in similar pairs) about 6X 10-11 mCi per milliliter. How many disintegrations of 24.60 A 135-lb person absorbs 3.3X 10-7 J of energy from 40Knuclei are there per minute in 1.0 qt of milk? radioactive emissions. (a) How many rads does she receive? 24.46 Plutonium-239 (tl/2 = 2041 X 104 yr) represents a serious (b) How many grays (Gy) does she receive? nuclear waste disposal problem. If seven half-lives are required 24.61 A 3.6-kg laboratory animal receives a single dose of to reach a tolerable level of radioactivity, how long must 239pU 8.92X 10-4 Gy. (a) How many rads did the animal receive? be stored? (b) How many joules did the animal absorb? 24.47 A rock that contains 2.1XlO-I5 mol of 232Th (t1/2 = 24.62 A 70.-kg person exposed to 90Sr absorbs 6.0X 105 13 parti- lAX 1010 yr) has 9.5X104 fission tracks, each representing the cles, each with an energy of 8.74X 10-14 J. (a) How many grays fission of one atom of 232Th.How old is the rock? does the person receive? (b) If the RBE is 1.0, how many mil- 24.48 A volcanic eruption melts a large area of rock, and all gases lirems is this? (c) What is the equivalent dose in sieverts (Sv)? are expelled. After cooling, i~Ar accumulates from the ongoing 24.63 A laboratory rat weighs 265 g and absorbs 1.77 X 1010f3 par- decay of i8K in the rock (tl/2 = 1.25 X 109 yr). When a piece ticles, each with an energy of 2.20X 10-13 J. (a) How many rads of rock is analyzed, it is found to contain 1.38 mmol of 40K and does the animal receive? (b) What is this dose in Gy? (c) If the 1.14 mmol of 40Ar. How long ago did the rock cool? RBE is 0.75, what is the equivalent dose in Sv? Nuclear Transmutation: Induced Changes in Nuclei •• Problems in Context Concept Review Questions 24.64 If 2.50 pCi [I pCi (picocurie) = I X 10-12 Ci] of radioac- 24.49 Irene and Frederic Joliot-Curie converted i~Al to ~gP in tivity from 239puis emitted in a 95-kg human for 65 h, and each 1933. Why was this transmutation significant? disintegration has an energy of 8.25XIO-13 J, how many grays 24.50 Early workers mistakenly thought neutron beams were "I ra- does the person receive? diation. Why were they misled? What evidence led to the correct 24.65 A small region of a cancer patient's brain is exposed for conclusion? 27.0 min to 475 Bq of radioactivity from 60Cofor treatment of a 24.51 Why must the electrical polarity of the tubes in a linear ac- tumor. If the brain mass exposed is 1.588 g and each 13 particle celerator be reversed at very short time intervals? emitted has an energy of 5.05 X 10-14 J, what is the dose in rads?
  • 42. Problems 1085 binding energy (a) per nucleon in MeV; (b) per atom in MeV; (c) per mole in kJ. E:::1 Concept Review Questions 24.82 Iodine-131 is one of the most important isotopes used in 24.66 Describe two ways that radioactive tracers are used in or- the diagnosis of thyroid cancer. One atom has a mass of ganisms. 130.906114 amu. Calculate the binding energy (a) per nucleon in 24.67 Why is neutron activation analysis (NAA) useful to art his- MeV; (b) per atom in MeV; (c) per mole in kJ. torians and criminologists? 24.68 Positrons cannot penetrate matter more than a few atomic le Problem in Context diameters, but positron emission of radiotracers can be moni- 24.83 The 80Br nuclide decays either by 13 decay or by elec- tored in medical diagnosis. Explain. tron capture. (a) What is the product of each process? 24.69 A steel part is treated to form some iron-59. Oil used to lu- (b) Which process releases more energy? (Masses of atoms: bricate the part emits 298 13 particles (with the energy charac- 80Br = 79.918528 amu; 80Kr = 79.916380 amu; 80Se teristic of 59Fe)per minute per milliliter of oil. What other infor- 79.916520 amu; neglect the mass of the electron involved.) mation would you need to calculate the rate of removal of the Fission Fusion steel from the part during use? le Concept Review Questions ~ Problem in Context 24.84 What is the minimum number of neutrons from each 24.70 The oxidation of methanol to formaldehyde can be accom- fission event that must be absorbed by other nuclei for a chain plished by reaction with chromic acid: reaction to occur? 6H+(aq) + 3CH30H(aq) + 2H2Cr04(aq) - 24.85 In what main way is fission different from radioactive de- 3CH20(aq) + 2Cr3+(aq) + 8H20(I) cay? Are all fission events in a chain reaction identical? Explain. The reaction can be studied with the stable isotope tracer 180 24.86 What is the purpose of enrichment in the preparation of fuel and mass spectrometry. When a small amount of CH3180H is rods? How is it accomplished? present in the alcohol reactant, H2CI80 forms. When a small 24.87 Describe the nature and purpose of these components of a amount ofH2Crl804 is present, H2180 forms. Does chromic acid nuclear reactor: (a) control rods; (b) moderator; (c) reflector. or methanol supply the 0 atom to the aldehyde? Explain. 14.88 State an advantage and a disadvantage of heavy-water reac- tors compared to light-water reactors. tnterconversion Mass 24.89 What are the expected advantages of fusion reactors over (Sample Problem 24.6) fission reactors? Note: Use the following data to solve the problems in this 24.90 Why is there more iron in Earth than any other element? section: mass of IH atom = 1.007825 amu; mass of neutron = 24.91 Why do so many nuclides have isotopic masses close to 1.008665 amu. multiples of 4 amu? fJ!!::J Concept Review Questions 24.92 What is the cosmic importance of unstable 8Be? 24.71 Many scientists at first reacted skeptically to Einstein's le Problem in Context equation, E = me". Why? 24.93 The reaction that will probably power the first commercial 24.72 What is a mass defect, and how does it arise? fusion reactor is 24.73 When a nuclide forms from nucleons, is energy absorbed or iH + iH - iHe + bn released? Why? How much energy would be produced per mole of reaction? 24.74 What is the binding energy per nucleon? Why is the binding (Masses of atoms: iH = 3.01605 amu; iH = 2.0140 amu; energy per nucleon, rather than per nuclide, used to compare nu- iHe = 4.00260 amu; mass of {In= 1.008665 amu.) clide stability? lE! Skill-Building Exercises (grouped in similar pairs) rehensive Problems 24.75 A 3H nucleus decays with an energy of 0.01861 MeV Con- 24.94 Some 2~~Amwas present when Earth formed, but it all de- vert this energy into (a) electron volts; (b) joules. cayed in the next billion years. The first three steps in this decay 24.76 Arsenic-84 decays with an energy of 1.57X 10-15 kJ per nu- series are emission of an ex particle, a 13 particle, and another cleus. Convert this energy into (a) eV; (b) MeV ex particle. What other isotopes were present on the young Earth 24.77 How many joules are released when 1.0 mol of 239pU in a rock that contained some 2~~Am? decays, if each nucleus releases 5.243 MeV? 24.95 Curium-243 undergoes ex decay to plutonium-239: 243Cm_ 239pU+ 4He 24.78 How many MeV are released per nucleus when 3.2X 10-3 mol of chromium-49 releases 8.11 X 105 kJ? (a) Calculate the change in mass, Sm (in kg). (Masses: 243Cm = 243.0614 amu; 239pU = 239.0522 amu; 4He = 4.0026 amu; 24.79 Oxygen-16 is one of the most stable nuclides. The mass of 1 amu = 1.661 X 10-24 g.) a 160 atom is 15.994915 amu. Calculate the binding energy (b) Calculate the energy released in joules. (a) per nucleon in MeV; (b) per atom in MeV; (c) per mole in kJ. (c) Calculate the energy released in kl/rnol of reaction, and com- 24.80 Lead-206 is the end product of 238Udecay. One 206Pbatom ment on the difference between this value and a typical heat of has a mass of 205.974440 amu. Calculate the binding energy reaction for a chemical change of a few hundred kl/mol, (a) per nucleon in MeV; (b) per atom in MeV; (c) per mole in kJ. 24.96 Plutonium "triggers" for nuclear weapons were manufac- 24.81 Cobalt-59 is the only stable isotope of this transition metal. tured at the Rocky Flats plant in Colorado. An 85-kg worker One 59COatom has a mass of 58.933198 amu. Calculate the inhaled a dust particle containing 1.00 fLg of 2§~PU,which
  • 43. 1086 Chapter 24 Nuclear Reactions and Their Applications resided in his body for 16 h (t 1/2 of 239pu = 2.41 X 104 yr; each 24.106 Technetium-99m is a metastable nuclide used in numerous disintegration released 5.15 MeV). (a) How many rads did he re- cancer diagnostic and treatment programs. It is prepared just be- ceive? (b) How many grays? fore use because it decays rapidly through -y emission: 24.97 Archeologists removed some charcoal from a Native Amer- 99mTc --->- 99Tc + -y ican campfire, burned it in O2, and bubbled the CO2 formed into Use the data below to determine: Ca(OH)2 solution (limewater). The CaC03 that precipitated was (a) The half-life of 99mTc filtered and dried. If 4.38 g of the CaC03 had a radioactivity of (b) The percentage of the isotope that is lost if it takes 2.0 h to 3.2 d/min, how long ago was the campfire? prepare and administer the dose 24.98 A 5.4-f.Lg sample of 226RaCI2 has a radioactivity of 1.5 X 105 Bq. Calculate tl/2 of 226Ra.. Time (h) 'Y Emission (photons/s) 24.99 How many rads does a 65-kg human receive each year from the approximately 10-8 g of I~C naturally present in her body o 5000. 4 3150. (t1/2 = 5730 yr; each disintegration releases 0.156 MeV)? 8 2000. 24.100 The major reaction taking place during hydrogen burning 12 1250. in a young star is 16 788 4J H --->- iHe + 2?[3 + 28-y + energy How much energy (in Me V) is released per He nucleus formed? 20 495 Per mole of He? (Masses: ]H atom = 1.007825 amu; 24.107 How many curies are produced by 1.0 mol of 40K (t1/2 = iHe atom = 4.00260 amu; positron = 5.48580X 10-4 amu.) 1.25 X 109 yr)? How many becquerels? 24.101 A sample of AgCI emits 175 nCi/g. A saturated solution 24.108 The fraction of a radioactive isotope remaining at time t is prepared from the solid emits 1.25 Xl 0-2 Bq/mL due to radioac- (1)111112, where l vr: is the half-life. If the half-life of carbon-14 is tive Ag + ions. What is the molar solubility of AgCl? 5730 yr, what fraction of carbon-14 in a piece of charcoal re- 24.102 Due to burning of fossil fuels, the proportion of CO2 in our mains after (a) 10.0 yr; (b) 1O.0X 103 yr; (c) 1O.0X 104 yr? atmosphere continues to increase. Moreover, as a result of nu- (d) Why is radiocarbon dating more reliable for the fraction re- clear explosions and similar events, the CO2 also contains more maining in part (b) than that in part (a) or in part (c)? 14C. How will these factors affect the efforts of future archeolo- 24.109 The isotopic mass of 2~~Rn is 209.989669 amu. When this gists to determine ages of our artifacts by radiocarbon dating? nuclide decays by electron capture, it emits 2.368 MeY. What is 24.103 What fraction of the 235U (t 1/2 = 7 .OX 108 yr) created when the isotopic mass of the resulting nuclide? Earth was formed would remain after 2.8 Xl 09 yr? 24.110 Exactly 0.1 of the radioactive nuclei in a sample decay 24.104 In the event of a nuclear accident, radiation officers must each hour. Thus, after n hours, the fraction of nuclei remaining is obtain many pieces of data to decide on appropriate action. (0.900)". Find the value of n equal to one half-life. (a) If a person ingests radioactive material, which of the follow- 24.111 In neutron activation analysis (NAA), stable isotopes are ing is the most important quantity in deciding whether a serious bombarded with neutrons. Depending on the isotope and the en- medical emergency has occurred? ergy of the neutron, various emissions are observed. What are (1) The number of rems he receives the products when the following neutron-activated species de- (2) The number of curies he absorbs cay? Write an overall equation in shorthand notation for the re- (3) The length of time he is exposed to the radiation action starting with the stable isotope before neutron activation. (4) The number of moles of radioisotopes he ingests (a) ~~V* --->- [[3 emission] (5) The energy emitted per disintegration by the radioisotopes (b) ~~Cu* --->- [positron emission] (b) If the drinking water in a town becomes contaminated with radioactive material, what is the most important factor in decid- (c) i~Al* --->- [[3 emission] ing whether drastic and expensive action is warranted? 24.112 In the 1950s, radioactive material was spread over the land (1) The radioactivity per volume, Ci/m3 from above-ground nuclear tests. A woman drinks some contam- (2) How long the water supply has been contaminated inated milk and ingests 0.0500 g of 90Sr, which is taken up by (3) (Ci/m3) X energy per disintegration bones and teeth and not eliminated. (a) How much 90Sr (tl/2 = (4) The type of radiation emitted 29 yr) is present in her body after 10 yr? (b) How long will it take (5) The radioisotopes involved for 99.9% of the 90Sr to decay? 24.105 Cosmologists modeling the origin of the elements postu- 24.113 Isotopic abundances are relatively constant throughout late nuclides with very short half-lives. Earth's crust. Could the science of chemistry have developed if, (a) One of these nuclides, 8Be (t1/2 = 7XlO-17 s), plays a key for example, one sample of tin(II) oxide contained mostly 112Sn role in stellar nucleogenesis (p. 1078) because it must fuse with and another mostly 124Sn? Explain. a 4He to form 12C before decaying. Another explanation in- 24.114 What volume of radon will be produced per hour at STP volves the simultaneous fusion of three 4He nuclei to form 12c. from 1.000 g of 226Ra (tl/2 = 1599 yr; 1 yr = 8766 h; mass of Comment on the validity of this alternative mechanism. one 226Ra atom = 226.025402 amu)? (b) Another question involves the instability of the two nuclides 24.115 A sample of 9°Kr (t1/2 = 32 s) is to be used in a study of a with A = 5, SHe and sLi, each of which has a tl/2 nearly 10-5 patient's respiration. How soon after being made must it be ad- times that of 8Be. Write nuclear equations for the 0' decay of 8Be, ministered to the patient if the activity must be at least 90% of SHe, and sLi. the original activity?
  • 44. Problems 1087 24.116 Which isotope in each pair would you predict to be more 240125 Tritium eH; t1/2 = 12.26 yr) is continually formed in the stable? Why? upper troposphere by interaction of solar particles with nitrogen. (a) l~~CSor l~~CS (b) ~~Bror ~~Br As a result, natural waters contain a small amount of tritium. (c) r~Mg or riMg (d) ljN or l~N Two samples of wine are analyzed, one known to be made in 24.117 A sample of bone contains enough strontium-90 (t1/2 1941 and another made earlier. The water in the 1941 wine has 29 yr) to emit 8.0 X 104 I?> particles per month. How long will it 2.32 times as much tritium as the water in the other. When was take for the emission to decrease to 1.0X 104 particles per the other wine produced? month? 24.126 Plutonium-239 (t1/2 = 2.41 X 104 yr) is a serious radiation 24.118 The 23rd -century starship Enterprise uses a substance hazard present in spent uranium fuel from nuclear power plants. called "dilithium crystals" as its fuel. How many years does it take for 99% of the plutonium-239 in (a) Assuming this material is the result of fusion, what is the spent fuel to decay? product of the fusion of two 6Li nuclei? 24.127 Carbon from the most recent remains of an extinct (b) How much energy is released per kilogram of dilithium Australian marsupial, called Diprotodon, has a specific activity of formed? (Mass of one 6Li atom is 6.015121 amu.) 0.61 pCi/g. Modem carbon has a specific activity of 6.89 pCi/g. (c) When four 'n atoms fuse to form 4He, how many positrons How long ago did the Diprotodon apparently become extinct? are released? 24.128 The reaction that allows for radiocarbon dating is the con- (d) To determine the energy potential of the fusion processes in tinual formation of carbon-14 in the upper atmosphere: parts (b) and (c), compare the changes in mass per kilogram of ljN + bn --* l~C + (H dilithium and of 4He. What is the energy change associated with this process in (e) Compare the change in mass per kilogram in part (b) to that eV/reaction and in kJ/mol reaction? (Masses of atoms: ljN = for the formation of 4He by the method used in current fusion re- 14.003074 amu; l~C = 14.003241 amu; (H = 1.007825 amu; actors (Section 24.7). (For masses, see Problem 24.93.) mass of bn = 1.008665 amu.) (f) Using early 21SI-century fusion technology, how much tri- 24.129 What is the nuclear binding energy of a lithium-7 nucleus tium can be produced per kilogram of 6Li in the following reac- in units of kJ/mol and eV/nucleus? (Mass of a lithium-7 atom = tion: ~Li + bn --* iHe + ~H? When this amount of tritium is 7.016003 amu.) fused with deuterium, what is the change in mass? How does this quantity compare with the use of dilithium in part (b)? 24.130 Suggest a reason the critical mass of a fissionable sub- 24.119 Uranium and radium are found in many rocky soils stance depends on its shape. throughout the world. Both undergo radioactive decay, and one ),4.131 Using early 21st_century technology, hydrogen fusion re- of the products is radon-222, the heaviest noble gas (tl/2 = quires temperatures around 108 K, but lower temperatures can 3.82 days). Inhalation of indoor air containing this gas con- be used if the hydrogen is compressed. In the late 24th century, tributes to many lung cancers. According to Environmental Pro- the starship Leinad uses such methods to fuse hydrogen at 106 K. tection Agency recommendations, the level of radioactivity from (a) What is the kinetic energy of an H atom at 1.00 X 106 K? radon in homes should not exceed 4.0 pCi/L of air. (b) How many H atoms are heated to 1.00X106 K from the en- (a) What is the safe level of radon in Bq/L of air? ergy of one H and one anti-H atom annihilating each other? (b) A home has a radon measurement of 43.5 pCi/L. The owner (c) If these H atoms fuse into 4He atoms (with the loss of two vents the basement in such a way that no more radon enters the positrons per 4He formed), how much energy (in J) is generated? living area. What is the activity of the radon remaining in the (d) How much more energy is generated by the fusion in (c) than room air (in Bq/L) after 8.5 days? by the hydrogen-antihydrogen collision in (b)? (c) How many more days does it take to reach the EPA recom- (e) Should the captain of the Leinad change the technology and mended level? produce 3He (mass = 3.01603 amu) instead of4He? 24.120 Nuclear disarmament could be accomplished if weapons 24.132 A metastable (excited) form of 50SCchanges to its stable were not "replenished." The tritium in warheads decays to he- form by emitting 'Yradiation with a wavelength of 8.73 pm. lium with a half-life of 12.26 yr and must be replaced or the What is the change in mass of 1 mol of the isotope when it un- weapon is useless. What fraction of the tritium is lost in 5.50 yr? dergoes this change? 24.121 A decay series starts with the synthetic isotope 2§~U.The 24.133 A sample of cobalt-60 (tl/2 = 5.27 yr), a powerful 'Yemitter first four steps are emissions of a I?> particle, another I?>, an 0' par- used to treat cancer, was purchased by a hospital on March 1, ticle, and another 0'. Write a balanced nuclear equation for each 2005. The sample must be replaced when its activity reaches step. Which natural series could be started by this sequence? 70.% of the original value. On what date must it be replaced? 24.122 How long can a 48-lb child be exposed to 1.0 mCi of radi- 24.134 Uranium-233 decays to thorium-229 by 0' decay, but the ation from 222Rnbefore accumulating 1.0 mrad if the energy of emissions have different energies and products: 83% emit an 0' each disintegration is 5.59 MeV? particle with energy 4.816 MeV and give 229Th in its ground 24.123 The approximate date of a San Francisco earthquake is to state; 15% emit an 0' particle of 4.773 MeV and give 229Thin ex- be found by measuring the 14Cactivity (t1/2 = 5730 yr) of parts cited state I; and 2% emit a lower energy 0' particle and give of a tree uprooted during the event. The tree parts have an activ- 229Thin the higher excited state n. Excited state Il emits a 'Yray ity of 12.9 d/min-g C, and a living tree has an activity of of 0.060 MeV to reach excited state 1. (a) Find the 'Y-rayenergy 15.3 d/min-g C. How long ago did the earthquake occur? and wavelength that would convert excited state I to the ground 24.124 Were organisms a billion years ago exposed to more or less state. (b) Find the energy of the 0' particle that would convert ionizing radiation than similar organisms today? Explain. 233Uto excited state n.
  • 45. 1088 Chapter 24 Nuclear Reactions and Their Applications 24.135 Uranium-238 undergoes a slow decay step (tl/2 = 4.5 X 109 24.142 Determine the age of a rock containing 0.065 g of uranium- yr) followed by a series of fast steps to form the stable isotope 238 (t1/2 = 4.5 X 109 yr) and 0.023 g oflead-206. (Assume all the 206Pb. Thus, on a time scale of billions of years, 238U effectively lead-206 came from 238U decay.) decays "directly" to 206Pb, and the relative amounts of these iso- 24.143 Plutonium-242 decays to uranium-238 by emission of an ex topes are used to find the age of some rocks (see margin note, particle with an energy of 4.853 MeV The 238U that forms is un- p. 1059). Two students derive equations relating number of half- stable and emits a'Y ray (lI. = 0.02757 nm). (a) Write balanced lives (n) since the rock formed to the amounts of the isotopes: equations for these reactions. (b) What would be the energy of the ex particle if 242pU decayed directly to the more stable 238U? I 11 20~U Student 1: ('2) = 2~~Pb 24.144 Seaborgium-263 (Sg; Z = 106) was the first isotope of this element synthesized. It was made, together with four neutrons, I 11 20~U by bombarding californium-249 with oxygen-18. It then de- Student 2: = 238U + 206Pb ('2) 92 82 cayed by three ex emissions. Write balanced equations for the (a) Which equation is correct, and why? synthesis and three decay steps of 263Sg. (b) If a rock contains exactly twice as much 238U as 206Pb, what 24.145 Some nuclear power plants use plutonium-239, which is is its age in years? produced in breeder reactors (see margin note, p. 1077). The 24.136 In the naturally occurring thorium-232 decay series, the rate-determining step is the second (3emission. How long does it steps emit this sequence of particles: ex, (3, (3, ex, ex, ex, ex,(3, (3, and take to make 1.00 kg of 239pU if the reaction is complete when ex. Write a balanced equation for each step. the product is 90. % 239pu? 24,137 At death, a nobleman in ancient Egypt was mummified and 24.146 A random-number generator can be used to simulate the his body contained lAXlO-3 g of 40K (t1/2 = 1.25X109 yr), probability of a given atom decaying over a given time. For ex- 1.2XlO- 8 g of 14C (t1/2 = 5730 yr), and 4.8XlO-14 g of 3H ample, the formula "= RANDO" in the Excel spreadsheet returns (t1/2 = 12.26 yr). Which isotope would give the most accurate a random number between 0 and I; thus, for one radioactive estimate of the mummy's age? Explain. atom and a time of one half-life, a number less than 0.5 means 24.138 Assuming that many radioactive isotopes can be consid- the atom decays and a number greater than 0.5 means it doesn't. ered safe after 20 half-lives, how long will it take for each of the (a) Place the "=RANDO" formula in cells Al to AlO of an Ex- following isotopes to be safe? cel spreadsheet. In cell Bl, place "=IF(A1<0.5, 0,1)." This for- (a) 242Cm (tl/2 = 163 days) mula returns 0 if Al is <0.5 (the atom decays) and 1 if Al is >0.5 (b) 214pO (t1/2 = 1.6x 10-4 s) (the atom does not decay). Place analogous formulas in cells B2 (c) 232Th (t 1/2 = 1.39 X 1010 yr) to BI0 (using the "Fill Down" procedure in Excel). To determine 24.139 An ancient sword has a blade from the early Roman Em- the number of atoms remaining after one half-life, sum cells B 1 pire, around 100 AD, but the wooden handle, inlaid wooden dec- to BIO by placing "=SUM(Bl:BlO)" in cell B12. To create a orations, leather ribbon, and leather sheath have different styles. new set of random numbers, click on an empty cell (e.g., Bl3) Given the following activities, estimate the age of each part. and hit "Delete." Perform 10 simulations, each time recording Which part was made near the time of the blade (t1/2 of 14C = the total number of atoms remaining. Do half of the atoms re- 5730 yr; .silo = 15.3 d/min-g)? main after each half-life? If not, why not? (b) Increase the number of atoms to 100 by placing suitable for- Part .silt (d/min'g) mulas in cells Al to A100, Bl to B100, and B102. Perform 10 simulations, and record the number of atoms remaining each Handle 10.1 time. Are these results more realistic for radioactive decay? Inlaid wood 13.8 Explain. Ribbon 12.1 24.147 In the following Excel-based simulation, the fate of 256 Sheath 15.0 atoms is followed over five half-lives. Set up formulas in columns A and B, as in Problem 24.146, and simulate the 24.140 The starship Voyager, like many other vessels of the newly fate of the sample of 256 atoms over one half-life. Cells designed 24th-century fleet, uses antimatter as fuel. B 1 to B256 should contain I or O. In cell Cl, enter (a) How much energy is released when 1.00 kg each of antimat- "=IF(Bl=O, 0, RAND(»." This returns 0 if the original atom ter and matter annihilate each other? decayed in the previous half-life or a random number between 0 (b) When the antimatter is atomic antihydrogen, a small amount and I if it did not. Fill the formula in Cl down to cell C256. Col- of it is mixed with excess atomic hydrogen (gathered from inter- umn D should have formulas similar to those in B, but with mod- stellar space during flight). The annihilation releases so much ified references, as should columns F, H, and J. Columns E, G, heat that the remaining hydrogen nuclei fuse to form 4He. If each and I should have formulas similar to those in C, but with modi- hydrogen-antihydrogen collision releases enough heat to fuse fied references. In cell B258, enter "=SUM(Bl:B256)." This 1.00 Xl 05 hydrogen atoms, how much energy (in kJ) is released records the number of atoms remaining after the first half-life. per kilogram of antihydrogen? Put formulas in cells D258, F258, H258, and J258 to record (c) Which produces more energy per kilogram of antihydrogen, atoms remaining after subsequent half-lives. the procedure in part (a) or that in part (b)? (a) Ideally, how many atoms should remain after each half-life? 24.141 Use Einstein's equation, the mass in grams of 1 amu, and (b) Make a table of the atoms remaining after each half-life in the relation between electron volts and joules to find the energy four separate simulations. Compare these outcomes to the ideal equivalent (in Me V) of a mass defect of 1 amu. outcome. How would you make the results more realistic?