silberberg chemistry molecular nature of matter and change 4e copy2

Fusing nuclei The Z machine of Sandia National Laboratory, the mostpowerful 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 thefundamental nature of atomic nuclei and their remark-

able practical applications.

Nuclear Reactions andTheir Applications24.1 Radioactive Decay and Nuclear Stability

Components of the NucleusTypesof Radioactive EmissionsTypes of Radioactive Decay;

Nuclear EquationsThe Mode of Decay

24.2 The Kinetics of Radioactive DecayRateof Radioactive DecayRadioisotopic Dating

24.3 Nuclear Transmutation: InducedChanges in NucleiEarlyTransmutation ExperimentsParticle Accelerators

24.4 The Effects of Nuclear Radiationon MatterExcitation and IonizationIonizing Radiation and Living Matter

24.5 Applications of RadioisotopesRadioactive TracersApplications of Ionizing Radiation

24.6 The Interconversion of Mass and EnergyThe MassDefectNuclear Binding Energy

24.7 Applications of Fission and FusionNuclear FissionNuclear Fusion

Far below the outer fringes of the cloud of electrons l~€s the atom'stiny, 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 andbehavior of the nucleus itself, there is the scene of real action, one that holdsenormous potential benefit and great mystery and wonder.

Society is ambivalent about the applications of nuclear research, however. Thepromise of abundant energy and treatments for disease comes hand-in-hand withthe threat of nuclear waste contamination, reactor accidents, and unimaginabledestruction from nuclear war or terrorism. Can the power of the nucleus be har-nessed for our benefit, or are the risks too great? In this chapter, we discuss theprinciples that can help you answer this vital question.

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 theiridentities. In nuclear reactions, the roles are reversed: electrons in their orbitalsare usually bystanders as the nuclei undergo changes that, in nearly every case,form different elements. Nuclear reactions are often accompanied by energychanges a million times greater than those in chemical reactions, energy changesso great that changes in mass are detectable. Moreover, nuclear reaction yieldsand rates are typically not subject to the effects of pressure, temperature, andcatalysis that so clearly influence chemical reactions. Table 24.1 summarizes thegeneral differences between chemical and nuclear reactions.

I1mIID Comparison of Chemical and Nuclear ReactionsChemical Reactions

1. One substance is converted into another, but atoms neverchange identity.

2. Orbital electrons are involved as bonds break and form;nuclear particles do not take part.

3. Reactions are accompanied by relatively small changes inenergy and no measurable changes in mass.

4. Reaction rates are influenced by temperature,concentration, catalysts, and the compound in which anelement occurs.

• discoveryof the atomic nucleus(Section2.4)

• protons,neutrons,massnumber,andthe~Xnotation (Section2.S)

• half-life andfirst-order reaction rate(Section16.4)

Nuclear Reactions

1. Atoms of one element typically are converted into atoms ofanother element.

2. Protons, neutrons, and other particles are involved; orbitalelectrons rarely take part.

3. Reactions are accompanied by relatively large changes inenergy and measurable changes in mass.

4. Reaction rates are affected by number of nuclei, but not bytemperature, catalysts, or, normally, the compound inwhich an element occurs.

IN THIS CHAPTER ... We survey the field of nuclear chemistry, beginning withan investigation of nuclear stability-why some nuclei are stable, whereas oth-ers are unstable and undergo radioactive decay. You'll see how radioactivity isdetected 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 ofradioactive emissions on matter, especially living matter, focusing on somemajor applications in science, technology, and medicine. A major focus is tocalculate the energy released in nuclear fission and fusion and discuss currentand future attempts to harness this energy. Finally, we end with a look at thenuclear processes that create the chemical elements in the stars.

1045

1046

The Tiny, Massive Nucleus If youcould strip the electrons from the atomsin an object and compress the nuclei to-gether, the object would lose only a frac-tion of a percent of its mass, but it wouldshrink to 0.0000000001 % (10-1°%) of itsvolume. An atom the size of the HoustonAstrodome would have a nucleus the sizeof a grapefruit, which would contain vir-tually all the atom's mass.

Chapter 24 Nuclear Reactions and Their Applications

24.1 RADIOACTIVE DECAYAND NUCLEAR STABILITYA stable nucleus remains intact indefinitely, but the great majority of nuclei areunstable. An unstable nucleus exhibits radioactivity: it spontaneously disinte-grates, or decays, by emitting radiation. In the next section, you'll see that eachtype of unstable nucleus has its own characteristic rate of radioactive decay, whichcan 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 inthe discovery of radioactivity, and describe the various types of radioactive decayand how to predict which type occurs for a given nucleus.

The Components of the Nucleus: Terms and NotationRecall from Chapter 2 that the nucleus contains essentially all the atom's massbut is only about 10-4 times its diameter (or 10-12 times its volume). Obviously,the nucleus is incredibly dense: about 1014 g/ml., Protons and neutrons, theelementary particles that make up the nucleus, are collectively called nucleons.The term nuclide refers to a nucleus with a particular composition, that is, withspecific numbers of the two types of nucleons. Most elements occur in nature asa mixture of isotopes, atoms with the characteristic number of protons of the ele-ment but different numbers of neutrons. Therefore, each isotope of an elementhas a particular nuclide that we identify by the numbers of protons and neutronsit contains. The nuclide of the most abundant isotope of oxygen, for example,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 elementaryparticle, or a nuclide-is described by the notation ~X, where X is the symbolfor the particle, A is the mass number, or the total number of nucleons, and Z isthe charge of the particle; for nuclides, A is the sum of protons and neutrons andZ is the number of protons (atomic number). Using this notation, we write thethree 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 protonis also sometimes represented as lH.) The number of neutrons (N) in a nucleusis 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), butone 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 massnumber, for example, chlorine-35 and chlorine-37. Despite some small variations,in naturally occurring samples of an element or its compounds, the isotopes ofthe element are present in particular, fixed proportions. Thus, in a sample ofsodium chloride (or any Cl-containing substance), 75.77% of the Cl atoms arechlorine-35 and the remaining 24.23% are chlorine-37.

To understand this chapter, it's very important for you to be comfortable withnuclear notations, so please take a moment to review Sample Problem 2.2 onp. 51 and Problems 2.37 to 2.44 at the end of Chapter 2.

The Discovery of Radioactivity and the Types of EmissionsIn 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 photographicplate. Becquerel also found that the radiation creates an electric discharge in air,

24.1 Radioactive Decay and Nuclear Stability

thus providing a means for measuring its intensity. Two years later, a youngdoctoral student named Marie Sklodowska Curie began a search for other miner-als that behaved like uranium in this way. She found that thorium minerals alsoemit 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 ofthe 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 moreradioactive than pure uranium, which implied that they contained traces of oneor more as yet unknown, highly radioactive elements. She and her husband, thephysicist 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-tated with bismuth compounds and another that precipitated with alkaline earthcompounds. Through chemical and spectroscopic analysis, Marie Curie was ableto show that these fractions contained two new elements, which she named polo-nium (after her native Poland) and radium. Polonium (Po; Z = 84), the mostmetallic member of Group 6A(l6), lies to the right of bismuth in Period 6.Radium (Ra; Z = 88), which is the heaviest alkaline earth metal, lies under bar-ium in Group 2A(2).

Purifying radium proved to be another arduous task. Starting with several tonsof pitchblende residues from which the uranium had been extracted, Curie pre-pared compounds of the larger Group 2A(2) elements, continually separatingminuscule amounts of radium compounds from enormously larger amounts ofchemically similar barium compounds. It took her four years to isolate 0.1 g ofradium chloride, which she melted and electrolyzed to obtain pure metallicradium.

During the next few years, Henri Becquerel, the Curies, and P. Villard inFrance and Emest Rutherford and his coworkers in England studied the nature ofradioactive emissions. Rutherford and his colleague Frederick Soddy observedthat elements other than radium were formed when radium decayed. In 1902, theyproposed that radioactive emission results in the change of one element intoanother. To their contemporaries, this idea sounded like a resurrection of alchemyand was met with disbelief and ridicule. We now know it to be true: under mostcircumstances, when a nuclide of one element decays, it changes into a nuclideof a different element.

These studies led to an understanding of the three most common types ofradioactive emission:

• Alpha particles (symbolized a or iHe) are dense, positively charged particlesidentical to helium nuclei.

• Beta particles (symbolized r3, r3-, or more usually - ?r3) are negatively chargedparticles identified as high-speed electrons. (The emission of electrons from thenucleus may seem strange, but as you'll see shortly, r3 particles arise as a resultof a nuclear reaction.)

• Gamma rays (symbolized as 'Y, or sometimes 8'Y) are very high-energy pho-tons, about 105 times as energetic as visible light.

The behavior of these three emissions in an electric field is shown in Figure 24.1.Note that a particles bend to a small extent toward the negative plate, r3 particlesbend to a great extent toward the positive plate, and 'Y rays are not affected bythe electric field. We'll discuss the effects of these emissions on matter later.

1047

Her Brilliant Career Marie Curie(1867-1934) is the only person to beawarded Nobel Prizes in two different sci-ences, one in physics in 1903 for her re-search into radioactivity and the other inchemistry in 1911 for the discovery ofpolonium and the discovery, isolation,and study of radium and its compounds.

ZnS-coated screen(or photographic plate)

Leadblock

Radioactivematerial

Voltagesource

mmDI Three types of radioactiveemissions in an electric field. Positivelycharged ex particles bend toward the neg-ative plate; negatively charged 13 particlesbend toward the positive plate. The cur-vature is greater for 13 particles becausethey have much lower mass. The 'I rays,uncharged high-energy photons, are un-affected by the field.

1048 Chapter 24 Nuclear Reactions and Their Applications

Types of Radioactive Decay; Balancing Nuclear EquationsWhen a nuclide decays, it forms a nuclide of lower energy, and the excess energyis carried off by the emitted radiation. The decaying, or reactant, nuclide is calledthe parent; the product nuclide is called the daughter. Nuclides can decay inseveral ways. As we discuss the major types of decay, which are summarized inTable 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 thereactants equal those of the products:

~~~~:~ Reactants = ~~:~l~Products (24.1)

1. Alpha decay involves the loss of an et particle (iHe) from a nucleus. Foreach et particle emitted by the parent nucleus, A decreases by 4 and Z decreasesby 2. Every element that is heavier than lead (Pb; Z = 82), as well as a few lighterones, exhibits et decay. In Rutherford's classic experiment that established theexistence of the atomic nucleus (Section 2.4, pp. 47-48), radium was the sourceof the et particles that were used as projectiles. Radium undergoes ex decay toyield radon (Rn; Z = 86):

emED Modes of Radioactive Decay*

Mode Emission Decay Process

Change in

A Z N

et Decay et CiHe)

Reactant (parent)

f3Decay" 1no

in nucleus

Positron emission t "..%'~,p'

nucleus withxp+ and ynO

hv +

high-energyphoton

Electron capture t °e +-1

absorbed fromlow-energy

orbital

1p1

in nucleus

x-ray photon

-4 -2 -2+

Product (daughter) a expelled

1p•1

in nucleus

+ O~ ()-1

~ expelled

o +1 -1

O~O1

+1o -1+

positron expellednucleus with

(x- 1)p+ and (y+ 1)nO

1noin nucleus

+1o -1

'Y Emission + o o

excitednucleus

o

stablenucleus

y photonradiated

"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.


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 forRn 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 inthe nucleus, but rather the conversion of a neutron into a proton, which remainsin the nucleus, and a f3 particle, which is expelled immediately:

bn -+ ip + -?f3As always, the totals of the A and the Z values for reactant and products are equal.Radioactive nickel-63 becomes stable copper-63 through 13decay:

~~Ni -+ ~§Cu + -?f3Another example is the 13decay of carbon-14, applied in radiocarbon dating:

I~C -+ IjN + -?f3Note that f3 decay results in a product nuclide with the same A but with Zonehigher (one more proton) than in the reactant nuclide. In other words, an atomof the element with the next higher atomic number is formed.

3. Positron decay involves the emission of a positron from the nucleus. Akey idea of modem physics is that every fundamental particle has a correspond-ing antiparticle, another particle with the same mass but opposite charge. Thepositron (symbolized ?13;note the positive Z) is the antiparticle of the electron.Positron decay occurs through a process in which a proton in the nucleus is con-verted into a neutron, and a positron is expelled.' Positron decay has the oppo-site effect of f3 decay, resulting in a daughter nuclide with the same A but with Zone lower (one fewer proton) than the parent; thus, an atom of the element withthe next lower atomic number forms. Carbon-l I , a synthetic radioisotope, decaysto a stable boron isotope through emission of a positron:

l~C -+ l~B + ?f34. Electron capture occurs when the nucleus of an atom draws in an elec-

tron from an orbital of the lowest energy level. The net effect is that a nuclearproton 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 downfrom 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 "I photons froman excited nucleus. Recall that an atom in an excited electronic state reduces itsenergy by emitting photons, usually in the DV and visible ranges. Similarly, anucleus in an excited state lowers its energy by emitting "I photons, which are ofmuch higher energy (much shorter wavelength) than DV photons. Many nuclearprocesses leave the nucleus in an excited state, so 'Yemission accompanies mostother types of decay. Several "I photons ("I rays) of different frequencies can be

*In formal nuclear chemistry terminology, {3decay indicates a more general phenomenon thatalso 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.

1049

The Little Neutral One A neutral par-ticle called a neutrino (v) is also emittedin many nuclear reactions, including thechange of a neutron to a proton:

6n -+ ip + -?f3 + v

Theory suggests that neutrinos have amass much less than 10-4 times that of anelectron, and that at least 109 neutrinosexist in the universe for every proton.Neutrinos interact with matter so slightlythat it would take a piece of lead 1 light-year thick to absorb them. We will not dis-cuss them further, except to mention thatexperiments in Japan in the 1990s de-tected neutrinos and obtained evidencethat they have mass. Using a cathedral-sized pool containing 50,000 tons of ultra-pure water buried 1 mile undergroundin a zinc mine, an international team ofscientists obtained results that suggestthat neutrinos may account for a signifi-cant portion of the "missing" matter in theuniverse and may provide enough mass(and, thus, gravitational attraction) to pre-vent the universe from expanding forever.


emitted from an excited nucleus as it returns to the ground state. Many of MarieCurie'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 ReactionsProblem 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 thetotal of mass numbers and the total of charges on the left side and the right side must beequal, 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 + ~HeSolving for A and Z and balancing the equation: For A, 232 = A + 4, so A = 228. ForZ, 90 = Z + 2, so Z = 88. From the periodic table, we see that the element withZ = 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~SCheck Always read across superscripts and then across subscripts, with the yield arrowas an equal sign, to check your arithmetic. In part (a), for example, 232 = 228 + 4, and90 = 88 + 2.

FOLLOW-UP PROBLEM 24.1 Write a balanced equation for the reaction in whicha nuclide undergoes [3decay and produces cesium-133.

Nuclear Stability and the Mode of DecayThere are several ways that an unstable nuclide might decay, but can we predicthow 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, butsome patterns emerge from observation of the naturally occurring nuclides.

The Band of Stability and the Neutron-to-Proton (N/Z) Ratio A key factor thatdetermines the stability of a nuclide is the ratio of the number of neutrons to thenumber of protons, the N/Z ratio, which we calculate from (A - Z}/Z. For lighternuclides, 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 exceedthe number of protons, and often by quite a lot. But, if the N/Z ratio is either toohigh 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 thestable nuclides. The nuclides form a narrow band of stability that graduallyincreases from an N/Z ratio of 1, near Z = 10, to an N/Z ratio slightly greaterthan 1.5, near Z = 83 for 209Bi. Several key points are as follows:


140

130

120

110

100

90

80<:Cl) 70c2-SQ)

z 60

50

Cl. decay209Bi

N83

~('Z = 1.52) ::......... .

10

Region shown in 8

...107A ••• r ,47 g~ ••!.

( t::' = 1 .28 ) :.r: .z • :.:..:.

.:.: .::i.

....I·: .:.:-:

40 ~~Fe~ ;.!':(t::'=1.15) ;:.Z .i::

:-:....iJ•....

Positron emission and/orelectron capture

30

20

o 60 7010 20 30 40 50Protons (Z)

A

1051

• stable

• ~ emitter

• a emitter

o e- capture and/or positron emitter

W\J••••000•••••00•••••000:H~:8~0••••~Q!00•••• ~~O

"<. _ •••••• O~~ ••• OOOOU

80 I I I I

55 60Protons (Z)

Cl)

c 852-SQ)

z

I

65I

708

80

~ A plot of number of neutrons vs. number of protonsfor the stable nuclides. A, A plot of N vs. Z for all stable nuclidesgives rise to a narrow band that veers above N/Z = 1 shortly beyondZ = 10. The N/Z values for several stable nuclides are given. Themost common modes of decay for unstable nuclides in a particularregion are shown: nuclides with a high N/Z ratio often undergo13 decay; those with a low ratio undergo e- capture or positron emis-sion; heavy nuclei beyond the stable band (and a few lighter ones)undergo Cl. decay. B, The blue box in part A is expanded to show thestable and many of the unstable nuclides in that area. Note themodes of decay: Cl. decay decreases both Nand Z by 2; 13 decay de-

90 creases N and increases Z by 1; positron emission and e- captureincrease N and decrease Z by 1.

• 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 T8Ne are partic-ularly stable.

• The N/Z ratio of stable nuclides gradually increases as Z increases. No stablenuclide 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 stablenuclide. 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 theelements of the fourth transition series (Period 7).

Stability and Nuclear Structure Given that protons are positively charged andneutrons uncharged, what holds the nucleus together? Nuclear scientists answerthis 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 nucleusapart 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 timesstronger than the repulsive force but operates only over the short distances withinthe nucleus. Competition between the attractive strong force and the repulsiveelectrostatic force determines nuclear stability.

1052

I11mIm Number of StableNuclides for Elements 48 to 54*

Atomic No.ofElement No. Nudides

CdInSoSbTeIXe

82

102819

48495051525354

*EvenZ shown in boldface.

I.mlIm An Even-OddBreakdown of the Stable Nuclides

No. ofZ N Nuclides

Even Even 157Even Odd 53Odd Even 50Odd Odd 7

TOTAL 267


Curiously, the oddness or evenness of Nand Z values is related to someimportant patterns of nuclear stability. Two interesting points become apparentwhen we classify the known stable nuclides:

• Elements with an even Z (number of protons) usually have a larger number ofstable nuclides than elements with an odd Z. Table 24.3 demonstrates this pointfor cadmium (Z = 48) through xenon (Z = 54).

• Well over half the stable nuclides have both even N and even Z (Table 24.4).(Only seven nuclides with odd N and odd Z are either stable-s-jl-l, ~Li, l~B,I:jN-or decay so slowly that their amounts have changed little since Earthformed-~~V, 1~~La, and 1~7Lu.)

One model of nuclear structure that attempts to explain these findings postu-lates that protons and neutrons lie in nucleon shells, or energy levels, and thatstability results from the pairing of like nucleons. This arrangement leads to thestability of even values of Nand Z. (The analogy to electron energy levels andthe stability that arises from electron pairing is striking.)

Just as noble gases-the elements with 2, 10, 18, 36, 54, and 86 electrons-are exceptionally stable because of their filled electron shells, nuclides with Nor Z values of 2, 8, 20, 28, 50, 82 (and N = 126) are exceptionally stable.These so-called magic numbers are thought to correspond to the numbers of protonsor neutrons in filled nucleon shells. A few examples are ~gTi (N = 28),~~Sr (N = 50), and the ten stable nuclides of tin (Z = 50). Some extremely sta-ble nuclides have double magic numbers: iHe, l~O, i8Ca, and 2~~Pb (N = 126).

SAMPJE PROBLEM 24.2 Predicting Nuclear StabilityProblem Which of the following nuclides would you predict to be stable and whichradioactive: (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 areeven or odd.

18 - 10Solution (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 mostlikely 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 showsN/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 modethat 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 24.2Ato show all of the stable and many of the radioactive nuclides in that region, aswell as their modes of decay. Note the following points, and then we'll applythem in a sample problem:

1. Neutron-rich nuclides. Nuclides with too many neutrons for stability (a highNIZ) lie above the band of stability. They undergo f3 decay, which converts aneutron into a proton, thus reducing the value of NIZ.


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 ofwhich 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 bandand undergo Cl' decay, which reduces their Z and N values by two units peremission. (Several lighter nuclides also exhibit Cl' decay.)

~A"'~P~.EPROBLEM 24.3 Predicting the Mode of Nuclear DecayProblem Predict the nature of the nuclear change(s) each of the following radioactivenuclides 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 tothe band.Solution (a) This nuclide has an NjZ ratio of 1.4, which is too high for this region of theband. 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 probablyundergo 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, soit 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-ble daughter nuclide forms. The succession of steps is called a decay series, ordisintegration series, and is typically depicted on a gridlike display. Figure 24.3shows the decay series from uranium-238 to lead-206. Numbers of neutrons (N)are plotted against numbers of protons (Z) to form the grid, which displays a seriesof QC and f3 decays. The zigzag pattern is typical and occurs because QC decaydecreases both Nand Z, whereas f3 decay decreases N but increases Z. Note thatit is quite common for a given nuclide to undergo both types of decay. (Gammadecay accompanies many of these steps, but it does not affect the mass or typeof the nuclide.) This decay series is one of three that occur in nature. All end withisotopes of lead whose nuclides all have one (Z = 82) or two (N = 126, Z = 82)magic numbers. A second series begins with uranium-235 and ends with lead-207,and a third begins with thorium-232 and ends with lead-208. (Neptunium-237began a fourth series, but its half-life is so much less than the age of Earth thatonly traces of it remain today.)-Nuclear reactions are not affected by reaction conditions or chemical composition andrelease much more energy than chemical reactions. A radioactive nuclide is unstableand may emit ex particles (~He nuclei), f3 particles (-~f3; high-speed electrons),positrons (~f3), or "/ rays (8,,/; high-energy photons) or may capture an orbital electron(_~e). A narrow band of neutron-to-proton ratios (N/Z) includes those of all the sta-ble nuclides. Radioactive decay allows an unstable nuclide to achieve a more stableN/Z ratio. Certain "magic numbers" of neutrons and protons are associated with verystable 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-richnuclides undergo f3 decay, and proton-rich nuclides undergo positron emission orelectron capture. Three naturally occurring decay series all end in isotopes of lead.

148

146

144

142

140

138

g 136Cf!c 134e:Jill 132Z

130

128

126

124

1053

/adeCay

" ~ decay

12278 80 82 84 86 88 90 92

Protons (Z)

Figure 14.3 The 238U decay series.Uranium-238 (top right) decays through aseries of emissions of ex or [3 particles tolead-206 (bottom left) in 14 steps.


24.2 THE KINETICS OF RADIOACTIVE DECAYChemical and nuclear systems both tend toward maximum stability. Just as theconcentrations in a chemical system change in a predictable direction to give astable equilibrium ratio, the type and number of nucleons in an unstable nucleuschange 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 abouthow long that process will take, and the same holds true for nuclear systems. Inthis section, we examine the kinetics of nuclear change; later, we'll examine theenergetics of such change. To begin, a Tools of the Laboratory essay on the oppo-site page describes how radioactivity is detected and measured.

~ Animation: Radioactive Decay~ Online Learning Center

The Rate of Radioactive DecayRadioactive nuclei decay at a characteristic rate, regardless of the chemical sub-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). Aswe saw with chemical reaction rates, because the number of nuclei is decreasing,a minus sign precedes the expression for the decay rate:

i1NDecay 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 ofradioactivity is the curie (Ci): 1 curie equals the number of nuclei disintegratingeach 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 specificactivity, the decay rate per gram.

An activity is meaningful only when we consider the large number of nucleiin a macroscopic sample. Suppose there are 1X 1015 radioactive nuclei of a par-ticular type in a sample and they decay at a rate of 10% per hour. Although anyparticular nucleus in the sample might decay in a microsecond or in a millionhours, the average of all decays results in 10% of the entire collection of nucleidisintegrating each hour. During the first hour, 10% of the original number, or1X 1014 nuclei, will decay. During the next hour, 10% of the remaining 9X 1014

nuclei, or 9X 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, thenumber 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 obtaini1N

.511 = -- = kN (24.3)I1t

Note that the activity depends only on H raised to the first power (and on theconstant value of k). Therefore, radioactive decay is a first-order process (seeSection 16.4). The only difference in the case of nuclear decay is that we con-sider the number of nuclei rather than their concentration.

Half-Life of Radioactive Decay Decay rates are also commonly expressed in termsof 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 hasthe same meaning for a nuclear change as for a chemical change (Section 16.4).

~ Animation: Half-Life~ Online Learning Center

Counters for the Detection of Radioactive Emissions

Radioactive emissions interact with atoms in surrounding ma-terials. To determine the rate of nuclear decay, we measurethe radioactivity of a sample by observing the effects of these

interactions over time. Because these effects can be electricallyamplified billions of times, it is even possible to detect the decayof a single nucleus. Ionization counters and scintillation countersare two devices used to measure radioactive emissions.

An ionization counter detects radioactive emissions as theyionize a gas. Ionization produces free electrons and gaseouscations, which are attracted to electrodes that conduct a current toa recording device. The most common type of ionization counteris a Geiger-Miiller counter (Figure B24.1). It consists of a tubefilled with argon gas; the tube housing acts as the cathode, and athin wire in the center of the tube acts as the anode. Emissionsfrom the sample enter the tube through a thin window and strikeargon atoms, producing free electrons that are accelerated towardthe anode. These electrons collide with other argon atoms and freemore electrons in an avalanche effect. The current created is am-plified and appears as a meter reading and/or an audible click. Theinitial 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 toionize surrounding atoms are detected by their ability to exciteatoms and cause them to emit light. The light-emitting substancein the counter, called a phosphor, is coated onto part of a photo-multiplier tube, a device that increases the original electrical sig-nal. Incoming radioactive particles strike the phosphor, which

e\ I\ .

/~/ /l /-

Sample ~ //

emits photons. Each photon, in turn, strikes a cathode, releasingan electron through the photoelectric effect (Section 7.1). Thiselectron hits other portions of the tube that release increasingnumbers of electrons, and the resulting current is recorded. Liquidscintillation counters employ an organic mixture that contains aphosphor and a solvent (Figure B24.2). This "cocktail" dissolvesthe sample and emits light when excited by the emission. Thesecounters are often used to measure emissions from dissolved ra-dioactive biological samples.

Figure 824.2 Vials of a scintillation "cocktail" emitting light.A radioactive substance dissolved in an organic mixture (cocktail)emits particles that excite the phosphor component to emit light. Lightintensity is proportional to the concentration of the substance.

Emittedparticle

r~---. \ Argon gas

(+)

e

Towardcathode H

Figure 824.1 Detection of radioactivity by an ionization counter. When an Ar atom absorbs the energy of aradioactive particle (red), it is ionized to an Ar+ ion (purple) and an electron (yellow). The free electron collides withand ionizes another Ar atom. As the process continues, the Ar+ ions migrate to the negative electrode, and theelectrons migrate to the positive electrode, resulting in a current.

1055

1056

~ Decrease in number of 14Cnuclei over time. A plot of number of 14C

nuclei vs. time gives a decreasing curve.In each half-life (5730 years), half the i4C

nuclei present undergo decay. A plot ofmass of i4C vs. time is identical.

Il.mrIm Decay Constants (k)and Half-Lives (t,/2)of Beryllium Isotopes

Nuclide k tV2

~Be

~Be

~BeI~Be

IlBe

l.30X 1O~2/day

l.OX 1016/s

Stable4.3XlO-7/yr

5.02X 1O~2/s

53.3 days6.7X 1O~17 s


'l{o

iIDU::lC

U 1;0 "2 'l{o'0Q;.0 1E "4 'l{o::lZ 1"8 'l{o

0

Numberof nucleiat time t

N..t =

Initial Number ofnumber half-livesof nuclei /

N..o x Wn

After 1sthalf-life (5730 yr)

: After 2ndI half-life (11,460 yr)

-----i------ After 3rd_____~ l half-life (17,190 yr)

t I Y10,000

Time (yr)

20,000

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 + -?f3We can also consider the half-life in terms of mass of substance. As 14C decaysto the product 14N, its mass decreases. If we start with 1.0 g of carbon-14, halfthat 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 nucleipresent, 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 HoIn - -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-ing at any time t. (Note the similarity to Equation 16.4, p. 686.) To calculate thehalf-life (tI/2), we set Nt equal to 1N0 and solve for t1/2:

Ho ~2ln 1.'r = kt1/2 so t1/2 = -k (24.5)

2J' 0

Exactly analogous to the half-life of a first-order chemical change, this half-lifeis not dependent on the number of nuclei and is inversely related to the decayconstant:

large k =? short tl/2 and small k =? long t1/2

The decay constants and half-lives of radioactive nuclides vary over a verywide range, even those for the nuclides of a given element (Table 24.5).

SAMPLE PROBLEM 24.4 Finding the Number of Radioactive NucleiProblem 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 bymammals, 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 fractionof 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, expressedas a fraction of the starting number. The activity of the sample (s1.) is proportional to thenumber of nuclei (H), so we know that

Ho - Ht s1.0 - s1.tFraction 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-orderrate 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).

24.2 The Kinetics of Radioactive Decay 1057

Solution Calculating the decay constant k:

In 2 0.693k = - = -- = 0.024 yr-I

tl/2 29 yr

Applying Equation 24.4 to calculate sat, the activity remaining at time t:

Ho saoIn-=ln-=kt

Ht sa,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/sFraction decayed = ,.// 012

,)CJ-o 1.2X 1 d/sCheck The answer is reasonable: t is about 2 half-lives, so sa, should be about ~sao, orabout 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 thefraction 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

H, (I)'/'1/2In - = In -

Ho 2

In 2tl/2 = k so

or In sao - In sal = kt

So,

0.76

Thus,

Taking the antilog givesN (1)'/11

/2 (1)59/29

Fraction remaining = H~ = 2" = 2" = 0.24

So, Fraction decayed = 1.00 - 0.24 = 0.76

FOLLOW-UP PROBLEM 24.4 Sodium-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, howmuch of the activity is present in the patient's body and excreted fluids after 4.0 days?

Radioisotopic DatingThe historical record fades rapidly with time and virtually disappears for eventsof more than a few thousand years ago. Much of our understanding of prehistorycomes from a technique called radioisotopic dating, which uses radioisotopesto determine the age of an object. The method supplies data about the ages ofobjects in fields as diverse as art history, archeology, geology, and paleontology.

The technique of radiocarbon dating, for which the American chemist WillardF. Libby won the Nobel Prize in chemistry in 1960, is based on measuring theamounts of 14C and 12C in materials of biological origin. The accuracy of themethod falls off after about six half-lives of 14C (t1/2 = 5730 yr), so it is used todate objects up to about 36,000 years old.

Here is how the method works. High-energy neutrons resulting from cosmicray 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 + jpThrough the processes of formation and radioactive decay, the amount of 14C inthe 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 of14C slightly. Taking these factors into account improves the accuracy of the dating method.

1058

The Case of the Shroud of Turin Oneof the holiest Christian relics is the famedShroud of Turin. It is a piece of linen thatbears a faint image of a man's body andwas thought to be the burial cloth used towrap the body of Jesus Christ. In 1988,the Vatican allowed scientific testing ofthe cloth by radiocarbon dating. Threelabs in Europe and the United States inde-pendently measured the 12C:14Cratio of aSO-mg piece of the linen and determinedthat the flax from which the cloth wasmade was grown between 1260 AD and1390 AD. Despite this evidence, theshroud lost none of its fascination: 10years later, in 1998, when the shroud wasagain put on display, about 2 million peo-ple lined up to view it.

Figure 24.5 Radiocarbon dating for de-termining the age of artifacts. The naturallogarithms of the specific activities of 14C(activity/g 14C) for various artifacts areprojected onto a line whose slope equals-k, the negative of the 14C decay con-stant. The age (in years) of an artifact isdetermined from the horizontal axis.


The 14C atoms combine with 02, diffuse throughout the lower atmosphere,and enter the total carbon pool as gaseous 14C02 and aqueous H14C03 -. Theymix with ordinary l2C02 and H12C03 -, reaching a constant 12C:14C ratio of about1012:1. The CO2 is taken up by plants during photosynthesis, and then taken upand excreted by animals that eat the plants. Thus, the l2C: 14C ratio of a livingorganism 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 becausethe amount of 14C decreases as it decays:

l~C _ ljN + -?13The 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 beexpressed in terms of a ratio of activities:

No .woIn-=ln-=ktNt .wt

We use this expression in radiocarbon dating, where stlo is the activity in a liv-ing organism and sl, is the activity in the object whose age is unknown. Solvingfor t gives the age of the object:

1 .wot = - In - (24.6)k .wt

A useful graphical method in radioisotopic dating shows a plot of the natu-ral logarithm of the specific activity vs. time, which gives a straight line with aslope of -k, the negative of the decay constant. Using such a plot and measur-ing the 14C specific activity of an object, we can determine its age; several exam-ples appear in Figure 24.5. To determine the ages of more ancient objects or ofobjects that do not contain carbon, different radioisotopes are measured. (See themargin note on the opposite page.)

3.00

~~ Charcoai from earliest Polynesian culture in H~waii

.i .'.~., Linen,wrap...•.•.p...ing..s.....from Book of Isaia,~; Deq~ s~~.Scrolls

H ' ':!',.,Chhrcoal fr~m earliest settlement in JapaQ

2.00Bur.ASdtree from eruption that createdCrater"Lake, Oregon

Burned bones of sloth in -Ct:1ilEiancave. Earlies,!trace of human presenceat tip of South America

Burned bison bones associated withFolsom Man, found at Lubbock, Texas

Me~6Iithic-Neolithic transitionsite.Belt Cave, Iran

Charcoal from LascauxCaves, France, site of .extensive cavepalntinqs ~ •(see background)

16,000

24_3 Nuclear Transmutation: Induced Changes in Nuclei

SAMPLE PROBLEM 24.5 Applying Radiocarbon DatingProblem The charred bones of a sloth in a cave in Chile represent the earliest evidenceof 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 ratioof 12C:14C in living organisms results in a specific activity of 15.3 d/min-g, how old arethe 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 tofind 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-1t1/2 5730 yr

Calculating the age (t) of the bones:

l.wo 1 (15.3 d/min-g)t = -In - = ------In ----- = 8.89x103 yrk .wt 1.21XlO-4yr-1 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, sothe age should be between one and two half-lives (5730 to 11,460 yr).

FOLLOW·UP PROBLEM 24.5 A sample of wood from an Egyptian mummy casehas 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 ofradioactive nuclei. Nuclear decay is a first-order process, so the half-life does notdepend 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 CHANGESIN NUCLEI

The alchemists' dream of changing base metals into gold was never realized, butin the early 20th century, atomic physicists found that they could change one ele-ment into another. Research into nuclear transmutation, the induced conversionof one nucleus into another, was closely linked with research into atomic struc-ture and led to the discovery of the neutron and to the production of artificialradioisotopes. Later, high-energy bombardment of nuclei in particle acceleratorsbegan a scientific endeavor, which continues to this day, of creating many newnuclides and a growing number of new elements.

Early Transmutation Experiments; Discovery of the NeutronThe first recognized transmutation occurred in 1919, when Emest Rutherfordshowed that Q' particles emitted from radium bombarded atmospheric nitrogen toform a proton and oxygen-17:

'jN + j:He _ iH + I~O

By 1926, experimenters had found that Q' bombardment transmuted most elementswith low atomic numbers to the next higher element, with ejection of a proton.

A notation for nuclear bombardment reactions shows the reactant (target)nucleus to the left and the product nucleus to the right of a set of parentheses,within which a comma separates the projectile particle from the ejected particle(s):

reactant nucleus (particle in, particlets) out) product nucleusUsing this notation, the previous reaction is 14N (o.p) 170.

1059

How Old Is the Solar System?By comparing the ratio of 238Uto its finaldecay product, 206pb,geochemists foundthat the oldest known surface rocks onEarth-granite in western Greenland-are about 3.7 billion years old. The ratioof 238U:206Pbin meteorites gives 4.65 bil-lion years for the age of the Solar System,and therefore Earth. From this and otherisotope ratios, such as 4°K:40Ar (tl/2 of40K = 1.3XIQ9 yr) as well as 87Rb:87Sr(t1/2 of 87Rb= 4.9X 1010 yr), Moon rockscollected by Apollo astronauts have beenshown to be 4.2 billion years old, and theyprovide evidence for volcanic activity onthe Moon's surface about 3.3 billion yearsago. That was about the time that, accord-ing to these methods, the first organismswere evolving on Earth.

1060

The Joliot-Curies in their laboratory.

Protonsource

A


An unexpected finding in a transmutation experiment led to the discovery ofthe neutron. When lithium, beryllium, and. boron were bombarded with a parti-cles, they emitted highly penetrating radiation that could not be deflected by amagnetic or electric field. Unlike "y radiation, these emissions were massiveenough to eject protons from the substances they penetrated. In 1932, JamesChadwick, a student of Rutherford, proposed that these emissions consisted ofneutral 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-lawof 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 27Al (o..n) 30p

Since then, other techniques for producing artificial radioisotopes have beendeveloped. In fact, the majority of the nearly 1000 known radionuclides have beenproduced artificially.

Particle Accelerators and the Transuranium ElementsDuring the 1930s and 1940s, researchers probing the nucleus bombarded elementswith neutrons, a particles, protons, and deuterons (nuclei of the stable hydrogenisotope deuterium, 2H). Neutrons are especially useful as projectiles because theyhave no charge and thus are not repelled as they approach a target nucleus. Theother particles are all positive, so early researchers found it difficult to give themenough energy to overcome their repulsion by the target nuclei. Beginning in the1930s, however, particle accelerators were invented to impart high kinetic ener-gies to particles by placing them in an electric field, usually in combination witha magnetic field. In the simplest and earliest design, protons are introduced at oneend 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 ofincreasing length that, through a source of alternating voltage, change their chargefrom positive to negative in synchrony with the movement of the particle throughthem (Figure 24.6A). A proton, for example, exits the first tube just when thattube becomes positive and the next tube negative. Repelled by the first tube andattracted by the second, the proton accelerates across the gap between them. A40-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

Alternatingvoltage sources

To vacuum

+/- t6

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 thesection 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 StanfordUniversity in California. B

24.3 Nuclear Transmutation: Induced Changes in Nuclei

Alternating voltage source

Path of protonbeam 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 timesfaster, with correspondingly greater kinetic energies.

The cyclotron (Figure 24.7), invented by E. O. Lawrence in 1930, applies theprinciple of the linear accelerator but uses electromagnets to give the particle aspiral path, thus saving space. The magnets lie within an evacuated chamber aboveand below two "dees," open, D-shaped electrodes that function like the tubes inthe linear design. The particle is accelerated as it passes from one dee, which ismomentarily positive, to the other, which is momentarily negative. Its speed andradius increase until it is deflected toward the target nucleus. The synchrotron usesa synchronously increasing magnetic field to make the particle's path circularrather than spiral. 0

Accelerators have many applications, from producing radioisotopes used inmedical applications to studying the fundamental nature of matter. Perhaps theirmost specific application for chemists is the synthesis of transuranium elements,those with atomic numbers higher than uranium, which is the heaviest naturallyoccurring element. Some reactions that were used to form several of these ele-ments appear in Table 24.6. The transuranium elements include the remainingactinides (Z = 93 to 103), in which the Sf sub level is being filled, and the ele-ments in the fourth transition series (Z = 104 to 112), in which the 6d sublevel

Im'm:DI Formation of Some Transuranium NuclidesReaction 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

1061

The Powerful Bevatron The bevatron,used to study the physics of high-energyparticle collisions, includes a linearsection and a synchrotron section. The in-strument at the Lawrence Berkeley Labo-ratory in California increases the kineticenergy of the particles by a factor of morethan 6 billion. A beam of 1010 protonsmakes more than 4 million revolutions, adistance of 300,000 miles, in 1.8 s, attain-ing a final speed about 90% of the speedof light! Even more powerful bevatronsare in use at the Brookhaven NationalLaboratory in New York and at CERN,outside Geneva, Switzerland.

1062

Naming the Transuranium ElementsThe last naturally occurring element wasnamed after Uranus, thought at the time tobe the outermost planet; then, the first twoartificial elements were named after themore recently discovered Neptune andPluto. The next few elements were namedafter famous scientists, as in curium, andplaces, as in americium. But conflictingclaims of discovery by scientists in differ-ent countries led to controversies aboutnames for elements 104 and higher. Toprovide interim names until the disputescould be settled, the International Unionof Pure and Applied Chemistry (IUPAC)adopted a system that uses the atomicnumber as the basis for a Latin name.Thus, for example, element 104 wasnamed unnilquadium (un = 1, nil = 0,quad = 4, ium = element suffix), with thesymbol Unq. After much compromise, theIUPAC has finalized these names: 104,rutherfordium (Rf); 105, dubnium (Db);106, seaborgium (Sg); 107, bohrium (Bh);108, hassium (Hs); 109, meitnerium (Mt);and 110, darmstadtium (Ds). Elementswith atomic numbers 111 and higher havenot yet been named.


is being filled. (In 1999, one research group reported the synthesis of elements114, 116, and 118, but later retracted the data for elements 116 and 118. Anothergroup, using different reactant nuclides, has since synthesized and confirmed theexistence of element 116. Very recently, data for elements 113 and 115 have beenreported, but they have not been confirmed as of mid-2004.)_11. . "~~

One nucleus can be transmuted to another through bombardment with high-energyparticles. Accelerators increase the kinetic energy of particles in nuclear bombard-ment experiments and are used to produce transuranium elements.

24.4 THE EFFECTSOF NUCLEAR RADIATIONON MATTER

In 1986, an accident at the Chernobyl nuclear facility in the former Soviet Unionreleased radioactivity that is estimated to have already caused thousands of can-cer deaths. In the same year, isotopes used in medical treatment emitted radioac-tivity that prevented thousands of cancer deaths. In this section and the next, weexamine the harmful and beneficial effects of radioactivity.

The key to both of these outcomes is that nuclear changes cause chemicalchanges in surrounding matter. In other words, even though the nucleus of anatom undergoes a reaction with little or no involvement of the atom's electrons,the emissions do affect the electrons of nearby atoms.

The Effects of Radioactive Emissions:Excitation and IonizationRadioactive 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 thenre-emits it. Because electrons are not lost from the atom, the radiation thatcauses excitation is called nonionizing radiation. If the absorbed energycauses the atoms to move, vibrate, or rotate more rapidly, the material becomeshotter. Concentrated aqueous solutions of plutonium salts boil because theemissions excite the surrounding water molecules. (Polonium has thereforebeen suggested as a lightweight heat source, with no moving parts, for use onspace stations.) Particles of somewhat higher energy excite electrons in otheratoms to higher energy levels. As the atoms return to their ground state, theyemit 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-electronpairs 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 ionizingradiation. The free electron of the pair often collides with another atom andejects a second electron (see the description of Geiger-Muller counters in theTools of the Laboratory essay, p. 1055).

Effects of Ionizing Radiation on Living MatterWhereas nonionizing radiation is relatively harmless, ionizing radiation has adestructive 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.

24.4 The Effects of Nuclear Radiation on Matter

Units of Radiation Dose and Its Effects To measure the effects of ionizing radia-tion, we need a unit for radiation dose. Units of radioactive decay, such as thebecquerel and curie, measure the number of decay events in a given time but nottheir energy or absorption by matter. The number of cation-electron pairs producedin 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 jouleof energy absorbed per kilogram of body tissue: 1 Gy = 1 J/kg. A more widelyused unit is the rad (radiation-absorbed dose), which is equal to 0.01 Gy:

1 rad = 0.01 J/kg = 0.01 GyTo 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, wemultiply 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 bodypart. 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 RBEDoses 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 absorbeddose in grays; thus, 1 rem = 0.01 Sv.

Penetrating Power of Emissions The effect on living tissue of a radiation dosedepends 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 massand charge of the emission. In other words, if a particle interacts strongly withmatter, it penetrates only slightly, and vice versa:

• a Particles. Alpha particles are massive and highly charged, which means thatthey interact with matter most strongly of the three common types of emis-sions. As a result, they penetrate so little that a piece of paper, light clothing,or the outer layer of skin can stop a radiation from an external source. How-ever, if ingested, an a emitter such as plutonium-239 causes grave localizeddamage through extensive ionization. .

• f3 Particles and positrons. Beta particles and positrons have less charge andmuch less mass than a particles, so they interact less strongly with matter. Eventhough a given particle has less chance of causing ionization, a [3(or positron)emitter is a more destructive external source because the particles penetratedeeper. Specialized heavy clothing or a thick (0.5 cm) piece of metal is requiredto stop these particles.

• 'Y Rays. Neutral, massless "I rays interact least with matter and, thus, penetratemost. A block of lead several inches thick is needed to stop them. Therefore,an external "I ray source is the most dangerous because the energy can ionizemany layers of living tissue.

Molecular Interactions How does the damage take place on the molecular level?When ionizing radiation interacts with a molecule, it causes the loss of an elec-tron from a bond or a lone pair. The resulting charged species go on to formfree radicals, molecular or atomic species with one or more unpaired electrons.As we've seen several times already, species with lone electrons are very reac-tive and tend to form electron pairs by bonding to other species. To do this, theyattack bonds in other molecules, sometimes forming more free radicals.

When "I radiation strikes biological tissue, for instance, the most likely mol-ecule to absorb it is water, which forms an electron and a water ion-radical:

H20 +"y ----+ H20'+ + e-

1063

a (-0.03 mm)

I IP (-2 mm)

Figure 24.8 Penetrating power of radio-active emissions. Penetrating power is of-ten measured in terms of the depth ofwater that stops 50% of the incoming ra-diation. (Water is the main component ofliving tissue.) Alpha particles, with thehighest mass and charge, have the low-est penetrating power, and -y rays havethe highest. (Average values of actualpenetrating distances are shown.)

A Tragic Way to Tell Time in the DarkIn the early20th century,wristwatchandclock dials were painted by hand withpaint containingradium so they wouldglow in the dark. To write numbersclearly,the youngwomenhiredto applythepaint"tipped"finebrushesrepeatedlybetweentheir lips. Smallamountsof in-gested226Ra2+wereincorporatedintothebonesof the women,alongwith normalea2+, which led to numerouscases ofbonefractureandjaw cancer. --......,...•


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 ofthe double-bonded carbons and the H', and the other electron resides on the othercarbon 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 inenzymes lead to their malfunction as catalysts of metabolic reactions. Changes inthe 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 andegg 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 ionizingradiation from natural and artificial sources (Table 24.7). Indeed, life evolved inthe presence of natural ionizing radiation, called background radiation. The

mmIJ Ty'pical Radiation Doses from Natural and Artificial SourcesSource of Radiation Adult [>q:lo!uue

Natural

Cosmic radiationRadiation from the ground

From clay soil and rocksIn wooden housesIn brick housesIn concrete (cinder block) houses

Radiation from the air (mainly radon)Outdoors, average valueIn wooden housesIn brick housesIn concrete (cinder block) houses

Internal radiation from minerals in tapwater and daily intake of food(4oK, 14C, Ra)

ArtificialDiagnostic x-ray methods

Lung (local)Kidney (local)Dental (dose to the skin)

Therapeutic radiation treatmentOther sources

Jet flight (4 h)Nuclear testingNuclear power industry

TOTAL AVERAGE VALUE

30-50 mrem/yr

~25-170 mrem/yr10-20 mrem/yr60- 70 mrem/yr60-160 mrem/yr

20 mrem/yr70 mrem/yr

130 mrem/yr260 mrem/yr

~40 mrem/yr

0.04-0.2 rad/film1.5-3 rad/film:s1 rad/filmLocally :s 10,000rad

~1 mrem<4 mrem/yr<1 mrem/yr

100-200 mrem/yr

24.4 The Effects of Nuclear Radiation on Matter

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 LosAngeles; even a jet flight involves measurable absorption. The sources of mostbackground 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-nium and thorium decay, and its concentration in the air we breathe varies withtype of local soil and rocks. About 150 g of K+ ions is dissolved in the waterin the tissues of an average adult, and 0.0118% of that amount is radioactive 4oK.The presence of these substances and of atmospheric 14C02 means that all food,water, clothing, and building materials are slightly radioactive.

The largest artificial source of radiation, and the easiest to control, is associ-ated with medical diagnostic techniques, especially x-rays. The radiation dosagefrom nuclear testing and radioactive waste disposal is miniscule for most people,but exposures for those living near test sites, nuclear energy facilities, or disposalareas may be many times higher.

Assessing the Risk from Ionizing Radiation How much radiation is too much? Toapproach this question, we must ask several others: How strong is the exposure?How long is the exposure? Which tissue is exposed? Are offspring affected? Onereason we lack clear data to answer these questions is that scientific ethical stan-dards forbid the intentional exposure of humans in an experimental setting. How-ever, accidentally exposed radiation workers and Japanese atomic bomb survivorshave been studied extensively. Table 24.8 summarizes the immediate tissue effectson humans of an acute single dose of ionizing radiation to the whole body. Theseverity 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

Dose Lethal Dose

(rem) Effect Population (%) No. of Days

5-20 Possible late effect; possiblechromosomal aberrations

20-100 Temporary reduction inwhite blood cells

50+ Temporary sterility in men(100+ rem = 1 yr duration)

100-200 "Mild radiation sickness":vomiting, diarrhea, tiredness ina few hours

Reduction in infection resistancePossible bone growth retardation

in children300+ Permanent sterility in women500 "Serious radiation sickness": 50-70 30

marrow/intestine destruction400-1000 Acute illness, early deaths 60-95 303000+ Acute illness, death in hours 100 2

to days

1065

pCi/L

.0.00

.0.50~ 1.00n 1.50

.2.00liiIJ 2.50.' 3.00.3.50III 4.00

Predicted county medianconcentration

o Risk of Radon Radon (Rn; Z = 86),the largest noble gas, is a natural decayproduct of uranium. Therefore, the ura-nium content of the local soil and rocks isa critical factor in the extent of the threat,but radon occurs everywhere in varyingconcentrations. Radon itself decays to ra-dioactive nuclides of Po, Pb, and Bi,through a, 13, and "y emission. Theseprocesses occur inside the body whenradon is inhaled and pose a serious poten-tial hazard. The emissions damage lungtissue, and the heavy-metal atoms formedaggravate the problem. The latest EPAes-timates indicate that radon contributes to15% of annual lung cancer deaths.

~

1066

Dose

Modeling Radiation Risk There aretwo current models of effect vs. dose. Thelinear response model proposes that radi-ation effects, such as cancer risks, accu-mulate over time regardless of dose andthat populations should not be exposed toany radiation above background levels.The S-shaped response model assumes anextremely low risk at low doses and advo-cates concern only at higher doses. If thelinear model is more accurate, we shouldlimit all excess exposure, but this wouldseverely restrict medical diagnosis and re-search, military testing, and nuclear en-ergy production.


and cancers appear after massive whole-body exposure, with rapidly dividing cellsaffected 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 immatureanimal 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 showa 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 thanis the fruit fly's, a total dose given over a long period created one-third as manygenetic defects as the same dose given over a short period. Therefore, rate ofexposure is a key factor. The children of atomic bomb survivors show higher-than-normal childhood cancer rates, implying that their parents' reproductive sys-tems were affected.

•Relatively low-energy emissions cause excitation of atoms in surrounding matter,whereas high-energy emissions cause ionization. The effect of ionizing radiation onliving matter depends on the quantity of energy absorbed and the extent of ioniza-tion in a given type of tissue. Radiation dose for the human body is measured in rem.Ionization forms free radicals, some of which proliferate and destroy biomolecularfunction. All organisms are exposed to varying quantities of natural ionizing radiation.Studies show that a large acute dose and a chronic small dose are both harmful.

24.5 APPLICATIONS OF RADIOISOTOPESOur ability to detect minute amounts of radioisotopes makes them powerful toolsfor studying processes in biochemistry, medicine, materials science, environmen-tal studies, and many other scientific and industrial fields. Such uses depend onthe fact that isotopes of an element exhibit very similar chemical and physicalbehavior. In other words, except for having a less stable nucleus, a radioisotopehas 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 wayas 12C02 forms the basis of radiocarbon dating.

Radioactive Tracers: Applications of Nonionizing RadiationJust think how useful it could be to follow a substance through a complex processor from one region of a system to another. A tiny amount of a radioisotope mixedwith 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 waterfrom a carboxylic acid and alcohol. Which portions of the reactants end up in theester 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 bondstrengths and therefore reaction rates. Such behavior is called a kinetic isotope effect and isparticularly important for isotopes of hydroqen-c--'H, 2H, and 3H-because their masses differby such large proportions. Section 22.4 discussed how the kinetic isotope effect is employed inthe industrial production of heavy water, D20.

24.5 Applications of Radioisotopes

A

:0:I1 .. 18"

R-C-OH + R'- OH~.

:0:11 ••

R-C-.1§Q-R' + H-Q-H

B

:0:1I 18" •.

R-C-OH + R'-OH~.

:0:11 ••

R-C-Q-R' +

cated in red) 1311-, we find that the 12is radioactive, not the 103-:

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 12forms 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- isradioactive, not the 12:

131104 -(aq) + 21-(aq) + H20(l) - Iz(s) + 131103 -(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 onEarth, in which energy from sunlight is used to form the chemical bonds of glu-cose, has an overall reaction that looks quite simple:

light6C02(g) + 6H20(l) ) C6H1206(s) + 602(g)

chlorophyll

However, the actual process is extremely complex, requiring 13 enzyme-catalyzedsteps for each C atom from CO2 incorporated; thus these steps must occur sixtimes for each molecule of C6H1206 that forms. Melvin Calvin and his coworkerstook seven years to determine the pathway, using 14C in CO2 as the tracer andpaper chromatography as the means of separating the products formed after dif-ferent times of light exposure. Calvin won the Nobel Prize in chemistry in 1961for this remarkable achievement.

Tracers are used in many studies of biological function. Most recently, life inspace has required answers to new questions. In an animal study of red blood cellloss during extended space flight, blood plasma volume was measured with12sI-Iabeled albumin (a blood protein), and slCr-labeled red blood cells were usedto assess survival of blood cells. In another study, blood flow in skin under longperiods 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 toexchange 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 processof 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 bombtests eH in H20, 90Sr2+, and 137Cs +), scientists have mapped the flow of waterfrom land to lakes and streams to oceans. Surface and deep ocean currents thatcirculate around the globe are also studied, as are the mechanisms of hurricaneformation and the mixing of the troposphere and stratosphere. Industries employtracers to study material flow during the manufacturing process, such as theflow of ore pellets in smelting kilns, the paths of wood chips and bleach in papermills, 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.

1067

Figure 24.9 Which reactant contributeswhich group to the ester? An ester formswhen a carboxylic acid reacts with analcohol. To determine which reactant sup-plies the 0 atom in the -OR' part of theester group, acid and alcohol were la-beled with the 180 and used as tracers.A, When R180H reacts with the unlabeledacid, the ester contains 180 but the waterdoesn't. S, When RC0180H reacts withthe unlabeled alcohol, the water contains180. Thus, the alcohol supplies the -OR'part of the ester, and the acid suppliesthe RC~O part.

1068

Spirit on the surface of Mars.

mlIID Some RadioisotopesUsed as Medical Tracers

Body Partor ProcessIsotope

lIC,18p,

13N,1506OCO,1921r64Cu

PET studies ofbrain, heart

Cancer therapyMetabolism of

copperBlood flow, spleenTumor imagingThyroidBrain, colonBlood flowLungHeart, thyroid,

liver, lung, boneHeart muscleCancer, arthritis

59Pe670a1231,13111111n42K81mKr

99Tc

201Tl90y

Animation: Nuclear MedicineOnline Learning Center


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 exhibitcharacteristic decay patterns, such as v-ray spectra, that reveal the elements pres-ent. Unlike chemical analysis, NAA leaves the sample virtually intact, so themethod can be used to determine the composition of a valuable object or a verysmall 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 thepigments used by the Dutch masters. Forensic chemists use NAA to detect tracesof ammunition on a suspect's hand or traces of arsenic in the hair of a victim ofpoisoning. In 2004, space scientists used NAA instrumentation in the Spirit andOpportunity robot vehicles to analyze the composition of Martian soils and rocks(see photo).

Automotive engineers employ NAA and v-ray detectors to measure frictionand 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 radioactive59Fe 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'sability to reduce wear.

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 fromradioisotopes. Tracers with half-lives of a few minutes to a few days are employedto observe specific organs and body parts. For example, a healthy thyroid glandincorporates dietary 1- into iodine-containing hormones at a known rate. Toassess thyroid function, the patient drinks a solution containing a trace amountof Na131I, and a scanning monitor follows the uptake of 1311- into the thyroid(Figure 24. lOA). Technetium-99 (Z = 43) is also used for imaging the thyroid(Figure 24. lOB), as well as the heart, lungs, and liver. Technetium does not occurnaturally, so the radioisotope (actually a metastable form, 99mTc) is prepared justbefore use from radioactive molybdenum:

~~Mo -----+ 994~Tc+ -?f3Tracers are also used to measure physiological processes, such as blood flow.

The rate at which the heart pumps blood, for example, can be observed by inject-ing 59Fe, which concentrates in the hemoglobin of blood cells. Several radioiso-topes used in medical diagnosis are listed in Table 24.9.

A B

Figure 24.10 The use of radioisotopes to image the thyroid gland. Thyroid scanning is used toassess nutritional deficiencies, inflammation, tumor growth, and other thyroid-related ailments.A, In 1311scanning, the thyroid gland absorbs 1311- ions whose ~ emissions expose a photographicfilm. The asymmetric image indicates disease. B, A 99Tc scan of a healthy thyroid.

24.5 Applications of Radioisotopes

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 activitywithin a region.

Positron-emission tomography (PET) is a powerful imaging method forobserving brain structure and function. A biological substance is synthesized withone of its atoms replaced by an isotope that emits positrons. The substance isinjected into a patient's bloodstream, from which it is taken up into the brain. Theisotope emits positrons, each of which annihilates a nearby electron. In the anni-hilation process, two 'Y photons are emitted simultaneously 1800 from each other:

?13 + _?e -- 22'YAn 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, injectedas H2

150 to measure blood flow, and 18Fbonded to a glucose analog to measureglucose uptake, which is a marker for energy metabolism. Among many fasci-nating PET findings are those that show how changes in blood flow and glucoseuptake accompany normal or abnormal brain activity (Figure 24.11). In a recentnonmedical development, substances incorporating IIC and 150 are being inves-tigated by PET to learn how molecules interact with and move along the surfaceof a catalyst.

Applications of Ionizing RadiationTo 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 beused to eliminate it. Cancer cells divide more rapidly than normal cells, soradioisotopes that interfere with the cell-division process kill more cancer cellsthan normal ones. Implants of 198Au or of a mixture of 90Sr and 90y have beenused to destroy pituitary and breast tumor cells, and 'Y rays from 60Co have beenused to destroy brain tumors.

Irradiation of food increases shelf life by killing microorganisms that causefood to rot (Figure 24.12), but the practice is quite controversial. Advocates pointto 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 animalfeed has brought about an increased incidence of illness from newer, more resis-tant bacterial strains, providing a stronger argument for the use of irradiation. TheUnited Nations has approved irradiation for potatoes, wheat, chicken, and straw-berries, and the United States allows irradiation of chicken.

Nonirradiated

1069

Irradiated

Figure 24.12 The increased shelf life ofirradiated food.


Ionizing radiation has been used to control harmful insects. Captured malesare sterilized by radiation and released to mate, thereby reducing the number ofoffspring. 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 spoilfood, and control insect populations.

24.6 THE INTERCONVERSION OF MASS AND ENERGYMost of the nuclear processes we've considered so far have involved radioactivedecay, in which a nucleus emits one or a few small particles or photons to becomea slightly lighter nucleus. Two other nuclear processes cause much greaterchanges. In nuclear fission, a heavy nucleus splits into two much lighter nuclei,emitting several small particles at the same time. In nuclear fusion, the oppositeprocess occurs as two lighter nuclei combine to form a heavier one. Both fissionand fusion release enormous quantities of energy. Let's take a look at the originsof this energy by first examining the change in mass that accompanies the breakupof a nucleus into its nucleons and then considering the energy that is equivalentto this mass change.

The Mass DefectWe have known for most of the 20th century that mass and energy are intercon-vertible. The traditional mass and energy conservation laws have been combinedto 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 anaccompanying loss or gain in mass.

This relation between mass and energy did not concern us earlier because theenergy changes involved in breaking or forming chemical bonds are so small thatthe 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/molf1m = 8 2 = 1.04X 10-11 kg/mol = 1.04X 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 thecombined masses of 2 mol of Hand 1 mol of 0 (products), a change too smallto measure with even the most sophisticated balance. Such minute mass changeswhen bonds break or form allow us to assume that mass is conserved in chemi-cal reactions.

24.6 The Interconversion of Mass and Energy

The much larger mass change that accompanies a nuclear process is relatedto 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 nucleusbreaks up into its nucleons: six protons and six neutrons. We calculate this changein 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 1H atoms) cancel six e - (in one 12C atom)]. The mass ofone IH atom is 1.007825 arnu, and the mass of one neutron is 1.008665 amu, so

Mass of six IH atoms = 6.046950 amuMass 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) isthe 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 itsnucleons. The mass decrease that occurs when nucleons are united into a nucleusis called the mass defect. The size of this mass change (9.89X 10-2 g/mol) isnearly 10 million times that of the previous bond breakage (lOAX 10-9 g/mol)and is easily observed on any laboratory balance.

Nuclear Binding EnergyEinstein's equation for the relation between mass and energy also allows us tofind the energy equivalent of a mass defect. For 12e, after converting grams tokilograms, 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. Ingeneral, the nuclear binding energy is the quantity of energy required to break up1 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

We use joules to express the binding energy per mole of nuclei, but the jouleis an impractically large unit to express the binding energy of a single nucleus.Instead, nuclear scientists use the electron volt (eV), the energy an electronacquires when it moves through a potential difference of 1 volt:

1 eV = 1.602XlO-J9 J

Binding energies are commonly expressed in millions of electron volts, that is, inmega-electron volts (MeV):

1 MeV = 106 eV = 1.602X 10-13 J

A particularly useful factor converts a given mass defect in atomic mass units toits energy equivalent in electron volts:

1 amu = 931.5 X 106 eV = 931.5 MeV (24.8)

Earlier we found the mass defect of the J2e nucleus to be 0.098940 amu.Therefore, the binding energy per 12e nucleus, expressed in MeV, is

Binding energy 931.5 MeV12 = 0.098940 amu X ---- = 92.16 MeV

C nucleus 1 amu

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The Force That Binds Us According tocurrent theory, the nuclear binding energyis related to the strong force, which holdsnucleons together in a nucleus. There arethree other fundamental forces: (I) theweak nuclear force, which is important inf3 decay, (2) the electrostatic force that weobserve between charged particles, and(3) the gravitational force. Toward the endof his life, Albert Einstein tried unsuc-cessfully to develop a theory to explainhow the four forces were really differentaspects of one unified force that governsall nature. The 2004 Nobel Prize inphysics was awarded to David J. Gross,H. David Politzer, and Frank Wilczek fortheir explanation of the strong force who,with others, may one day realize Ein-stein's dream.


We can compare the stability of nuclides of different elements by determining thebinding energy per nucleon. For 12C, we have

binding energyBinding energy per nucleon = ------

no. of nucleons92.16 MeV---- = 7.680 MeV/nucleon12 nucleons

SAMPLE PROBLEM 24.6 Calculating the Binding Energy per NucleonProblem Iron-56 is an extremely stable nuclide. Compute the binding energy per nucleonfor 56Pe and compare it with that for 12C(mass of 56Pe atom = 55.934939 amu; mass ofIH 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 defectby finding the sum of the masses of 26 IH atoms and 30 neutrons and subtracting thegiven mass of I 56Pe atom. Then we multiply Ism by the equivalent in MeV(931.5 MeV/amu) and divide by 56 (no. of nucleons) to obtain the binding energy pernucleon.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/nucleon56 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 BLEM 24.6 Uranium- 235 is the essential component of the fuelin nuclear power plants. Calculate the binding energy per nucleon for 235U.Is this nuclidemore or less stable than 12C (mass of 235Uatom = 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 bindingenergy per nucleon varies considerably. The essential point is that the greater thebinding 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 processesnuclides can undergo to form more stable nuclides. Nuclides with fewer than 10nucleons have a relatively small binding energy per nucleon. The 4He nucleus hasan 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 to8.8 MeY.

The most important observation is that the binding energy per nucleon peaksfor elements with A = 60. In other words, nuclides become more stable withincreasing mass number up to around 60 nucleons and then become less stablewith higher numbers of nucleons. The existence of a peak of stability suggeststhat 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) byundergoing fission. The product nuclei have greater binding energy per nucleon(are more stable) than the reactant nucleus, and the difference in energy isreleased. Nuclear power plants generate energy through fission, as do atomicbombs (Section 24.7).

24.7 Applications of Fission and Fusion 1073

9 348 5BFe 84Kr 1198n

s 8 205TI 235URegion of veryQ)

stable nuclides6 7 238Uc0Q) 6U::JC

0; 5 BLi0-Fusion Fission>,

E' 4 ~ ~Q)

cQ)

3 3HDJc;

3Heis 2cm

2H

0 20 40 60 80 100 120 140 160 180 200 220 240 260Mass number (A)

IilmDiI The variation in binding energy per nucleon. A plot of the binding energy pernucleon vs. mass number shows that nuclear stability is greatest in the region near 56Fe. Lighternuclei 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 allcurrent 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 anamount called the mass defect. The energy equivalent to the mass defect is thenuclear binding energy, usually expressed in units of MeV. The binding energy pernucleon is a measure of nuclide stability and varies with the number of nucleons ina nuclide. Nuclides with A = 60 are most stable. Lighter nuclides can join (fusion) orheavier nuclides can split (fission) to become more stable.

24.7 APPLICATIONS OF FISSION AND FUSIONOf 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. Ourexperience 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 thisenergy source safely and economically. In this section, we discuss how fissionand fusion occur and how we are applying them.

The Process of Nuclear FissionDuring the mid-1930s, Enrico Fermi and coworkers bombarded uranium (Z = 92)with neutrons in an attempt to synthesize transuranium elements. Many of the

1074

Use Meitner (1878-1968) Until veryrecently, this extraordinary physicist re-ceived little of the acclaim she deserved.Meitner worked in the laboratory of thechemist Otto Hahn, and she was responsi-ble for the discovery of protactinium (Pa;Z = 91) and numerous radioisotopes. Af-ter leaving Germany in advance of theNazi domination, Meitner proposed thecorrect explanation of nuclear fission. In1944 Hahn received the Nobel Prize inchemistry, but he did not even acknowl-edge Meitner in his acceptance speech.Today, most physicists believe Meitnershould have received the prize. Despitecontroversy over names for elements 104to 109, it was widely agreed that element109 should be named meitnerium.


Figure 24.14 Induced fission of mU. A neutron bombarding a 235Unucleus results in an extremelyunstable 236Unucleus, which becomes distorted in the act of splitting. In this case, which showsone of many possible splitting patterns, the products are 92Kr and 141Ba. Three neutrons and agreat deal of energy are released also.

unstable nuclides produced were tentatively identified as having Z > 92, but otherscientists were skeptical. Four years later, the German chemist Otto Hahn and hisassociate F. Strassmann showed that one of these unstable nuclides was an iso-tope of barium (Z = 56). The Austrian physicist Lise Meitner, a coworker ofHahn, 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 fissionbecause 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 variousdaughter nuclei, but all routes have the same general features. Figure 24.14 depictsone of these fission patterns. Neutron bombardment results in a highly excited236U nucleus, which splits apart in 10-14 s. The products are two nuclei of unequalmass, two or three neutrons (average of 2.4), and a large quantity of energy. Asingle 23SU nucleus releases 3.5XlO-lJ J when it splits; 1 mol of 23SU (about~ Ib) releases 2.1 X 1013 J -a billion times as much energy as burning ~ lb of coal(about 2X 104 J)!

We harness the energy of nuclear fission, much of which appears as heat, bymeans of a chain reaction, illustrated in Figure 24.15: the two to three neutronsthat are released by the fission of one nucleus collide with other fissionable nucleiand cause them to split, releasing more neutrons, which then collide with othernuclei, and so on, in a self-sustaining process. In this manner, the energy releasedincreases rapidly because each fission event in a chain reaction releases two tothree times as much energy as the preceding one.

Whether a chain reaction occurs depends on the mass (and thus the volume)of the fissionable sample. If the piece of uranium is large enough, the productneutrons strike another fissionable nucleus before flying out of the sample, and achain reaction takes place. The mass required to achieve a chain reaction is calledthe critical mass. If the sample has less than the critical mass (called a subcrit-ical mass), most of the product neutrons leave the sample before they have theopportunity to collide with and cause the fission of another 23SU nucleus, and thusa chain reaction does not occur.

24.7 Applications of Fission and Fusion

Figure 24.15 A chain reaction of mU. If a sample exceeds the critical mass, neutrons produced bythe 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 linesidentify succeeding "generations" of neutrons.

Uncontrolled Fission:The Atomic Bomb An uncontrolled chain reaction can beadapted 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. InAugust 1939, Albert Einstein wrote the president of the United States, FranklinDelano 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 nuclearfission, which was initiated in 1941.* In August 1945, the United States detonatedtwo atomic bombs over Japan, and the horrible destructive power of these bombswas a major factor in the surrender of the Japanese a few days later.

In an atomic bomb, small explosions of trinitrotoluene (TNT) bring subcrit-ical masses of fissionable material together to exceed the critical mass, and theensuing chain reaction brings about the explosion (Figure 24.16). The prolifera-tion of nuclear power plants, which use fissionable materials to generate energyfor electricity, has increased concern that more countries (and unscrupulous indi-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 concernhas been heightened. After all, only 1 kg of fissionable uranium was used in thebomb dropped on Hiroshima, Japan.

*For an excellent scientific and historical account of the development of the atomic bomb, seeR. Rhodes, The Making of the Atomic Bomb, New York, Simon and Schuster, 1986.

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Separatedsubcriticalmasses

TNTexplosive

Figure 24.16 Diagram of an atomic bomb.Small TNT explosions bring subcriticalmasses together, and the chain reactionoccurs.


Controlled Fission: Nuclear Energy Reactors Controlled fission can produce elec-tric power more cleanly than can the combustion of coal. Like a coal-fired powerplant, 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 byburning 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 tubesof a corrosion-resistant zirconium alloy. The fuel is uranium(IV) oxide (U02) thathas 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 ofnuclear fuel is the most important application of Graham's law; see the marginnote, p. 205.) Sandwiched between the fuel rods are movable control rods madeof cadmium or boron (or, in nuclear submarines, hafnium), substances that absorbneutrons 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 thatleave the fuel-rod assembly collide with a reflector, usually made of a beryllium

A

Figure 24.17 A light-water nuclear reac-tor. A, Photo of a facility showing theconcrete containment shell and nearbywater source. B, Schematic of a Iight-water reactor.

Contalnrnent shell (

Reactor core 11

@Control rods regulaterate of chain reaction

Moderator

(J)Enriched uranium infuel rods releasesenergy from fission

B

-: @Steamproducedoperates»< turbine-generator

11

~Electric power

Coolantwater out

24.7 Applications of Fission and Fusion

alloy, which absorbs very few neutrons. Reflecting the neutrons back to the fuelrods 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 modemreactors, the moderator also acts as the coolant, the fluid that transfers the releasedheat to the steam-producing region. Because lH absorbs neutrons, light-waterreactors use H20 as the moderator; in heavy-water reactors, D20 is used. Theadvantage of D20 is that it absorbs very few neutrons, leaving more available forfission, so heavy-water reactors can use unenriched uranium. As the coolant flowsaround the encased fuel, pumps circulate it through coils that transfer its heat tothe water reservoir. Steam formed in the reservoir turns the turbine that runs thegenerator. 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.

Some major accidents at nuclear plants have caused decidedly negative pub-lic reactions. In 1979, malfunctions of coolant pumps and valves at the Three-Mile Island facility in Pennsylvania led to melting of some of the fuel, seriousdamage to the reactor core, and the release of radioactive gases into the atmo-sphere. In 1986, a million times as much radioactivity was released when a cool-ing system failure at the Chernobyl plant in Ukraine caused a much greatermelting of fuel and an uncontrolled reaction. High-pressure steam and ignitedgraphite moderator rods caused the reactor building to explode and expel radioac-tive debris. Carried by prevailing winds, the radioactive particles contaminatedvegetables and milk in much of Europe. Health officials have evidence that thou-sands of people living near the accident have already or may eventually developcancer from radiation exposure. The design of the Chernobyl plant was particu-larly unsafe because, unlike reactors in the United States and western Europe, thereactor was not enclosed in a massive, concrete containment building.

Despite potential safety problems, nuclear power remains an important sourceof electricity. In the late 1990s, nearly every European country employed nuclearpower, and it is the major power source in some countries-Sweden creates 50%of its electricity this way and France almost 80%. Currently, the United Statesobtains about 20% of its electricity from nuclear power, and Canada slightly less.As our need for energy grows, safer reactors will be designed.

However, even a smoothly operating plant has certain inherent problems. Theproblem of thermal pollution is common to all power plants. Water used to con-dense the steam is several degrees warmer when returned to its source, which canharm aquatic organisms (Section 13.4). A more serious problem is nuclear wastedisposal. 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 cannotpossibly be field-tested for the thousands of years the material will remain harm-ful. Leakage of radioactive material into groundwater is a danger, and earthquakescan 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 wecan operate fission reactors and dispose of the waste safely and economically.

The Promise of Nuclear FusionNuclear fusion is the ultimate source of nearly all the energy on Earth becausenearly all other sources depend, directly or indirectly, on the energy produced bynuclear 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 decayprocesses within stars, as the upcoming Chemical Connections essay describes.

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"Breeding" Nuclear Fuel Uranium-235 is not an abundant isotope. One solu-tion to a potential fuel shortage is abreeder reactor, designed to consume onetype of nuclear fuel as it produces another.Fuel rods are surrounded by natural U30g,

which contains 99.3% nonfissionable238U atoms. As fast neutrons, formed dur-ing 235U fission, escape the fuel rod, theycollide with 238U, transmuting it into239pU,another fissionable nucleus:

2§~U + 6n ---+ 2§~U(tl/2 of 2§~U = 23.5 min)

2§~U ---+ 2§~Np + -?f3(tl/2 of 2§~Np = 2.35 days)

2§~Np ---+ 2§~PU+ -?f3(tl/2 of 2§~pu = 2AX 104 yr)

Although breeder reactors can make fuelas they operate, they are difficult and ex-pensive to build, and 239pUis extremelytoxic and long lived. Breeder reactors arenot used in the United States, althoughseveral are operating in Europe and Japan.

,,~m""CosmologyOrigin of the Elements in the Stars

HOW did the universe begin? Where did matter come from?How were the elements formed? Every culture has creationmyths that address such questions, but only recently have as-

tronomers, physicists, and chemists begun to offer a scientificexplanation. The most accepted current model proposes thata sphere of unimaginable properties-diameter of 10-28 cm, den-sity of 1096g/mL (density of a nucleus = 1014g/ml.), and tem-perature of 1032K-exploded in a "Big Bang," for reasons not yeteven guessed, and distributed its contents through the void ofspace. Cosmologists consider this moment the beginning of time.

One second later, the universe was an expanding mixture ofneutrons, protons, and electrons, denser than rock and hotter thanan exploding hydrogen bomb (about 1010 K). During the next fewminutes, it became a gigantic fusion reactor creating the firstatomic nuclei: 2H, 3He, and 4He.After 10 minutes, more than 25%of the mass of the universe existed as 4He, and only about 0.025%as 2H.About 100 million years later, or about 15 billion years ago,gravitational forces pulled this cosmic mixture into primitive,contracting stars.

This account of the origin of the universe is based on the ob-servation of spectra from the Sun, other stars, nearby galaxies, andcosmic (interstellar) dust. Spectral analysis of planets and chemi-cal analysis of Earth and Moon rocks, meteorites, and cosmic-rayparticles furnish data about isotope abundance. From these, amodel has been developed for stellar nucleogenesis, the origin ofthe elements in the stars. The overall process occurs in severalstages during a star's evolution, and the entire sequence of stepsoccurs only in very massive stars, having 10 to 100 times the massof the Sun. Each step involves a contraction of the star that pro-duces higher temperature and heavier nuclei. Such events areforming elements in stars today. The key stages in the process areshown in Figure B24.3 and described below:

1. Hydrogen burning produces He. The initial contraction ofa star heats its core to about 107K, at which point a fusion processcalled hydrogen burning begins, which produces helium from theabundant protons:

4lH --+ iHe + 2?f3+ 2-y+ energy2. Helium burning produces C, 0, Ne, and Mg. After several

billion years of hydrogen burning, about 10% of the IH is con-sumed, and the star contracts further. The 4He forms a dense core,hot enough (2X 108K) to fuse 4He. The energy released during he-lium burning expands the remaining IH into a vast envelope: thestar becomes a red giant, more than 100 times its original diame-ter. Within its core, pairs of 4He nuclei (a particles) fuse into un-stable 8Be nuclei (tl/2 = 7 X 10-17 s). These collide with another4He to form stable 12C.Then, further fusion with 4He creates nu-clei up to 24Mg:

a a a12C ~ 160 ~ 20Ne ~ 24Mg

3. Elements through Fe and Ni form. For another 10 millionyears, 4He is consumed, and the heavier nuclei created form acore. This core contracts and heats, expanding the star into asupergiant. Within the hot core (7X 108 K), carbon and oxygenburning occur:

12C+ 12C--+ 23Na + IH12C+ 160 --+ 28Si + -y

1078

Absorption of a particles forms nuclei up to 40Ca:

a a a a12C ~ 160 ~ 20Ne ~ 24Mg ~

a a a28Si --"----t 32S ~ 36Ar ~ 40Ca

Further contraction and heating to a temperature of 3 X 109 K al-low reactions in which nuclei release neutrons, protons, and a par-ticles and then recapture them. As a result, nuclei with lowerbinding energies supply nucleons to create those with higher bind-ing energies. This process, which takes only a few minutes, stopsat iron (A = 56) and nickel CA = 58), the nuclei with the highestbinding energies.

4. Heavier elements form. In very massive stars, the nextstage is the most spectacular. With all the fuel consumed, the corecollapses within a second. Many Fe and Ni nuclei break down intoneutrons and protons. Protons capture electrons to form neutrons,and the entire core forms an incredibly dense neutron star. (AnEarth-sized star that became a neutron star would fit in the Hous-ton Astrodome!) As the core implodes, the outer layers explodein a supernova, which expels material throughout space. A super-nova occurs an average of every few hundred years in eachgalaxy; the one shown in Figure B24.4 was observed from thesouthern hemisphere in 1987, about 160,000 years after the eventoccurred. The heavier elements are formed during supernovaevents and are found in second-generation stars, those that coa-lesce from interstellar 'n and 4He and the debris of exploded first-generation stars.

Heavier elements form through neutron-capture processes. Inthe s-process, a nucleus captures a neutron and emits a -y ray.Days, months, or even thousands of years after this event, the nu-cleus emits a f3particle to form the next element, as in this con-version of 68Znto 700e:

The stable isotopes of most heavy elements form by thes-process.

Less stable isotopes and those with A greater than 230 cannotform by the s-process because their half-lives are too short. Theseform by the r-process during the fury of the supernova. Multipleneutron captures, followed by multiple f3decays, occur in a sec-ond, as when 56Feis converted to 79Br:

~~Fe+ 23bn --+ i~Fe --+ ~§Br + 9-?f3

We know from the heavy elements present in the Sun that it is atleast a second-generation star presently undergoing hydrogenburning. Together with its planets, it was formed from the dust ofexploded stars about 4.6X 109 years ago. This means that many ofthe atoms on Earth, including some within you, came from ex-ploded stars and are older than the Solar System itself!

Any theory of element formation must be consistent with theelement abundances we observe (Section 22.1). Although localcompositions, such as those of Earth and Sun, differ, large regionsof the universe have, on average, similar compositions. Therefore,scientists believe that element forming reaches a dynamic equilib-rium, which leads to relatively constant amounts of the isotopes.

Figure 824.3 Elementsynthesis in the life cycleof a star.

Figure 824.4 A view ofSupernova 1987A.

1080

Figure 24.18 The tokamak design formagnetic containment of a fusion plasma.The don ut-shaped chamber of the toka-mak (photo, top; schematic, bottom) con-tains the plasma within a helical magneticfield.


Much research is being devoted to making nuclear fusion a practical, directsource of energy on Earth. To understand the advantages of fusion, let's considerone of the most discussed fusion reactions, in which deuterium and tritium react:

fH + fH - iHe + bnThis reaction produces 1.7X 109 kJ/mol, an enormous quantity of energy with

no radioactive by-products. Moreover, the reactant nuclei are relatively easy tocome by. We obtain deuterium from the electrolysis of water (Section 22.4). Innature, tritium forms through the cosmic (neutron) irradiation of 14N:

ljN + bn - fH + l~CHowever, this process results in a natural abundance of only 10-7% 3H. Morepractically, tritium can be produced in nuclear accelerators by bombardinglithium-6 or by surrounding the fusion reactor itself with material containinglithium-6:

~Li + bn - fH + iHeThus, fusion seems very promising, at least in principle. However, some

extremely difficult problems remain. Fusion requires enormous energy in the formof 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 temperaturesbe 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 detonatingatomic 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 agaseous plasma, a neutral mixture of positive nuclei and electrons. Because ofthe extreme temperatures needed for fusion, no material can contain the plasma.The most successful approach to date has been to enclose the plasma within amagnetic 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 haveachieved some success in generating energy from fusion this way. In anotherapproach, 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 sourceof energy, fusion still seems to be a long way off.--In nuclear fission, neutron bombardment causes a nucleus to split, releasing neutronsthat split other nuclei to produce a chain reaction. A nuclear power plant controls therate 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-posal of nuclear waste, remain current concerns. Nuclear fusion holds great promiseas a source of clean abundant energy, but it requires extremely high temperaturesand is not yet practical. The elements were formed through a complex series ofnuclear reactions in evolving stars.

Chapter PerspectiveWith this chapter, our earlier picture of the nucleus as a static point of positive massat the atom's core has changed radically. Now we picture a dynamic body, capableof a host of changes that involve incredible quantities of energy. Our attempts to apply

For Review and Reference 1081

the behavior of this minute system to benefit society have created some of the mostfascinating and challenging fields in science today.

We began our investigation of chemistry 24 chapters ago, by seeing how thechemical elements and the products we make from them influence nearly every aspectof 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, arecontinually 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 newabilities to visualize molecular events and solve problems in whatever field youchoose. For the science of chemistry, future challenges are great: What greener energysources can satisfy our needs while sustaining our environment? What new productscan feed, clothe, and house the world's people and maintain precious resources? Howcan we apply our new genetic insight to defend against cancer, AIDS, and otherdreaded diseases? What new materials and technologies can make life moreproductive and meaningful? The questions are many, but the science of chemistry willalways be one of our most powerful means of answering them.

(Numbers in parentheses refer to pages, unless noted otherwise.)

Learning ObjectivesRelevant section and/or sample problem (SP)numbers appearin parentheses.

Understand These Concepts1. How nuclear changes differ, in general, from chemical changes(Introduction)2. The meanings of radioactivity, nucleon, nuclide, and isotope(Section 24.1)3. Characteristics of three types of radioactive emissions: ex, [3,and "y (Section 24.1)4. The various forms of radioactive decay and how each changesthe values of A and Z (Section 24.1)5. How the N /Z ratio and the even-odd nature of Nand Z correlatewith nuclear stability (Section 24.1)6. How the N/Z ratio correlates with the mode of decay of an un-stable nuclide (Section 24.1)7. How a decay series combines numerous decay steps and endswith a stable nuclide (Section 24.1)8. Why radioactive decay is a first-order process; the meanings ofdecay rate and specific activity (Section 24.2)9. The meaning of half-life in the context of radioactive decay(Section 24.2)10. How the specific activity of an isotope in an object is used todetermine the object's age (Section 24.2)11. How particle accelerators are used to synthesize new nuclides(Section 24.3)12. The distinction between excitation and ionization and the ex-tent of their effects on matter (Section 24.4)13. The units ofradiation dose; the effects on living tissue of var-ious dosage levels; the inverse relationship between the mass andcharge of an emission and its penetrating power (Section 24.4)14. How ionizing radiation creates free radicals that damage tis-sue; sources and risks of ionizing radiation (Section 24.4)

15. How radioisotopes are used in research, analysis, and diagno-sis (Section 24.5)16. Why the mass of a nuclide is less than the sum of its nucleons'masses (mass defect) and how this mass difference is related to thenuclear binding energy (Section 24.6)17. How nuclear stability is related to binding energy per nucleon(Section 24.6)18. How unstable nuclides undergo either fission or fusion to in-crease their binding energy per nucleon (Section 24.6)19. The current application of fission and potential application offusion to produce energy (Section 24.7)

Master These Skills1. Expressing the mass and charge of a particle with the ~X nota-tion (Section 24.1; see also Section 2.5)2. Using changes in the values of A and Z to write and balance nu-clear equations (SP 24.1)3. Using the N/Z ratio and the even-odd nature of Nand Z to pre-dict nuclear stability (SP 24.2)4. Using the N/Z ratio to predict the mode of nuclear decay(SP 24.3)5. Converting units of radioactivity (Section 24.2)6. Calculating specific activity, decay constant, half-life, andnumber of nuclei (Section 24.2 and SP 24.4)7. Estimating the age of an object from the specific activity andhalf-life of carbon-14 (SP 24.5)8. Writing and balancing equations for nuclear transmutation(Section 24.3)9. Calculating radiation dose and converting units (Section 24.4)10. Calculating the mass defect and its energy equivalent in J andeV (Section 24.6)11. Calculating the binding energy per nucleon and using it tocompare stabilities of nuclides (SP 24.6)


Section 24.1radioactivity (1046)nucleon (1046)nuclide (1046)isotope (1046)alpha (a) particle (1047)beta (f3) particle (1047)gamma ("'/)ray (1047)alpha decay (1048)beta decay (1049)positron decay (1049)positron (1049)electron capture (1049)gamma emission (1049)N/2 ratio (1050)

band of stability (1050)strong force (1051)decay (disintegration) series

(1053)Section 24.2activity (31) (1054)becquerel (Bq) (1054)curie (Ci) (1054)decay constant (1054)half-life (t1/2) (1054)Geiger-Muller counter (1055)scintillation counter (1055)radioisotopic dating (1057)radioisotope (1057)

Key Equations and Relationships24.1 Balancing a nuclear equation (1048):

~~:~[1Reactants = ~~:~[1Products24.2 Defining the unit of radioactivity (curie, Ci) (1054):

1 Ci = 3.70X 1010 disintegrations per second (d/s)24.3 Expressing the decay rate (activity) for radioactive nuclei(1054):

6.NDecay rate (.sil) = -----s:r = kN

24.4 Finding the number of nuclei remaining after a given time,Nt (1056):

~~ and TablesThese figures (F)and tables (T) provide a review of key ideas.

T24.1 Chemical vs. nuclear reactions (1045)F24.1Radioactive emissions in an electric field (1047)

Br·ief Solutions to follow-up Problems24.1 1~~Xe --- l~~CS + -?f324.2 Phosphorus-31 has a slightly higher N/2 ratio and an even N(16).24.3 (a) N/Z = 1.35; too high for this region of band: f3 decay(b) Mass too high for stability: a decay24.41n slt = -kt + In.silo

(In 2 24 h) 9= - -. - X 4.0 days X -- + In (2.5 X10 )15 h 1 day

= 17.20.silt = 3.0X 107 d/s

Section 24.3nuclear transmutation (1059)deuteron (1060)particle accelerator (1060)transuranium element (1061)Section 24.4excitation (1062)nonionizing radiation (1062)ionization (1062)ionizing radiation (1062)gray (Gy) (1063)rad (radiation-absorbed dose)

(1063)rem (roentgen equivalent for

man) (1063)sievert (Sv) (1063)

free radical (1063)background radiation (1064)Section 24.5tracer (1066)Section 24.6fission (1070)fusion (1070)mass defect (1071)nuclear binding energy (1071)electron volt (eV) (1071)Section 24.7chain reaction (1074)critical mass (1074)reactor core (1076)stellar nucleogenesis (1078)

24.5 Finding the half-life of a radioactive nuclide (1056):In 2

tl/2=1::24.6 Calculating the time to reach a given specific activity (ageof an object in radioisotopic dating) (1058):

1 .silot= -In-

k slt24.7 Using Einstein's equation and the mass defect to calculatethe nuclear binding energy (1070):

6.E = 6.mc2

24.8 Relating the atomic mass unit to its energy equivalent inMeV (1071):

1 amu = 931.5X 106eV = 931.5 MeV

T24.2 Modes ofradioactive decay (1048)F24.2 N vs. Z for the stable nuclides (1051)F24.4 Decrease in number of 14Cnuclei over time (1056)F24.13The variation in binding energy per nucleon (1073)

1 .silo 5730 yr (15.3 d/min.g) 324.5 t = -In - = ---In ----- = 4.02X 10 yr

k slt In 2 9.41 d/rnin-gThe mummy case is about 4000 years old.24.6 235Uhas 92 [p and 143 6n.Sm = [(92 X 1.007825 amu) + (143 X 1.008665 amu)]

- 235.043924 amu = 1.9151 amu931.5 MeV

1.9151 amu X ----Binding energy 1 amu

nucleon 235 nucleons= 7.591 MeV/nucleon

Therefore, 23SU is less stable than 12C.

Problems 1083

Problems with colored numbers are answered in Appendix E.Sections match the text and provide the numbers of relevantsample problems. Most offer Concept Review Questions,Skill-Building Exercises (grouped in pairs covering the sameconcept), and Problems in Context. Comprehensive Problemsare based on material from any section or previous chapter.

Radioactive Decay and Nuclear Stability(Sample Problems 24.1 to 24.3)

•• Concept Review Questions24.1 How do chemical and nuclear reactions differ in

(a) Magnitude of the energy change?(b) Effect on rate of increasing temperature?(c) Effect on rate of higher reactant concentration?(d) Effect on yield of higher reactant concentration?

24.2 Sulfur has four naturally occurring isotopes. The one with thelowest mass number is sulfur-32, which is also the most abun-dant (95.02%).(a) What percentage of the S atoms in a matchhead are 32S?(b) The isotopic mass of 32S is 31.972070 amu. Is the atomicmass of S larger, smaller, or equal to this mass? Explain.

24.3 What led Marie Curie to draw the following conclusions?(a) Radioactivity is a property of the element and not the com-pound in which it is found.(b) A highly radioactive element, aside from uranium, occurs inpitchblende.

24.4 Which of the following types of radioactive decay producean atom of a different element: (a) alpha; (b) beta; (c) gamma;(d) positron; (e) electron capture? Show how Z and N change, ifat all, with each type.

24.5 Why is ~He stable but ~He so unstable that it has never beendetected?

24.6 How do the modes of decay differ for a neutron-rich nuclideand a proton-rich nuclide?

24.7 Why can't you use the position of a nuclide's NjZ ratio rela-tive to the band of stability to predict whether it is more likely todecay by positron emission or by electron capture?

EJ Skill-Building Exercises (grouped in similar pairs)24.8 Write balanced nuclear equations for the following:

(a) Alpha decay of 2§iu(b) Electron capture by neptunium-232(c) Positron emission by l~N

24.9 Write balanced nuclear equations for the following:(a) Beta decay of sodium-26(b) Beta decay offrancium-223(c) Alpha decay of 2gBi

24.10 Write balanced nuclear equations for the following:(a) Beta emission by magnesium-27(b) Neutron emission by ~Li(c) Electron capture by 1~~Pd

24.11 Write balanced nuclear equations for the following:(a) Simultaneous 13 and neutron emission by helium-S(b) Alpha decay of polonium-21S(c) Electron capture by l~gIn

24.12 Write balanced nuclear equations for the following:(a) Formation of i~Ti through positron emission

(b) Formation of silver-l 07 through electron captureCc)Formation ofpolonium-206 through a decay

24.13 Write balanced nuclear equations for the following:(a) Production of 2~~Am through 13 decay(b) Formation of 2~~Ac through [3decayCc)Formation of2g~Bi through a decay

24.14 Write balanced nuclear equations for the following:(a) Formation of 186Ir through electron capture(b) Formation of francium-221 through a decay(c) Formation of iodine-129 through [3decay

24.15 Write balanced nuclear equations for the following:(a) Formation of 52Mn through positron emission(b) Formation ofpolonium-215 through a decay(c) Formation of 81 Kr through electron capture

24.16 Which nuclide(s) would you predict to be stable? Why?(a) 2g0 Cb) ~~Co (c) ~Li

24.17 Which nuclide(s) would you predict to be stable? Why?(a) 1~8Nd (b) Il~Cd Cc) ~~Mo

.......... _._._ __ ._._._ .

24.18 Which nuclide(s) would you predict to be stable? Why?Ca) 1271 (b)tin-106 (c) 68As

24.19 Which nuclidets) would you predict to be stable? Why?(a) 48K Cb)79Br (c) argon-32

24.20 What is the most likely mode of decay for each?(a) 2§~U Cb)i~Cr Cc)~~Mn

24.21 What is the most likely mode of decay for each?(a) ~~Fe (b) i~Cl (c) I~Ru

------24.22 What is the most likely mode of decay for each?

(a) 15C (b) 120Xe (c) 224Th24.23 What is the most likely mode of decay for each?

(a) 234Th (b) 141Eu (c) 241Am

24.24 Why is ~~Cr the most stable isotope of chromium?24.25 Why is i8Ca the most stable isotope of calcium?

_ Problems in Context24.26 Neptunium-237 is the parent nuclide of a decay series that

starts with a emission, followed by [3 emission, and then twomore a emissions. Write a balanced nuclear equation for eachstep.

24.27 Why is helium found in deposits of uranium and thoriumores? What kind of radioactive emission produces it?

24.28 In the natural decay series that starts with uranium-235, asequence of a and [3emissions ends with lead-207. How many aand 13 particles are emitted per atom of uranium-235 to result inan atom of lead-20??

The Kinetics of Radioactive Decay(Sample Problems 24.4 and 24.5)

Concept Review Questions24.29 What electronic process is the basis for detecting radioac-

tivity in (a) a scintillation counter; (b) a Geiger-Muller counter?24.30 What is the reaction order of radioactive decay? Explain.24.31 After 1 minute, half the radioactive nuclei remain from an

original sample of six nuclei. Is it valid to conclude that tl/2

equals 1 minute? Would this conclusion be valid if the originalsample contained 6X 1012 nuclei? Explain.


24.32 Radioisotopic dating depends on the constant rate of decayand formation of various nuclides in a sample. How is the pro-portion of 14Ckept relatively constant in living organisms?

Skill-Building Exercises (grouped in similar pairs)24.33 What is the specific activity (in Ci/g) if 1.55 mg of an

isotope emits 1.66Xl 06 ex particles per second?24.34 What is the specific activity (in Ci/g) if 2.6 g of an isotope

emits 4.13 X 108 13 particles per hour?

24.35 What is the specific activity (in Bq/g) if 8.58 Jl-gof anisotope emits 7A Xl 04 ex particles per minute?

24.36 What is the specific activity (in Bq/g) if 1.07 kg of anisotope emits 3.77X 10713 particles per minute?

24.37 If one-trillionth of the atoms of a radioactive isotope disin-tegrate each hour, what is the decay constant of the process?

24.38 If 2.8X 10-10% of the atoms of a radioactive isotope disin-tegrate in 1.0 yr, what is the decay constant of the process?

24.39 If 1.00X 10-12 mol of l35Cs emits 1.39XlO5 13 particles in1.00 yr, what is the decay constant?

24.40 If 6AOXlO-9 mol of 176Wemits 1.07X 1015 positrons in1.00 h, what is the decay constant?

24.41 The isotope 2gBi has a half-life of 1.01 yr. What mass (inmg) of a 2.00-mg sample will not decay after 3.75 X103h?

24.42 The half-life of radium-226 is 1.60X 103 yr. How manyhours will it take for a 2.50-g sample to decay to the point where0.185 g of the isotope remains?

24.43 A rock contains 270 urnol oe38U (tl/2 = 4.5 X 109yr) and110 u.mol of 206Pb.Assuming that all the 206Pb comes fromdecay of the 238U,estimate the rock's age.

24.44 A fabric remnant from a burial site has a 14CYC ratio of0.735 of the original value. How old is the fabric?

Problems in Context24.45 Due to decay of 40K, cow's milk has a specific activity of

about 6X 10-11 mCi per milliliter. How many disintegrations of40Knuclei are there per minute in 1.0 qt of milk?

24.46 Plutonium-239 (tl/2 = 2041 X104 yr) represents a seriousnuclear waste disposal problem. If seven half-lives are requiredto reach a tolerable level of radioactivity, how long must 239pUbe stored?

24.47 A rock that contains 2.1XlO-I5 mol of 232Th (t1/2 =lAX 1010yr) has 9.5X104 fission tracks, each representing thefission of one atom of 232Th.How old is the rock?

24.48 A volcanic eruption melts a large area of rock, and all gasesare expelled. After cooling, i~Ar accumulates from the ongoingdecay of i8K in the rock (tl/2 = 1.25X109 yr). When a pieceof rock is analyzed, it is found to contain 1.38 mmol of 40K and1.14 mmol of 40Ar. How long ago did the rock cool?

Nuclear Transmutation: Induced Changes in NucleiConcept Review Questions

24.49 Irene and Frederic Joliot-Curie converted i~Al to ~gP in1933. Why was this transmutation significant?

24.50 Early workers mistakenly thought neutron beams were "I ra-diation. Why were they misled? What evidence led to the correctconclusion?

24.51 Why must the electrical polarity of the tubes in a linear ac-celerator be reversed at very short time intervals?

24.52 Why does bombardment with protons usually requirehigher energies than bombardment with neutrons?

IB!i'!i Skill-Building Exercises (grouped in similar pairs)24.53 Determine the missing species in these transmutations, and

write a full nuclear equation from the shorthand notation:(a) lOB (o.,n) _(b) 28Si (d,_) 29p (the deuteron, d, is 2H)(c) _ (o..Zn)244Cf

24.54 Determine the missing species in these transmutations, andexpress each process in shorthand notation:(a) Bombardment of a nuclide with a "I photon yields a proton, aneutron, and 29Si.(b) Bombardment of 252Cf with lOByields five neutrons and anuclide.(c) Bombardment of 238Uwith a particle yields three neutronsand 239pU.

r:::1I Problem in Context24.55 Names for elements 104, 105, and 106 have been approved

as rutherfordium (Rf), dubnium (Db), and seaborgium (Sg), re-spectively. These elements are synthesized from californium-249 by bombarding with carbon-12, nitrogen-IS, and oxygen-I 8nuclei, respectively. Four neutrons are formed in each reactionas well. (a) Write balanced nuclear equations for the formationof these elements. (b) Write the equations in shorthand notation.

The Effects of Nuclear Radiation on MatterConcept Review Questions

24.56 Gamma radiation and UV radiation cause differentprocesses in matter. What are they and how do they differ?

24.57 What is a cation-electron pair, and how does it form?24.58 Why is ionizing radiation more dangerous to children than

to adults?24.59 Why is ·OH more dangerous in an organism than OH-?••• Skill-Building Exercises (grouped in similar pairs)24.60 A 135-lb person absorbs 3.3X 10-7 J of energy from

radioactive emissions. (a) How many rads does she receive?(b) How many grays (Gy) does she receive?

24.61 A 3.6-kg laboratory animal receives a single dose of8.92X 10-4 Gy. (a) How many rads did the animal receive?(b) How many joules did the animal absorb?

24.62 A 70.-kg person exposed to 90Sr absorbs 6.0X 105 13 parti-cles, each with an energy of 8.74X 10-14 J. (a) How many graysdoes the person receive? (b) If the RBE is 1.0, how many mil-lirems is this? (c) What is the equivalent dose in sieverts (Sv)?

24.63 A laboratory rat weighs 265 g and absorbs 1.77X 1010f3 par-ticles, each with an energy of 2.20X 10-13 J. (a) How many radsdoes the animal receive? (b) What is this dose in Gy? (c) If theRBE is 0.75, what is the equivalent dose in Sv?

•• Problems in Context24.64 If 2.50 pCi [I pCi (picocurie) = I X 10-12 Ci] of radioac-

tivity from 239puis emitted in a 95-kg human for 65 h, and eachdisintegration has an energy of 8.25XIO-13 J, how many graysdoes the person receive?

24.65 A small region of a cancer patient's brain is exposed for27.0 min to 475 Bq of radioactivity from 60Cofor treatment of atumor. If the brain mass exposed is 1.588 g and each 13 particleemitted has an energy of 5.05 X 10-14 J, what is the dose in rads?

E:::1 Concept Review Questions24.66 Describe two ways that radioactive tracers are used in or-

ganisms.24.67 Why is neutron activation analysis (NAA) useful to art his-

torians and criminologists?24.68 Positrons cannot penetrate matter more than a few atomic

diameters, but positron emission of radiotracers can be moni-tored in medical diagnosis. Explain.

24.69 A steel part is treated to form some iron-59. Oil used to lu-bricate the part emits 298 13 particles (with the energy charac-teristic of 59Fe)per minute per milliliter of oil. What other infor-mation would you need to calculate the rate of removal of thesteel from the part during use?

~ Problem in Context24.70 The oxidation of methanol to formaldehyde can be accom-

plished by reaction with chromic acid:6H+(aq) + 3CH30H(aq) + 2H2Cr04(aq) -

3CH20(aq) + 2Cr3+(aq) + 8H20(I)The reaction can be studied with the stable isotope tracer 180and mass spectrometry. When a small amount of CH3180H ispresent in the alcohol reactant, H2CI80 forms. When a smallamount ofH2Crl804 is present, H2180 forms. Does chromic acidor methanol supply the 0 atom to the aldehyde? Explain.

tnterconversion Mass(Sample Problem 24.6)Note: Use the following data to solve the problems in thissection: mass of IH atom = 1.007825 amu; mass of neutron =1.008665 amu.

fJ!!::J Concept Review Questions24.71 Many scientists at first reacted skeptically to Einstein's

equation, E = me". Why?24.72 What is a mass defect, and how does it arise?24.73 When a nuclide forms from nucleons, is energy absorbed or

released? Why?24.74 What is the binding energy per nucleon? Why is the binding

energy per nucleon, rather than per nuclide, used to compare nu-clide stability?

lE! Skill-Building Exercises (grouped in similar pairs)24.75 A 3H nucleus decays with an energy of 0.01861 MeV Con-

vert this energy into (a) electron volts; (b) joules.24.76 Arsenic-84 decays with an energy of 1.57X10-15 kJ per nu-

cleus. Convert this energy into (a) eV; (b) MeV

24.77 How many joules are released when 1.0 mol of 239pUdecays, if each nucleus releases 5.243 MeV?

24.78 How many MeV are released per nucleus when 3.2X 10-3mol of chromium-49 releases 8.11 X105kJ?

24.79 Oxygen-16 is one of the most stable nuclides. The mass ofa 160 atom is 15.994915 amu. Calculate the binding energy(a) per nucleon in MeV; (b) per atom in MeV; (c) per mole in kJ.

24.80 Lead-206 is the end product of 238Udecay. One 206Pbatomhas a mass of 205.974440 amu. Calculate the binding energy(a) per nucleon in MeV; (b) per atom in MeV; (c) per mole in kJ.

24.81 Cobalt-59 is the only stable isotope of this transition metal.One 59COatom has a mass of 58.933198 amu. Calculate the

Problems 1085

binding energy (a) per nucleon in MeV; (b) per atom in MeV;(c) per mole in kJ.

24.82 Iodine-131 is one of the most important isotopes used inthe diagnosis of thyroid cancer. One atom has a mass of130.906114 amu. Calculate the binding energy (a) per nucleon inMeV; (b) per atom in MeV; (c) per mole in kJ.

le Problem in Context24.83 The 80Br nuclide decays either by 13 decay or by elec-

tron capture. (a) What is the product of each process?(b) Which process releases more energy? (Masses of atoms:80Br = 79.918528 amu; 80Kr = 79.916380 amu; 80Se79.916520 amu; neglect the mass of the electron involved.)

Fission Fusionle Concept Review Questions24.84 What is the minimum number of neutrons from each

fission event that must be absorbed by other nuclei for a chainreaction to occur?

24.85 In what main way is fission different from radioactive de-cay? Are all fission events in a chain reaction identical? Explain.

24.86 What is the purpose of enrichment in the preparation of fuelrods? How is it accomplished?

24.87 Describe the nature and purpose of these components of anuclear reactor: (a) control rods; (b) moderator; (c) reflector.

14.88 State an advantage and a disadvantage of heavy-water reac-tors compared to light-water reactors.

24.89 What are the expected advantages of fusion reactors overfission reactors?

24.90 Why is there more iron in Earth than any other element?24.91 Why do so many nuclides have isotopic masses close to

multiples of 4 amu?24.92 What is the cosmic importance of unstable 8Be?le Problem in Context24.93 The reaction that will probably power the first commercial

fusion reactor isiH + iH - iHe + bn

How much energy would be produced per mole of reaction?(Masses of atoms: iH = 3.01605 amu; iH = 2.0140 amu;iHe = 4.00260 amu; mass of {In= 1.008665 amu.)

rehensive Problems24.94 Some 2~~Amwas present when Earth formed, but it all de-

cayed in the next billion years. The first three steps in this decayseries are emission of an ex particle, a 13 particle, and anotherex particle. What other isotopes were present on the young Earthin a rock that contained some 2~~Am?

24.95 Curium-243 undergoes ex decay to plutonium-239:243Cm_ 239pU+ 4He

(a) Calculate the change in mass, Sm (in kg). (Masses: 243Cm=

243.0614 amu; 239pU= 239.0522 amu; 4He = 4.0026 amu;1 amu = 1.661X 10-24 g.)(b) Calculate the energy released in joules.(c) Calculate the energy released in kl/rnol of reaction, and com-ment on the difference between this value and a typical heat ofreaction for a chemical change of a few hundred kl/mol,

24.96 Plutonium "triggers" for nuclear weapons were manufac-tured at the Rocky Flats plant in Colorado. An 85-kg workerinhaled a dust particle containing 1.00 fLg of 2§~PU,which


resided in his body for 16 h (t 1/2of 239pu = 2.41 X 104 yr; eachdisintegration released 5.15 MeV). (a) How many rads did he re-ceive? (b) How many grays?

24.97 Archeologists removed some charcoal from a Native Amer-ican campfire, burned it in O2, and bubbled the CO2 formed intoCa(OH)2 solution (limewater). The CaC03 that precipitated wasfiltered and dried. If 4.38 g of the CaC03 had a radioactivity of3.2 d/min, how long ago was the campfire?

24.98 A 5.4-f.Lg sample of 226RaCI2 has a radioactivity of1.5 X 105 Bq. Calculate tl/2 of 226Ra..

24.99 How many rads does a 65-kg human receive each year fromthe approximately 10-8 g of I~C naturally present in her body(t1/2 = 5730 yr; each disintegration releases 0.156 MeV)?

24.100 The major reaction taking place during hydrogen burningin a young star is

4J H --->- iHe + 2?[3 + 28-y + energyHow much energy (in Me V) is released per He nucleus formed?Per mole of He? (Masses: ]H atom = 1.007825 amu;iHe atom = 4.00260 amu; positron = 5.48580X 10-4 amu.)

24.101 A sample of AgCI emits 175 nCi/g. A saturated solutionprepared from the solid emits 1.25 Xl 0-2 Bq/mL due to radioac-tive Ag + ions. What is the molar solubility of AgCl?

24.102 Due to burning of fossil fuels, the proportion of CO2 in ouratmosphere continues to increase. Moreover, as a result of nu-clear explosions and similar events, the CO2 also contains more14C. How will these factors affect the efforts of future archeolo-gists to determine ages of our artifacts by radiocarbon dating?

24.103 What fraction of the 235U (t 1/2 = 7 .OX 108 yr) created whenEarth was formed would remain after 2.8 Xl 09 yr?

24.104 In the event of a nuclear accident, radiation officers mustobtain many pieces of data to decide on appropriate action.(a) If a person ingests radioactive material, which of the follow-ing is the most important quantity in deciding whether a seriousmedical emergency has occurred?(1) The number of rems he receives(2) The number of curies he absorbs(3) The length of time he is exposed to the radiation(4) The number of moles of radioisotopes he ingests(5) The energy emitted per disintegration by the radioisotopes(b) If the drinking water in a town becomes contaminated withradioactive material, what is the most important factor in decid-ing whether drastic and expensive action is warranted?(1) The radioactivity per volume, Ci/m3

(2) How long the water supply has been contaminated(3) (Ci/m3) X energy per disintegration(4) The type of radiation emitted(5) The radioisotopes involved

24.105 Cosmologists modeling the origin of the elements postu-late nuclides with very short half-lives.(a) One of these nuclides, 8Be (t1/2 = 7XlO-17 s), plays a keyrole in stellar nucleogenesis (p. 1078) because it must fuse witha 4He to form 12C before decaying. Another explanation in-volves the simultaneous fusion of three 4He nuclei to form 12c.Comment on the validity of this alternative mechanism.(b) Another question involves the instability of the two nuclideswith A = 5, SHe and sLi, each of which has a tl/2 nearly 10-5

times that of 8Be. Write nuclear equations for the 0' decay of 8Be,SHe, and sLi.

24.106 Technetium-99m is a metastable nuclide used in numerouscancer diagnostic and treatment programs. It is prepared just be-fore use because it decays rapidly through -yemission:

99mTc --->- 99Tc + -y

Use the data below to determine:(a) The half-life of 99mTc(b) The percentage of the isotope that is lost if it takes 2.0 h toprepare and administer the dose

Time (h)

o48

121620

'Y Emission (photons/s)

5000.3150.2000.1250.788495

24.107 How many curies are produced by 1.0 mol of 40K (t1/2 =1.25 X 109 yr)? How many becquerels?

24.108 The fraction of a radioactive isotope remaining at time t is(1)111112, where l vr: is the half-life. If the half-life of carbon-14 is5730 yr, what fraction of carbon-14 in a piece of charcoal re-mains after (a) 10.0 yr; (b) 1O.0X 103 yr; (c) 1O.0X 104 yr?(d) Why is radiocarbon dating more reliable for the fraction re-maining in part (b) than that in part (a) or in part (c)?

24.109 The isotopic mass of 2~~Rn is 209.989669 amu. When thisnuclide decays by electron capture, it emits 2.368 MeY. What isthe isotopic mass of the resulting nuclide?

24.110 Exactly 0.1 of the radioactive nuclei in a sample decayeach hour. Thus, after n hours, the fraction of nuclei remaining is(0.900)". Find the value of n equal to one half-life.

24.111 In neutron activation analysis (NAA), stable isotopes arebombarded with neutrons. Depending on the isotope and the en-ergy of the neutron, various emissions are observed. What arethe products when the following neutron-activated species de-cay? Write an overall equation in shorthand notation for the re-action starting with the stable isotope before neutron activation.(a) ~~V* --->- [[3 emission](b) ~~Cu* --->- [positron emission](c) i~Al* --->- [[3 emission]

24.112 In the 1950s, radioactive material was spread over the landfrom above-ground nuclear tests. A woman drinks some contam-inated milk and ingests 0.0500 g of 90Sr, which is taken up bybones and teeth and not eliminated. (a) How much 90Sr (tl/2 =29 yr) is present in her body after 10 yr? (b) How long will it takefor 99.9% of the 90Sr to decay?

24.113 Isotopic abundances are relatively constant throughoutEarth's crust. Could the science of chemistry have developed if,for example, one sample of tin(II) oxide contained mostly 112Snand another mostly 124Sn? Explain.

24.114 What volume of radon will be produced per hour at STPfrom 1.000 g of 226Ra (tl/2 = 1599 yr; 1 yr = 8766 h; mass ofone 226Ra atom = 226.025402 amu)?

24.115 A sample of 9°Kr (t1/2 = 32 s) is to be used in a study of apatient's respiration. How soon after being made must it be ad-ministered to the patient if the activity must be at least 90% ofthe original activity?

24.116 Which isotope in each pair would you predict to be morestable? Why?(a) l~~CSor l~~CS (b) ~~Bror ~~Br(c) r~Mg or riMg (d) ljN or l~N

24.117 A sample of bone contains enough strontium-90 (t1/229 yr) to emit 8.0X104 I?> particles per month. How long will ittake for the emission to decrease to 1.0X 104 particles permonth?

24.118 The 23rd -century starship Enterprise uses a substancecalled "dilithium crystals" as its fuel.(a) Assuming this material is the result of fusion, what is theproduct of the fusion of two 6Li nuclei?(b) How much energy is released per kilogram of dilithiumformed? (Mass of one 6Li atom is 6.015121 amu.)(c) When four 'n atoms fuse to form 4He, how many positronsare released?(d) To determine the energy potential of the fusion processes inparts (b) and (c), compare the changes in mass per kilogram ofdilithium and of 4He.(e) Compare the change in mass per kilogram in part (b) to thatfor the formation of 4He by the method used in current fusion re-actors (Section 24.7). (For masses, see Problem 24.93.)(f) Using early 21SI-century fusion technology, how much tri-tium can be produced per kilogram of 6Li in the following reac-tion: ~Li + bn --* iHe + ~H? When this amount of tritium isfused with deuterium, what is the change in mass? How does thisquantity compare with the use of dilithium in part (b)?

24.119 Uranium and radium are found in many rocky soilsthroughout the world. Both undergo radioactive decay, and oneof the products is radon-222, the heaviest noble gas (tl/2 =3.82 days). Inhalation of indoor air containing this gas con-tributes to many lung cancers. According to Environmental Pro-tection Agency recommendations, the level of radioactivity fromradon in homes should not exceed 4.0 pCi/L of air.(a) What is the safe level of radon in Bq/L of air?(b) A home has a radon measurement of 43.5 pCi/L. The ownervents the basement in such a way that no more radon enters theliving area. What is the activity of the radon remaining in theroom air (in Bq/L) after 8.5 days?(c) How many more days does it take to reach the EPA recom-mended level?

24.120 Nuclear disarmament could be accomplished if weaponswere not "replenished." The tritium in warheads decays to he-lium with a half-life of 12.26 yr and must be replaced or theweapon is useless. What fraction of the tritium is lost in 5.50 yr?

24.121 A decay series starts with the synthetic isotope 2§~U.Thefirst four steps are emissions of a I?> particle, another I?>, an 0' par-ticle, and another 0'. Write a balanced nuclear equation for eachstep. Which natural series could be started by this sequence?

24.122 How long can a 48-lb child be exposed to 1.0 mCi of radi-ation from 222Rnbefore accumulating 1.0 mrad if the energy ofeach disintegration is 5.59 MeV?

24.123 The approximate date of a San Francisco earthquake is tobe found by measuring the 14Cactivity (t1/2= 5730 yr) of partsof a tree uprooted during the event. The tree parts have an activ-ity of 12.9 d/min-g C, and a living tree has an activity of15.3 d/min-g C. How long ago did the earthquake occur?

24.124 Were organisms a billion years ago exposed to more or lessionizing radiation than similar organisms today? Explain.

Problems 1087

240125 Tritium eH; t1/2 = 12.26 yr) is continually formed in theupper troposphere by interaction of solar particles with nitrogen.As a result, natural waters contain a small amount of tritium.Two samples of wine are analyzed, one known to be made in1941 and another made earlier. The water in the 1941 wine has2.32 times as much tritium as the water in the other. When wasthe other wine produced?

24.126 Plutonium-239 (t1/2 = 2.41 X 104 yr) is a serious radiationhazard present in spent uranium fuel from nuclear power plants.How many years does it take for 99% of the plutonium-239 inspent fuel to decay?

24.127 Carbon from the most recent remains of an extinctAustralian marsupial, called Diprotodon, has a specific activity of0.61 pCi/g. Modem carbon has a specific activity of 6.89 pCi/g.How long ago did the Diprotodon apparently become extinct?

24.128 The reaction that allows for radiocarbon dating is the con-tinual formation of carbon-14 in the upper atmosphere:

ljN + bn --* l~C + (HWhat is the energy change associated with this process ineV/reaction and in kJ/mol reaction? (Masses of atoms: ljN =14.003074 amu; l~C = 14.003241 amu; (H = 1.007825 amu;mass of bn = 1.008665 amu.)

24.129 What is the nuclear binding energy of a lithium-7 nucleusin units of kJ/mol and eV/nucleus? (Mass of a lithium-7 atom =7.016003 amu.)

24.130 Suggest a reason the critical mass of a fissionable sub-stance depends on its shape.

),4.131 Using early 21st_century technology, hydrogen fusion re-quires temperatures around 108 K, but lower temperatures canbe used if the hydrogen is compressed. In the late 24th century,the starship Leinad uses such methods to fuse hydrogen at 106K.(a) What is the kinetic energy of an H atom at 1.00X106K?(b) How many H atoms are heated to 1.00X106 K from the en-ergy of one H and one anti-H atom annihilating each other?(c) If these H atoms fuse into 4He atoms (with the loss of twopositrons per 4He formed), how much energy (in J) is generated?(d) How much more energy is generated by the fusion in (c) thanby the hydrogen-antihydrogen collision in (b)?(e) Should the captain of the Leinad change the technology andproduce 3He (mass = 3.01603 amu) instead of4He?

24.132 A metastable (excited) form of 50SCchanges to its stableform by emitting 'Yradiation with a wavelength of 8.73 pm.What is the change in mass of 1 mol of the isotope when it un-dergoes this change?

24.133 A sample of cobalt-60 (tl/2 = 5.27 yr), a powerful 'Yemitterused to treat cancer, was purchased by a hospital on March 1,2005. The sample must be replaced when its activity reaches70.% of the original value. On what date must it be replaced?

24.134 Uranium-233 decays to thorium-229 by 0' decay, but theemissions have different energies and products: 83% emit an 0'

particle with energy 4.816 MeV and give 229Th in its groundstate; 15% emit an 0' particle of 4.773 MeV and give 229Thin ex-cited state I; and 2% emit a lower energy 0' particle and give229Thin the higher excited state n. Excited state Il emits a 'Yrayof 0.060 MeV to reach excited state 1. (a) Find the 'Y-rayenergyand wavelength that would convert excited state I to the groundstate. (b) Find the energy of the 0' particle that would convert233Uto excited state n.


24.135 Uranium-238 undergoes a slow decay step (tl/2 = 4.5 X 109

yr) followed by a series of fast steps to form the stable isotope206Pb. Thus, on a time scale of billions of years, 238U effectivelydecays "directly" to 206Pb, and the relative amounts of these iso-topes are used to find the age of some rocks (see margin note,p. 1059). Two students derive equations relating number of half-lives (n) since the rock formed to the amounts of the isotopes:

I 11 20~U('2) = 2~~Pb

I 11 20~U('2) = 238U + 206Pb92 82

(a) Which equation is correct, and why?(b) If a rock contains exactly twice as much 238U as 206Pb, whatis its age in years?

24.136 In the naturally occurring thorium-232 decay series, thesteps emit this sequence of particles: ex, (3, (3, ex, ex, ex, ex, (3, (3, andex. Write a balanced equation for each step.

24,137 At death, a nobleman in ancient Egypt was mummified andhis body contained lAXlO-3 g of 40K (t1/2 = 1.25X109 yr),1.2XlO-8 g of 14C (t1/2 = 5730 yr), and 4.8XlO-14 g of 3H(t1/2 = 12.26 yr). Which isotope would give the most accurateestimate of the mummy's age? Explain.

24.138 Assuming that many radioactive isotopes can be consid-ered safe after 20 half-lives, how long will it take for each of thefollowing isotopes to be safe?(a) 242Cm (tl/2 = 163 days)(b) 214pO (t1/2 = 1.6x 10-4 s)(c) 232Th (t 1/2 = 1.39 X 1010 yr)

24.139 An ancient sword has a blade from the early Roman Em-pire, around 100 AD, but the wooden handle, inlaid wooden dec-orations, leather ribbon, and leather sheath have different styles.Given the following activities, estimate the age of each part.Which part was made near the time of the blade (t1/2 of 14C =5730 yr; .silo = 15.3 d/min-g)?

Student 1:

Student 2:

Part .silt (d/min'g)

10.113.812.115.0

HandleInlaid woodRibbonSheath

24.140 The starship Voyager, like many other vessels of the newlydesigned 24th-century fleet, uses antimatter as fuel.(a) How much energy is released when 1.00 kg each of antimat-ter and matter annihilate each other?(b) When the antimatter is atomic antihydrogen, a small amountof it is mixed with excess atomic hydrogen (gathered from inter-stellar space during flight). The annihilation releases so muchheat that the remaining hydrogen nuclei fuse to form 4He. If eachhydrogen-antihydrogen collision releases enough heat to fuse1.00 Xl 05 hydrogen atoms, how much energy (in kJ) is releasedper kilogram of antihydrogen?(c) Which produces more energy per kilogram of antihydrogen,the procedure in part (a) or that in part (b)?

24.141 Use Einstein's equation, the mass in grams of 1 amu, andthe relation between electron volts and joules to find the energyequivalent (in Me V) of a mass defect of 1 amu.

24.142 Determine the age of a rock containing 0.065 g of uranium-238 (t1/2 = 4.5 X 109 yr) and 0.023 g oflead-206. (Assume all thelead-206 came from 238U decay.)

24.143 Plutonium-242 decays to uranium-238 by emission of an exparticle with an energy of 4.853 MeV The 238U that forms is un-stable and emits a'Y ray (lI. = 0.02757 nm). (a) Write balancedequations for these reactions. (b) What would be the energy ofthe ex particle if 242pU decayed directly to the more stable 238U?

24.144 Seaborgium-263 (Sg; Z = 106) was the first isotope of thiselement synthesized. It was made, together with four neutrons,by bombarding californium-249 with oxygen-18. It then de-cayed by three ex emissions. Write balanced equations for thesynthesis and three decay steps of 263Sg.

24.145 Some nuclear power plants use plutonium-239, which isproduced in breeder reactors (see margin note, p. 1077). Therate-determining step is the second (3emission. How long does ittake to make 1.00 kg of 239pU if the reaction is complete whenthe product is 90. % 239pu?

24.146 A random-number generator can be used to simulate theprobability of a given atom decaying over a given time. For ex-ample, the formula "= RANDO" in the Excel spreadsheet returnsa random number between 0 and I; thus, for one radioactiveatom and a time of one half-life, a number less than 0.5 meansthe atom decays and a number greater than 0.5 means it doesn't.(a) Place the "=RANDO" formula in cells Al to AlO of an Ex-cel spreadsheet. In cell Bl, place "=IF(A1<0.5, 0,1)." This for-mula returns 0 if Al is <0.5 (the atom decays) and 1 if Al is >0.5(the atom does not decay). Place analogous formulas in cells B2to BI0 (using the "Fill Down" procedure in Excel). To determinethe number of atoms remaining after one half-life, sum cells B 1to BIO by placing "=SUM(Bl:BlO)" in cell B12. To create anew set of random numbers, click on an empty cell (e.g., Bl3)and hit "Delete." Perform 10 simulations, each time recordingthe total number of atoms remaining. Do half of the atoms re-main after each half-life? If not, why not?(b) Increase the number of atoms to 100 by placing suitable for-mulas in cells Al to A100, Bl to B100, and B102. Perform 10simulations, and record the number of atoms remaining eachtime. Are these results more realistic for radioactive decay?Explain.

24.147 In the following Excel-based simulation, the fate of 256atoms is followed over five half-lives. Set up formulas incolumns A and B, as in Problem 24.146, and simulate thefate of the sample of 256 atoms over one half-life. CellsB 1 to B256 should contain I or O. In cell Cl, enter"=IF(Bl=O, 0, RAND(»." This returns 0 if the original atomdecayed in the previous half-life or a random number between 0and I if it did not. Fill the formula in Cl down to cell C256. Col-umn D should have formulas similar to those in B, but with mod-ified references, as should columns F, H, and J. Columns E, G,and I should have formulas similar to those in C, but with modi-fied references. In cell B258, enter "=SUM(Bl:B256)." Thisrecords the number of atoms remaining after the first half-life.Put formulas in cells D258, F258, H258, and J258 to recordatoms remaining after subsequent half-lives.(a) Ideally, how many atoms should remain after each half-life?(b) Make a table of the atoms remaining after each half-life infour separate simulations. Compare these outcomes to the idealoutcome. How would you make the results more realistic?

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