Nuclear Reactions and Their Applications

Fusing nuclei The Z machine of Sandia National Laboratory, the most
powerful x-ray generator on Earth, helps scientists understand phe-
nomena from the origin of the universe to nuclear fusion. It is rou-
tinely used to fuse hydrogen nuclei at temperatures exceeding
those within the Sun. In this chapter, we explore both the
fundamental nature of atomic nuclei and their remark-
able practical applications.

Nuclear Reactions and
Their Applications
24.1 Radioactive Decay and Nuclear Stability 24.3 Nuclear Transmutation: Induced 24.5 Applications of Radioisotopes
Components of the Nucleus Changes in Nuclei Radioactive Tracers
Types of Radioactive Emissions Early Transmutation Experiments Applications of Ionizing Radiation
Types of Radioactive Decay; Particle Accelerators 24.6 The Interconversion of Mass and Energy
Nuclear Equations 24.4 The Effects of Nuclear Radiation The MassDefect
The Mode of Decay on Matter Nuclear Binding Energy
24.2 The Kinetics of Radioactive Decay Excitation and Ionization 24.7 Applications of Fission and Fusion
Rateof Radioactive Decay Ionizing Radiation and Living Matter Nuclear Fission
Radioisotopic Dating Nuclear Fusion

ar below the outer fringes of the cloud of electrons l~€s the atom's
F tiny, dense core, held together by the strongest force/in the universe.
For nearly the entire text so far, we have focused on an atom's elec-
trons, treating the nucleus as little more than their electrostatic anchor,
examining the effect of its positive charge on atomic properties and, ulti-
mately, chemical behavior. But, for the scientists probing the structure and
behavior of the nucleus itself, there is the scene of real action, one that holds
enormous potential benefit and great mystery and wonder.
Society is ambivalent about the applications of nuclear research, however. The
• discoveryof the atomic nucleus(Section
promise of abundant energy and treatments for disease comes hand-in-hand with 2.4)
the threat of nuclear waste contamination, reactor accidents, and unimaginable • protons, neutrons,massnumber,and the
destruction from nuclear war or terrorism. Can the power of the nucleus be har- ~X notation (Section2.S)
nessed for our benefit, or are the risks too great? In this chapter, we discuss the • half-life and first-order reaction rate
principles that can help you answer this vital question. (Section16.4)
The changes that occur in atomic nuclei are strikingly different from chemi-
cal changes. In the reactions you've studied so far, electrons are shared or trans-
ferred to form compounds, while nuclei sit by passively, never changing their
identities. In nuclear reactions, the roles are reversed: electrons in their orbitals
are usually bystanders as the nuclei undergo changes that, in nearly every case,
form different elements. Nuclear reactions are often accompanied by energy
changes a million times greater than those in chemical reactions, energy changes
so great that changes in mass are detectable. Moreover, nuclear reaction yields
and rates are typically not subject to the effects of pressure, temperature, and
catalysis that so clearly influence chemical reactions. Table 24.1 summarizes the
general differences between chemical and nuclear reactions.

I1mIID Comparison of Chemical and Nuclear Reactions
Chemical Reactions Nuclear Reactions

1. One substance is converted into another, but atoms never 1. Atoms of one element typically are converted into atoms of
change identity. another element.
2. Orbital electrons are involved as bonds break and form; 2. Protons, neutrons, and other particles are involved; orbital
nuclear particles do not take part. electrons rarely take part.
3. Reactions are accompanied by relatively small changes in 3. Reactions are accompanied by relatively large changes in
energy and no measurable changes in mass. energy and measurable changes in mass.
4. Reaction rates are influenced by temperature, 4. Reaction rates are affected by number of nuclei, but not by
concentration, catalysts, and the compound in which an temperature, catalysts, or, normally, the compound in
element occurs. which an element occurs.

IN THIS CHAPTER ... We survey the field of nuclear chemistry, beginning with
an investigation of nuclear stability-why some nuclei are stable, whereas oth-
ers are unstable and undergo radioactive decay. You'll see how radioactivity is
detected and how the kinetics of decay is applied. We explore how nuclei syn-
thesized in particle accelerators have extended the periodic table beyond ura-
nium, the last naturally occurring element. Then, we consider the effects of
radioactive emissions on matter, especially living matter, focusing on some
major applications in science, technology, and medicine. A major focus is to
calculate the energy released in nuclear fission and fusion and discuss current
and future attempts to harness this energy. Finally, we end with a look at the
nuclear processes that create the chemical elements in the stars.

1045

1046 Chapter 24 Nuclear Reactions and Their Applications

24.1 RADIOACTIVE DECAY AND NUCLEAR STABILITY
A stable nucleus remains intact indefinitely, but the great majority of nuclei are
unstable. An unstable nucleus exhibits radioactivity: it spontaneously disinte-
grates, or decays, by emitting radiation. In the next section, you'll see that each
type of unstable nucleus has its own characteristic rate of radioactive decay, which
can range from a fraction of a second to billions of years. In this section, we con-
sider important terms and notation for nuclei, discuss some of the key events in
the discovery of radioactivity, and describe the various types of radioactive decay
and how to predict which type occurs for a given nucleus.

The Components of the Nucleus: Terms and Notation
Recall from Chapter 2 that the nucleus contains essentially all the atom's mass
but is only about 10-4 times its diameter (or 10-12 times its volume). Obviously,
The Tiny, Massive Nucleus If you the nucleus is incredibly dense: about 1014 g/ml., Protons and neutrons, the
could strip the electrons from the atoms elementary particles that make up the nucleus, are collectively called nucleons.
in an object and compress the nuclei to- The term nuclide refers to a nucleus with a particular composition, that is, with
gether, the object would lose only a frac- specific numbers of the two types of nucleons. Most elements occur in nature as
tion of a percent of its mass, but it would a mixture of isotopes, atoms with the characteristic number of protons of the ele-
shrink to 0.0000000001 % (10-1°%) of its
ment but different numbers of neutrons. Therefore, each isotope of an element
volume. An atom the size of the Houston
has a particular nuclide that we identify by the numbers of protons and neutrons
Astrodome would have a nucleus the size
of a grapefruit, which would contain vir-
it contains. The nuclide of the most abundant isotope of oxygen, for example,
tually all the atom's mass. contains eight protons and eight neutrons, whereas the nuclide of the least abun-
dant isotope contains eight protons and ten neutrons.
The relative mass and charge of a particle-a nucleon, another elementary
particle, or a nuclide-is described by the notation ~X, where X is the symbol
for the particle, A is the mass number, or the total number of nucleons, and Z is
the charge of the particle; for nuclides, A is the sum of protons and neutrons and
Z is the number of protons (atomic number). Using this notation, we write the
three subatomic elementary particles as follows:
_?e (electron), jp (proton), and bn (neutron)
(In nuclear notation, the element symbol refers to the nucleus only, so a proton
is also sometimes represented as lH.) The number of neutrons (N) in a nucleus
is the mass number (A) minus the atomic number (Z): N = A - Z. The two nat-
urally occurring isotopes of chlorine, for example, have 17 protons (Z = 17), but
one has 18 neutrons mCl, also written 35Cl) and the other has 20 mCl, or 37Cl).
Nuclides can also be designated with the element name followed by the mass
number, for example, chlorine-35 and chlorine-37. Despite some small variations,
in naturally occurring samples of an element or its compounds, the isotopes of
the element are present in particular, fixed proportions. Thus, in a sample of
sodium chloride (or any Cl-containing substance), 75.77% of the Cl atoms are
chlorine-35 and the remaining 24.23% are chlorine-37.
To understand this chapter, it's very important for you to be comfortable with
nuclear notations, so please take a moment to review Sample Problem 2.2 on
p. 51 and Problems 2.37 to 2.44 at the end of Chapter 2.

The Discovery of Radioactivity and the Types of Emissions
In 1896, the French physicist Antoine-Henri Becquerel discovered, quite by acci-
dent, that uranium minerals, even when wrapped in paper and stored in the dark,
emit a penetrating radiation that can produce bright images on a photographic
plate. Becquerel also found that the radiation creates an electric discharge in air,

24.1 Radioactive Decay and Nuclear Stability 1047

thus providing a means for measuring its intensity. Two years later, a young
doctoral student named Marie Sklodowska Curie began a search for other miner-
als that behaved like uranium in this way. She found that thorium minerals also
emit radiation and discovered that the intensity of the radiation is directly pro-
portional to the concentration of the element in the mineral, not to the nature of
the mineral or compound in which the element occurs. Curie named the emis-
sions radioactivity and showed that they are unaffected by temperature, pressure,
or other physical and chemical conditions.
To her surprise, Curie found that certain uranium minerals were even more
radioactive than pure uranium, which implied that they contained traces of one
or more as yet unknown, highly radioactive elements. She and her husband, the
physicist Pierre Curie, set out to isolate all the radioactive components in pitch-
blende, the principal ore of uranium. After months of painstaking chemical work,
they isolated two extremely small, highly radioactive fractions, one that precipi- Her Brilliant Career Marie Curie
tated with bismuth compounds and another that precipitated with alkaline earth (1867-1934) is the only person to be
compounds. Through chemical and spectroscopic analysis, Marie Curie was able awarded Nobel Prizes in two different sci-
to show that these fractions contained two new elements, which she named polo- ences, one in physics in 1903 for her re-
nium (after her native Poland) and radium. Polonium (Po; Z = 84), the most search into radioactivity and the other in
metallic member of Group 6A(l6), lies to the right of bismuth in Period 6. chemistry in 1911 for the discovery of
Radium (Ra; Z = 88), which is the heaviest alkaline earth metal, lies under bar- polonium and the discovery, isolation,
and study of radium and its compounds.
ium in Group 2A(2).
Purifying radium proved to be another arduous task. Starting with several tons
of pitchblende residues from which the uranium had been extracted, Curie pre-
pared compounds of the larger Group 2A(2) elements, continually separating
minuscule amounts of radium compounds from enormously larger amounts of
chemically similar barium compounds. It took her four years to isolate 0.1 g of
radium chloride, which she melted and electrolyzed to obtain pure metallic ZnS-coated screen
(or photographic plate)
radium.
During the next few years, Henri Becquerel, the Curies, and P. Villard in
France and Emest Rutherford and his coworkers in England studied the nature of
radioactive emissions. Rutherford and his colleague Frederick Soddy observed
that elements other than radium were formed when radium decayed. In 1902, they
proposed that radioactive emission results in the change of one element into
another. To their contemporaries, this idea sounded like a resurrection of alchemy
and was met with disbelief and ridicule. We now know it to be true: under most
circumstances, when a nuclide of one element decays, it changes into a nuclide
of a different element.
These studies led to an understanding of the three most common types of
radioactive emission:
Lead Radioactive
block material
• Alpha particles (symbolized a or iHe) are dense, positively charged particles
identical to helium nuclei.
• Beta particles (symbolized r3, r3-, or more usually - ?r3) are negatively charged
Voltage
particles identified as high-speed electrons. (The emission of electrons from the source
nucleus may seem strange, but as you'll see shortly, r3 particles arise as a result
of a nuclear reaction.) mmDI Three types of radioactive
• Gamma rays (symbolized as 'Y, or sometimes 8'Y) are very high-energy pho- emissions in an electric field. Positively
charged ex particles bend toward the neg-
tons, about 105 times as energetic as visible light.
ative plate; negatively charged 13 particles
bend toward the positive plate. The cur-
The behavior of these three emissions in an electric field is shown in Figure 24.1.
vature is greater for 13 particles because
Note that a particles bend to a small extent toward the negative plate, r3 particles they have much lower mass. The 'I rays,
bend to a great extent toward the positive plate, and 'Y rays are not affected by uncharged high-energy photons, are un-
the electric field. We'll discuss the effects of these emissions on matter later. affected by the field.


Types of Radioactive Decay; Balancing Nuclear Equations
When a nuclide decays, it forms a nuclide of lower energy, and the excess energy
is carried off by the emitted radiation. The decaying, or reactant, nuclide is called
the parent; the product nuclide is called the daughter. Nuclides can decay in
several ways. As we discuss the major types of decay, which are summarized in
Table 24.2, note the principle used to balance nuclear reactions: the total Z
(charge, number of protons) and the total A (sum of protons and neutrons) of the
reactants equal those of the products:
~~~~: Reactants
~ = ~~:~l
~Products (24.1)

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

emED Modes of Radioactive Decay*
Change in
Mode Emission Decay Process A Z N

et Decay et CiHe) + -4 -2 -2

Reactant (parent) Product (daughter) a expelled

f3 Decay"
o
1n 1p•
1
+ O~ ()
-1
o +1 -1

..
in nucleus in nucleus ~ expelled

Positron emission t hv

high-energy
photon
+
"
%'~,p'

nucleus with
xp+ and ynO
nucleus with
(x- 1)p+ and (y+ 1)nO
+ O~O
1
positron expelled
o -1 +1

Electron capture t x-ray photon -1
°e +
1p
1
1n
o o -1 +1
absorbed from in nucleus in nucleus
low-energy
orbital

'Y Emission + o o o

excited stable y photon
nucleus nucleus radiated

"Neutrinos (v) are involved in several of these processes but are not shown.
"Nuclear chemists consider [3 decay to be a more general process that includes three decay modes: negatron emission (which the text calls
"[3 decay"), positron emission, and electron capture.


Note that the A value for Ra equals the sum of the A values for Rn and He
(226 = 222 + 4), and that the Z value for Ra equals the sum of the Z values for
Rn and He (88 = 86 + 2).
2. Beta decay involves the ejection of a 13particle (-?13) from the nucleus. *
This change does not involve the expulsion of a 13particle that was actually in
the nucleus, but rather the conversion of a neutron into a proton, which remains
in the nucleus, and a f3 particle, which is expelled immediately: The Little Neutral One A neutral par-
ticle called a neutrino (v) is also emitted
bn -+ ip + -?f3 in many nuclear reactions, including the
As always, the totals of the A and the Z values for reactant and products are equal. change of a neutron to a proton:
Radioactive nickel-63 becomes stable copper-63 through 13decay:
6n -+ ip + -?f3 + v
~~Ni -+ ~§Cu + -?f3
Theory suggests that neutrinos have a
Another example is the 13decay of carbon-14, applied in radiocarbon dating: mass much less than 10-4 times that of an
I~C -+ IjN + -?f3 electron, and that at least 109 neutrinos
Note that f3 decay results in a product nuclide with the same A but with Zone exist in the universe for every proton.
Neutrinos interact with matter so slightly
higher (one more proton) than in the reactant nuclide. In other words, an atom
that it would take a piece of lead 1 light-
of the element with the next higher atomic number is formed.
year thick to absorb them. We will not dis-
3. Positron decay involves the emission of a positron from the nucleus. A cuss them further, except to mention that
key idea of modem physics is that every fundamental particle has a correspond- experiments in Japan in the 1990s de-
ing antiparticle, another particle with the same mass but opposite charge. The tected neutrinos and obtained evidence
positron (symbolized ?13;note the positive Z) is the antiparticle of the electron. that they have mass. Using a cathedral-
Positron decay occurs through a process in which a proton in the nucleus is con- sized pool containing 50,000 tons of ultra-
verted into a neutron, and a positron is expelled.' Positron decay has the oppo- pure water buried 1 mile underground
site effect of f3 decay, resulting in a daughter nuclide with the same A but with Z in a zinc mine, an international team of
one lower (one fewer proton) than the parent; thus, an atom of the element with scientists obtained results that suggest
the next lower atomic number forms. Carbon-l I , a synthetic radioisotope, decays that neutrinos may account for a signifi-
cant portion of the "missing" matter in the
to a stable boron isotope through emission of a positron:
universe and may provide enough mass
l~C -+ l~B + ?f3 (and, thus, gravitational attraction) to pre-
4. Electron capture occurs when the nucleus of an atom draws in an elec- vent the universe from expanding forever.
tron from an orbital of the lowest energy level. The net effect is that a nuclear
proton is transformed into a neutron:
ip + _?e -+ 6n
(We use the symbol _?e to distinguish an orbital electron from a beta particle,
symbol _?13.)The orbital vacancy is quickly filled by an electron that moves down
from a higher energy level, and that energy difference appears as an x-ray photon.
Radioactive iron forms stable manganese through electron capture:
~~Fe + _?e -+ ~~Mn + hv (x-ray)
Electron capture has the same net effect as positron decay (Z lower by 1,
A unchanged), even though the processes are entirely different.
5. Gamma emission involves the radiation of high-energy photons from
"I

an excited nucleus. Recall that an atom in an excited electronic state reduces its
energy by emitting photons, usually in the DV and visible ranges. Similarly, a
nucleus in an excited state lowers its energy by emitting photons, which are of
"I

much higher energy (much shorter wavelength) than DV photons. Many nuclear
processes leave the nucleus in an excited state, so 'Yemission accompanies most
other types of decay. Several "I photons ("I rays) of different frequencies can be

*In formal nuclear chemistry terminology, {3 decay indicates a more general phenomenon that
also includes positron emission and electron capture (see footnote to Table 24.2).
tThe process, called pair production, involves a transformation of energy into matter. A high-
energy (>1.63x10-13 J) photon becomes an electron and a positron simultaneously. The elec-
tron and a proton in the nucleus form a neutron, while the positron is expelled.


emitted from an excited nucleus as it returns to the ground state. Many of Marie
Curie's experiments involved the release of v rays, such as
2~~U ---->- 2~riTh + ~He + 28-y
Because 'Y rays have no mass or charge, 'Y emission does not change A or Z.
Gamma rays also result when a particle and an antiparticle annihilate each other,
as when an emitted positron meets an orbital electron:
?[3 (from nucleus) + _?e (outside nucleus) ---->- 28-y

SAMPLE PROBLEM 24.1 Writing Equations for Nuclear Reactions
Problem Write balanced equations for the following nuclear reactions:
(a) Naturally occurring thorium-232 undergoes ex decay.
(b) Chlorine-36 undergoes electron capture.
Plan We first write a skeleton equation that includes the mass numbers, atomic numbers,
and symbols of all the particles, showing the unknown particles as 1x. Then, because the
total of mass numbers and the total of charges on the left side and the right side must be
equal, we solve for A and Z, and use Z to determine X from the periodic table.
Solution (a) Writing the skeleton equation:
2~6Th ---->- 1x + ~He
Solving for A and Z and balancing the equation: For A, 232 = A + 4, so A = 228. For
Z, 90 = Z + 2, so Z = 88. From the periodic table, we see that the element with
Z = 88 is radium (Ra). Thus, the balanced equation is
2§6Th - 2~~Ra + ~He
(b) Writing the skeleton equation:
f~Cl + _?e ---->- ~X
Solving for A and Z and balancing the equation: For A, 36 + 0 = A, so A = 36. For Z,
17 + (-1) = Z, so Z = 16. The element with Z = 16 is sulfur (S), so we have
1~Cl_?e -1~S
+
Check Always read across superscripts and then across subscripts, with the yield arrow
as an equal sign, to check your arithmetic. In part (a), for example, 232 = 228 + 4, and
90 = 88 + 2.
FOLLOW-UP PROBLEM 24.1
Write a balanced equation for the reaction in which
a nuclide undergoes [3 decay and produces cesium-133.

Nuclear Stability and the Mode of Decay
There are several ways that an unstable nuclide might decay, but can we predict
how it will decay? Indeed, can we predict if a given nuclide will decay at all?
Our knowledge of the nucleus is much less than that of the atom as a whole, but
some patterns emerge from observation of the naturally occurring nuclides.
The Band of Stability and the Neutron-to-Proton (N/Z) Ratio A key factor that
determines the stability of a nuclide is the ratio of the number of neutrons to the
number of protons, the N/Z ratio, which we calculate from (A - Z}/Z. For lighter
nuclides, one neutron for each proton (N/Z = 1) is enough to provide stability.
However, for heavier nuclides to be stable, the number of neutrons must exceed
the number of protons, and often by quite a lot. But, if the N/Z ratio is either too
high or not high enough, the nuclide is unstable and decays.
Figure 24.2A is a plot of number of neutrons vs. number of protons for the
stable nuclides. The nuclides form a narrow band of stability that gradually
increases from an N/Z ratio of 1, near Z = 10, to an N/Z ratio slightly greater
than 1.5, near Z = 83 for 209Bi. Several key points are as follows:


140
Cl. decay
209
130 Bi
83 • stable • a emitter
N ~
('Z = 1.52)
..
::
• ~ emitter o e- capture and/or positron emitter
120
.
...
... .
WJ
110
••••000
100
•••••00
•••••000
90

80
Region shown in 8
Cl)
c
2
-S
Q)
85 :H~:8~0
••••~Q!00
<: ..., z
Cl)
107A
47 g~
•••
••!.
r •••• ~~O
c
2
-S
70
( t::' = 1 .28 ) :.r: . "<. _ •••••• O~
Q)

z 60
z • :.:
..: . ~ ••• OOOOU
.:.: . 80 I I I I I I
::i. 55 60
Protons (Z)
65 70
50 ....I·: . 8

:.:-:
40 ~~Fe~ ;.!': ~ A plot of number of neutrons vs. number of protons
(t::'=1.15) ;:.
for the stable nuclides. A, A plot of N vs. Z for all stable nuclides
Z .i:: gives rise to a narrow band that veers above N/Z = 1 shortly beyond
30 :-: .. Positron emission and/or Z = 10. The N/Z values for several stable nuclides are given. The

....
..J•
i electron capture most common modes of decay for unstable nuclides in a particular
region are shown: nuclides with a high N/Z ratio often undergo
20
13 decay; those with a low ratio undergo e- capture or positron emis-
sion; heavy nuclei beyond the stable band (and a few lighter ones)
10
undergo Cl. decay. B, The blue box in part A is expanded to show the
stable and many of the unstable nuclides in that area. Note the
modes of decay: Cl. decay decreases both Nand Z by 2; 13 decay de-
o 10 20 30 40 50 60 70 80 90 creases N and increases Z by 1; positron emission and e - capture
Protons (Z) increase N and decrease Z by 1.
A

• Very few stable nuclides exist with N/Z < 1; the only two are ~H and ~He.
For lighter nuclides, N/Z =
1: for example, 'iHe, l~C, l~O, and are partic- T8Ne
ularly stable.
• The N/Z ratio of stable nuclides gradually increases as Z increases. No stable
nuclide exists with N/Z = 1 for Z > 20. Thus, for ~~Fe, N/Z = 1.15; for l~;Ag,
N/Z = 1.28; and for l~~W, N/Z = 1.49.
• All nuclides with Z > 83 are unstable. Bismuth-209 is the heaviest stable
nuclide. Therefore, the largest members of Groups lA(l), 2A(2), 4A(l4),
6A(l6), 7A(l7), and 8A(l8) are radioactive, as are all the actinides and the
elements of the fourth transition series (Period 7).

Stability and Nuclear Structure Given that protons are positively charged and
neutrons uncharged, what holds the nucleus together? Nuclear scientists answer
this question and explain the importance of the N/Z ratio in terms of two oppos-
ing forces. Electrostatic repulsive forces between protons would break the nucleus
apart if not for the presence of an attractive force that exists between all nucle-
ons (protons and neutrons) called the strong force. This force is about 1000 times
stronger than the repulsive force but operates only over the short distances within
the nucleus. Competition between the attractive strong force and the repulsive
electrostatic force determines nuclear stability.


I11mIm Number of Stable Curiously, the oddness or evenness of Nand Z values is related to some
important patterns of nuclear stability. Two interesting points become apparent
Nuclides for Elements 48 to 54*
when we classify the known stable nuclides:
Atomic No. of
Element No. Nudides • Elements with an even Z (number of protons) usually have a larger number of
Cd 48 8 stable nuclides than elements with an odd Z. Table 24.3 demonstrates this point
In 49 2 for cadmium (Z = 48) through xenon (Z = 54).
So 50 10 • Well over half the stable nuclides have both even N and even Z (Table 24.4).
Sb 51 2 (Only seven nuclides with odd N and odd Z are either stable-s-jl-l, ~Li, l~B,
Te 52 8 I:jN-or decay so slowly that their amounts have changed little since Earth
I 53 1 formed-~~V, 1~~La, and 1~7Lu.)
Xe 54 9
One model of nuclear structure that attempts to explain these findings postu-
*EvenZ shown in boldface. lates that protons and neutrons lie in nucleon shells, or energy levels, and that
stability results from the pairing of like nucleons. This arrangement leads to the
stability of even values of Nand Z. (The analogy to electron energy levels and
I.mlIm An Even-Odd the stability that arises from electron pairing is striking.)
Just as noble gases-the elements with 2, 10, 18, 36, 54, and 86 electrons-
Breakdown of the Stable Nuclides
are exceptionally stable because of their filled electron shells, nuclides with N
No. of or Z values of 2, 8, 20, 28, 50, 82 (and N = 126) are exceptionally stable.
Z N Nuclides
These so-called magic numbers are thought to correspond to the numbers of protons
Even Even 157 or neutrons in filled nucleon shells. A few examples are ~gTi (N = 28),
Even Odd 53 ~~Sr (N = 50), and the ten stable nuclides of tin (Z = 50). Some extremely sta-
Odd Even 50 ble nuclides have double magic numbers: iHe, l~O, i8Ca, and 2~~Pb (N = 126).
Odd Odd 7
TOTAL 267
SAMPJE PROBLEM 24.2 Predicting Nuclear Stability
Problem Which of the following nuclides would you predict to be stable and which
radioactive: (a) i~Ne; (b) i~s;(c) 2§8Th; (d) l~~Ba? Explain.
Plan In order to evaluate the stability of each nuclide, we determine the N/2 ratio from
(A - 2)/2, the value of 2, stable N/2 ratios (from Figure 24.2), and whether 2 and N are
even or odd.
18 - 10
Solution (a) Radioactive. The ratio N/2 ;= 10 ;= 0.8. The minimum ratio for sta-
bility is 1.0; so, despite even Nand Z, this nuclide has too few neutrons to be stable.
(b) Stable. This nuclide has N/Z ;= 1.0 and Z < 20, with even Nand Z. Thus, it is most
likely stable.
(c) Radioactive. Every nuclide with Z > 83 is radioactive.
(d) Radioactive. The ratio N/Z ;=1.20. For Z from 55 to 60, Figure 24.2A shows
N/Z 2: 1.3, so this nuclide probably has too few neutrons to be stable.
Check By consulting a table of isotopes, such as the one in the CRC Handbook of Chem-
istry and Physics, we find that our predictions are correct.
FOLLOW-UP PROBLEM 24.2 Why is i1p stable but igp unstable?

Predicting the Mode of Decay An unstable nuclide generally decays in a mode
that shifts its N/Z ratio toward the band of stability. This fact is illustrated in Fig-
ure 24.2B on the preceding page, which expands a small region of Figure 24.2A
to show all of the stable and many of the radioactive nuclides in that region, as
well as their modes of decay. Note the following points, and then we'll apply
them in a sample problem:

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


2. Neutron-poor nuclides. Nuclides with too few neutrons for stability (a low N/Z)
lie below the band. They undergo positron decay or electron capture, both of
which convert a proton into a neutron, thus increasing the value of N/Z.
3. Heavy nuclides. Nuclides with Z > 83 are too heavy to lie within the band
and undergo Cl' decay, which reduces their Z and N values by two units per
emission. (Several lighter nuclides also exhibit Cl' decay.)

~A"'~P~.EPROBLEM 24.3 Predicting the Mode of Nuclear Decay
Problem Predict the nature of the nuclear change(s) each of the following radioactive
nuclides is likely to undergo: (a) l~B; (b) 2§j:U; (c) ~~As;(d) l~~La.
Plan We use the NjZ ratio to decide where the nuclide lies relative to the band of stabil-
ity and how its ratio compares with others in the nearby region of the band. Then, we pre~
diet which of the decay modes just discussed will yield a product nuclide that is closer to
the band.
Solution (a) This nuclide has an NjZ ratio of 1.4, which is too high for this region of the
band. It will probably undergo f?> decay, increasing Z to 6 and lowering the NjZ ratio to 1.
(b) This nuclide is heavier than those close to it in the band of stability. It will probably
undergo ex decay and decrease its total mass.
(c) This nuclide, with an NjZ ratio of 1.24, lies in the band of stability, so it will proba-
bly undergo either f?> decay or positron emission.
(d) This nuclide has an NjZ ratio of 1.23, which is too low for this region of the band, so
it will decrease Z by either positron emission or electron capture.
Comment Both possible modes of decay are observed for the nuclides in parts (c) and (d).

FOLLOW·UP PROBLEM 24.3
What mode of decay would you expect for (a) ~~Fe;
(b) 2~~Am?

Decay Series A parent nuclide may undergo a series of decay steps before a sta- 148

ble daughter nuclide forms. The succession of steps is called a decay series, or 146
disintegration series, and is typically depicted on a gridlike display. Figure 24.3 /adeCay
144
shows the decay series from uranium-238 to lead-206. Numbers of neutrons (N) " ~ decay
are plotted against numbers of protons (Z) to form the grid, which displays a series 142

of QC and f3 decays. The zigzag pattern is typical and occurs because QC decay 140
decreases both Nand Z, whereas f3 decay decreases N but increases Z. Note that
138
it is quite common for a given nuclide to undergo both types of decay. (Gamma
decay accompanies many of these steps, but it does not affect the mass or type g 136
Cf!
of the nuclide.) This decay series is one of three that occur in nature. All end with c 134
e
isotopes of lead whose nuclides all have one (Z = 82) or two (N = 126, Z = 82) :J
ill 132
magic numbers. A second series begins with uranium-235 and ends with lead-207, Z

and a third begins with thorium-232 and ends with lead-208. (Neptunium-237 130

began a fourth series, but its half-life is so much less than the age of Earth that 128

-
only traces of it remain today.)
126

124

Nuclear reactions are not affected by reaction conditions or chemical composition and 122
release much more energy than chemical reactions. A radioactive nuclide is unstable 78 80 82 84 86 88 90 92
and may emit ex particles (~He nuclei), f3 particles (-~f3; high-speed electrons), Protons (Z)
positrons (~f3), or "/ rays (8,,/; high-energy photons) or may capture an orbital electron Figure 14.3 The 238 U decay series.
(_~e). A narrow band of neutron-to-proton ratios (N/Z) includes those of all the sta- Uranium-238 (top right) decays through a
ble nuclides. Radioactive decay allows an unstable nuclide to achieve a more stable series of emissions of ex or [3 particles to
N/Z ratio. Certain "magic numbers" of neutrons and protons are associated with very lead-206 (bottom left) in 14 steps.
stable nuclides. By comparing a nuclide's N/Z ratio with those in the band of stabil-
ity, we can predict that, in general, heavy nuclides undergo ex decay, neutron-rich
nuclides undergo f3 decay, and proton-rich nuclides undergo positron emission or
electron capture. Three naturally occurring decay series all end in isotopes of lead.


24.2 THE KINETICS OF RADIOACTIVE DECAY
Chemical and nuclear systems both tend toward maximum stability. Just as the
concentrations in a chemical system change in a predictable direction to give a
stable equilibrium ratio, the type and number of nucleons in an unstable nucleus
change in a predictable direction to give a stable N/Z ratio. As you know, how-
ever, the tendency of a chemical system to become more stable tells nothing about
how long that process will take, and the same holds true for nuclear systems. In
this section, we examine the kinetics of nuclear change; later, we'll examine the
energetics of such change. To begin, a Tools of the Laboratory essay on the oppo-
site page describes how radioactivity is detected and measured.

The Rate of Radioactive Decay
~ Animation: Radioactive Decay Radioactive nuclei decay at a characteristic rate, regardless of the chemical sub-
~ Online Learning Center
stance in which they occur. The decay rate, or activity (.stl), of a radioactive sam-
ple is the change in number of nuclei (H) divided by the change in time (r). As
we saw with chemical reaction rates, because the number of nuclei is decreasing,
a minus sign precedes the expression for the decay rate:
i1N
Decay rate (.511) = -&
The SI unit of radioactivity is the becquerel (Bq); it is defined as one disinte-
gration per second (d/s): 1 Bq = 1 d/s. A much larger and more common unit of
radioactivity is the curie (Ci): 1 curie equals the number of nuclei disintegrating
each second in 1 g of radium-226:
1 Ci = 3.70X 1010 d/s (24.2)
Because the curie is so large, the millicurie (mCi) and microcurie (/-LCi)are com-
monly used. We often express the radioactivity of a sample in terms of specific
activity, the decay rate per gram.
An activity is meaningful only when we consider the large number of nuclei
in a macroscopic sample. Suppose there are 1 X 1015 radioactive nuclei of a par-
ticular type in a sample and they decay at a rate of 10% per hour. Although any
particular nucleus in the sample might decay in a microsecond or in a million
hours, the average of all decays results in 10% of the entire collection of nuclei
disintegrating each hour. During the first hour, 10% of the original number, or
1X 1014 nuclei, will decay. During the next hour, 10% of the remaining 9X 1014
nuclei, or 9 X 1013 nuclei, will decay. During the next hour, 10% of those remain-
ing will decay, and so forth. Thus, for a large collection of radioactive nuclei, the
number decaying per unit time is proportional to the number present:
Decay rate (.511) ex N or .511 = kN
where k is called the decay constant and is characteristic of each type of nuclide.
The larger the value of k, the higher is the decay rate.
Combining the two rate expressions just given, we obtain
i1N
.511 = -- = kN (24.3)
I1t

Note that the activity depends only on H raised to the first power (and on the
constant value of k). Therefore, radioactive decay is a first-order process (see
Section 16.4). The only difference in the case of nuclear decay is that we con-
sider the number of nuclei rather than their concentration.
~ Animation: Half-Life Half-Life of Radioactive Decay Decay rates are also commonly expressed in terms
~ Online Learning Center
of the fraction of nuclei that decay over a given time interval. The half-life (t1/2)
of a nuclide is the time it takes for half the nuclei present in a sample to decay.
The number of nuclei remaining is halved after each half-life. Thus, half-life has
the same meaning for a nuclear change as for a chemical change (Section 16.4).

Counters for the Detection of Radioactive Emissions

R
adioactive emissions interact with atoms in surrounding ma- emits photons. Each photon, in turn, strikes a cathode, releasing
terials. To determine the rate of nuclear decay, we measure an electron through the photoelectric effect (Section 7.1). This
the radioactivity of a sample by observing the effects of these electron hits other portions of the tube that release increasing
interactions over time. Because these effects can be electrically numbers of electrons, and the resulting current is recorded. Liquid
amplified billions of times, it is even possible to detect the decay scintillation counters employ an organic mixture that contains a
of a single nucleus. Ionization counters and scintillation counters phosphor and a solvent (Figure B24.2). This "cocktail" dissolves
are two devices used to measure radioactive emissions. the sample and emits light when excited by the emission. These
An ionization counter detects radioactive emissions as they counters are often used to measure emissions from dissolved ra-
ionize a gas. Ionization produces free electrons and gaseous dioactive biological samples.
cations, which are attracted to electrodes that conduct a current to
a recording device. The most common type of ionization counter
is a Geiger-Miiller counter (Figure B24.1). It consists of a tube
filled with argon gas; the tube housing acts as the cathode, and a
thin wire in the center of the tube acts as the anode. Emissions
from the sample enter the tube through a thin window and strike
argon atoms, producing free electrons that are accelerated toward
the anode. These electrons collide with other argon atoms and free
more electrons in an avalanche effect. The current created is am-
plified and appears as a meter reading and/or an audible click. The
initial release of 1 electron can release 1010 electrons in a micro-
second, giving the Geiger-Muller counter great sensitivity.
In a scintillation counter, radioactive emissions too weak to
ionize surrounding atoms are detected by their ability to excite
atoms and cause them to emit light. The light-emitting substance Figure 824.2 Vials of a scintillation "cocktail" emitting light.
in the counter, called a phosphor, is coated onto part of a photo- A radioactive substance dissolved in an organic mixture (cocktail)
multiplier tube, a device that increases the original electrical sig- emits particles that excite the phosphor component to emit light. Light
nal. Incoming radioactive particles strike the phosphor, which intensity is proportional to the concentration of the substance.

e /~ I
Emitted
particle

Sample
~ //
/
.

l /-
/

r~---
. Argon gas

(+)

e

Toward
cathode H

Figure 824.1 Detection of radioactivity by an ionization counter.When an Ar atom absorbs the energy of a
radioactive particle (red), it is ionized to an Ar+ ion (purple) and an electron (yellow). The free electron collides with
and ionizes another Ar atom. As the process continues, the Ar+ ions migrate to the negative electrode, and the
electrons migrate to the positive electrode, resulting in a current.
1055


'l{o
~ Decrease in number of 14C
Number Initial Number of
nuclei over time. A plot of number of 14C number half-lives
of nuclei
nuclei vs. time gives a decreasing curve. i at time t of nuclei /
In each half-life (5730 years), half the i4C
nuclei present undergo decay. A plot of
U
ID
::l
N..t = N..o xn
W
C
mass of i4C vs. time is identical. After 1st
U 1
;0 "2 'l{o half-life (5730 yr)
'0 : After 2nd
Q; I half-life (11,460 yr)
-----i------
.0
1
E "4 'l{o After 3rd
Z
::l
1
"8 'l{o
_____ l
~ half-life (17,190 yr)
t I Y
0
10,000 20,000
Time (yr)

Figure 24.4 shows the decay of carbon-14, which has a half-life of 5730 years,
in terms of number of 14C nuclei remaining:
I~C - 'iN + -?f3
We can also consider the half-life in terms of mass of substance. As 14C decays
to the product 14N, its mass decreases. If we start with 1.0 g of carbon-14, half
that mass of 14C (0.50 g) will be left after 5730 years, half of that mass (0.25 g)
after another 5730 years, and so on. The activity depends on the number of nuclei
present, so the activity is halved after each succeeding half-life as well.
We determine the half-life of a nuclear reaction from its rate constant. Re-
arranging Equation 24.3 and integrating over time gives
HI Ho
In - -kt or In - = kt (24.4)
Ho Ht
where X 0 is the number of nuclei at t = 0, and Xt is the number of nuclei remain-
Il.mrIm Decay Constants (k) ing at any time t. (Note the similarity to Equation 16.4, p. 686.) To calculate the
and Half-Lives (t,/2) half-life (tI/2), we set Nt equal to 1N 0 and solve for t1/2:
of Beryllium Isotopes
Ho ~2
Nuclide k tV2 ln 1.'r = kt1/2 so t1/2 = -k (24.5)
2J' 0
~Be l.30X 1O~2/day 53.3 days Exactly analogous to the half-life of a first-order chemical change, this half-life
~Be l.OX 1016/s 6.7X 1O~17 s is not dependent on the number of nuclei and is inversely related to the decay
~Be Stable constant:
I~Be 4.3XlO-7/yr
large k =? short tl/2 and small k =? long t1/2

IlBe 5.02X 1O~2/s The decay constants and half-lives of radioactive nuclides vary over a very
wide range, even those for the nuclides of a given element (Table 24.5).

SAMPLE PROBLEM 24.4Finding the Number of Radioactive Nuclei
Problem Strontium-90 is a radioactive by-product of nuclear reactors that behaves bio-
logically like calcium, the element above it in Group 2A(2). When 90Sr is ingested by
mammals, it is found in their milk and eventually in the bones of those drinking the milk.
If a sample of 90Sr has an activity of 1.2XIOl2 d/s, what are the activity and the fraction
of nuclei that have decayed after 59 yr (tl/2 of 90Sr = 29 yr)?
Plan The fraction of nuclei that have decayed is the change in number of nuclei, expressed
as a fraction of the starting number. The activity of the sample (s1.) is proportional to the
number of nuclei (H), so we know that
Ho - Ht s1.-0 s1.t
Fraction decayed = Ho s1.
0
We are given s1.0 (1.2X 1012 d/s), so we find s1.t from the integrated form of the first-order
rate equation (Equation 24.4), in which t is 59 yr. To solve that equation, we first need k,
which we can calculate from the given t1/2 (29 yr).

24.2 The Kinetics of Radioactive Decay 1057

Solution Calculating the decay constant k:
In 2 In 2 0.693
tl/2 = k so k = -
tl/2
= --
29 yr
= 0.024 yr-I

Applying Equation 24.4 to calculate sat, the activity remaining at time t:
Ho
In-=ln-=kt
sao or In sao - In sal = kt
Ht sa,
So, In sa, = -kt + In sao = -(0.024 yr-1 X 59 yr) + In (1.2XlO12 d/s)
In sat = -1.4 + 27.81 = 26.4
sat = 2.9X1011 d/s
(All the data contain two significant figures, so we retained two in the answer.) Calculat-
ing the fraction decayed:
sao - sa, 1.2X 1012d/s - 2.9X 1011d/s
Fraction decayed = ,.// 0 0.76
,)CJ-o 1.2X 1 12 d/s
Check The answer is reasonable: t is about 2 half-lives, so sa, should be about ~sao, or
about 0.3XlO'2; therefore, the activity should have decreased by about j.
Comment An alternative approach is to use the number of half-lives (t/tl/2) to find the
fraction of activity (or nuclei) remaining. By combining Equations 24.4 and 24.5 and sub-
stituting (In 2)/tl/2 for k, we obtain

In No = (In 2)t = _t_In 2 = In 2t/II/2
N, tl/2 tl/2

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

Ho 2
Taking the antilog gives

Fraction remaining = H~ =
N (1)'/1
2"
12
/

=
(1)59/29
2" = 0.24
So, Fraction decayed = 1.00 - 0.24 = 0.76
FOLLOW-UP PROBLEM 24.4Sodium-24 (t1/2 = 15 h) is used to study blood cir-
culation. If a patient is injected with a 24NaCI solution whose activity is 2.5 X 109 d/s, how
much of the activity is present in the patient's body and excreted fluids after 4.0 days?

Radioisotopic Dating
The historical record fades rapidly with time and virtually disappears for events
of more than a few thousand years ago. Much of our understanding of prehistory
comes from a technique called radioisotopic dating, which uses radioisotopes
to determine the age of an object. The method supplies data about the ages of
objects in fields as diverse as art history, archeology, geology, and paleontology.
The technique of radiocarbon dating, for which the American chemist Willard
F. Libby won the Nobel Prize in chemistry in 1960, is based on measuring the
amounts of 14C and 12C in materials of biological origin. The accuracy of the
method falls off after about six half-lives of 14C (t1/2 = 5730 yr), so it is used to
date objects up to about 36,000 years old.
Here is how the method works. High-energy neutrons resulting from cosmic
ray collisions reach Earth continually from outer space. They enter the atmo-
sphere and cause the slow formation of 14C by bombarding ordinary 14N atoms:
ljN + 6n ---+ I~C + jp
Through the processes of formation and radioactive decay, the amount of 14C in
the atmosphere has remained nearly constant. *

'Cosmic ray intensity does vary slightly with time, which affects the amount of atmospheric 14C.
From 14C activity in ancient trees, we know the amount fell slightly about 3000 years ago to cur-
rent levels. Recently, nuclear testing and fossil fuel combustion have aiso altered the fraction of
14C slightly. Taking these factors into account improves the accuracy of the dating method.


The 14C atoms combine with 02, diffuse throughout the lower atmosphere,
and enter the total carbon pool as gaseous 14C02 and aqueous H14C03 -. They
mix with ordinary l2C02 and H12C03 -, reaching a constant 12C:14C ratio of about
1012:1. The CO2 is taken up by plants during photosynthesis, and then taken up
and excreted by animals that eat the plants. Thus, the l2C: 14C ratio of a living
organism has the same constant value as the environment. When an organism dies,
however, it no longer takes in 14C, so the l2C:14C ratio steadily increases because
the amount of 14C decreases as it decays:
l~C _ ljN + -?13
The difference between the l2e:14C ratio in a dead organism and the ratio in liv-
ing organisms reflects the time elapsed since the organism died.
As you saw in Sample Problem 24.4, the first-order rate equation can be
expressed in terms of a ratio of activities:
The Case of the Shroud of TurinOne No .wo
of the holiest Christian relics is the famed In-=ln-=kt
Shroud of Turin. It is a piece of linen that
Nt .wt
bears a faint image of a man's body and We use this expression in radiocarbon dating, where stlo is the activity in a liv-
was thought to be the burial cloth used to ing organism and sl, is the activity in the object whose age is unknown. Solving
wrap the body of Jesus Christ. In 1988, for t gives the age of the object:
the Vatican allowed scientific testing of
the cloth by radiocarbon dating. Three t =-
1
In -
.wo (24.6)
labs in Europe and the United States inde-
k .wt
pendently measured the 12C:14Cratio of a A useful graphical method in radioisotopic dating shows a plot of the natu-
SO-mg piece of the linen and determined ral logarithm of the specific activity vs. time, which gives a straight line with a
that the flax from which the cloth was slope of -k, the negative of the decay constant. Using such a plot and measur-
made was grown between 1260 AD and
ing the 14C specific activity of an object, we can determine its age; several exam-
1390 AD. Despite this evidence, the
ples appear in Figure 24.5. To determine the ages of more ancient objects or of
shroud lost none of its fascination: 10
years later, in 1998, when the shroud was
objects that do not contain carbon, different radioisotopes are measured. (See the
again put on display, about 2 million peo- margin note on the opposite page.)
ple lined up to view it.

3.00

~~ Charcoai from earliest Polynesian culture in H~waii
pp
.i .'.~., Linen, wra ...•.•. s from Book of Isaia,~; Deq~ s~~.Scrolls
...ng......
i .
H ' ':!',.,
Chhrcoal fr~m earliest settlement in JapaQ

2.00
Bur.ASdtree from eruption that created
Crater"Lake, Oregon

Burned bones ofsloth in -
Ct:1ilEiancave. Earlies,! Burned bison bones associated with
trace of human presence Folsom Man, found at Lubbock, Texas
at tip of South America Me~6Iithic-Neolithic transition
site.Belt Cave, Iran

Figure 24.5 Radiocarbon dating for de- Charcoal from Lascaux
termining the age of artifacts. The natural Caves, France, site of .
logarithms of the specific activities of 14C extensive cavepalntinqs ~ •
(see background)
(activity/g 14C) for various artifacts are
projected onto a line whose slope equals
-k, the negative of the 14C decay con- 16,000
stant. The age (in years) of an artifact is
determined from the horizontal axis.

24_3 Nuclear Transmutation: Induced Changes in Nuclei 1059

SAMPLE PROBLEM 24.5 Applying Radiocarbon Dating
Problem The charred bones of a sloth in a cave in Chile represent the earliest evidence
of human presence at the southern tip of South America. A sample of the bone has a spe-
cific activity of 5.22 disintegrations per minute per gram of carbon (d/min-g). If the ratio
of 12C:14C in living organisms results in a specific activity of 15.3 d/min-g, how old are
the bones (tl/2 of 14C = 5730 yr)?
Plan We first calculate k from the given t1/2 (5730 yr). Then we apply Equation 24.6 to
find the age (t) of the bones, using the given activities of the bones (.wt = 5.22 d/min-g)
and of a living organism (.wo = 15.3 d/min-g),
Solution Calculating k for 14Cdecay:

k= In2 = 0.693 = 1.21XlO-4yr-1
t1/2 5730 yr
Calculating the age (t) of the bones:
l.wo 1 (15.3 d/min-g)
t = -In - = ------In 4 1 ----- = 8.89x103 yr
k .wt 1.21XlO- yr- 5.22d/min-g
The bones are about 8900 years old.
Check The activity of the bones is between !and ± the activity of a living organism, so
the age should be between one and two half-lives (5730 to 11,460 yr).
FOLLOW·UP PROBLEM 24.5A sample of wood from an Egyptian mummy case
has a specific activity of 9.41 d/min-g. How old is the case?

Ionization and scintillation counters measure the number of emissions from a radioac-
tive sample. The decay rate (activity) of a sample is proportional to the number of
radioactive nuclei. Nuclear decay is a first-order process, so the half-life does not
depend on the number of nuclei. Radioisotopic methods, such as 14C dating, deter-
mine the ages of objects by measuring the ratio of specific isotopes in the sample.

24.3 NUCLEAR TRANSMUTATION: INDUCED CHANGES
IN NUCLEI
The alchemists' dream of changing base metals into gold was never realized, but
in the early 20th century, atomic physicists found that they could change one ele- How Old Is the Solar System?
ment into another. Research into nuclear transmutation, the induced conversion By comparing the ratio of 238Uto its final
of one nucleus into another, was closely linked with research into atomic struc- decay product, 206pb,geochemists found
ture and led to the discovery of the neutron and to the production of artificial that the oldest known surface rocks on
radioisotopes. Later, high-energy bombardment of nuclei in particle accelerators Earth-granite in western Greenland-
began a scientific endeavor, which continues to this day, of creating many new are about 3.7 billion years old. The ratio
of 238U:206Pb meteorites gives 4.65 bil-
in
nuclides and a growing number of new elements.
lion years for the age of the Solar System,
and therefore Earth. From this and other
Early Transmutation Experiments; Discovery of the Neutron isotope ratios, such as 4°K:40 (tl/2 of
Ar
The first recognized transmutation occurred in 1919, when Emest Rutherford 40K = 1.3XIQ9 yr) as well as 87Rb:87Sr
showed that Q' particles emitted from radium bombarded atmospheric nitrogen to (t1/2 of 87Rb = 4.9X 1010 yr), Moon rocks
form a proton and oxygen-17: collected by Apollo astronauts have been
shown to be 4.2 billion years old, and they
'jN + j:He _ iH + I~O
provide evidence for volcanic activity on
By 1926, experimenters had found that Q' bombardment transmuted most elements the Moon's surface about 3.3 billion years
with low atomic numbers to the next higher element, with ejection of a proton. ago. That was about the time that, accord-
A notation for nuclear bombardment reactions shows the reactant (target) ing to these methods, the first organisms
nucleus to the left and the product nucleus to the right of a set of parentheses, were evolving on Earth.
within which a comma separates the projectile particle from the ejected particle(s):
reactant nucleus (particle in, particlets) out) product nucleus
17
Using this notation, the previous reaction is 14N (o.p) 0.


An unexpected finding in a transmutation experiment led to the discovery of
the neutron. When lithium, beryllium, and. boron were bombarded with a parti-
cles, they emitted highly penetrating radiation that could not be deflected by a
magnetic or electric field. Unlike "y radiation, these emissions were massive
enough to eject protons from the substances they penetrated. In 1932, James
Chadwick, a student of Rutherford, proposed that these emissions consisted of
neutral particles with a mass similar to that of a proton, and he named them neu-
trons. Chadwick received the Nobel Prize in physics in 1935 for his discovery.
In 1933, Irene and Frederic Joliot-Curie (see photo), daughter and son-in-law
of Marie and Pierre Curie, created the first artificial radioisotope, phosphorus-30.
When they bombarded aluminum foil with a particles, phosphorus-30 and neu-
trons were formed:
gAl + iHe - bD + f~P or 27 Al (o..n) 30p

Since then, other techniques for producing artificial radioisotopes have been
developed. In fact, the majority of the nearly 1000 known radionuclides have been
produced artificially.
The Joliot-Curies in their laboratory.
Particle Accelerators and the Transuranium Elements
During the 1930s and 1940s, researchers probing the nucleus bombarded elements
with neutrons, a particles, protons, and deuterons (nuclei of the stable hydrogen
isotope deuterium, 2H). Neutrons are especially useful as projectiles because they
have no charge and thus are not repelled as they approach a target nucleus. The
other particles are all positive, so early researchers found it difficult to give them
enough energy to overcome their repulsion by the target nuclei. Beginning in the
1930s, however, particle accelerators were invented to impart high kinetic ener-
gies to particles by placing them in an electric field, usually in combination with
a magnetic field. In the simplest and earliest design, protons are introduced at one
end of a tube and attracted to the other end by a potential difference.
A major advance was the linear accelerator, a series of separated tubes of
increasing length that, through a source of alternating voltage, change their charge
from positive to negative in synchrony with the movement of the particle through
them (Figure 24.6A). A proton, for example, exits the first tube just when that
tube becomes positive and the next tube negative. Repelled by the first tube and
attracted by the second, the proton accelerates across the gap between them. A
40-ft linear accelerator with 46 tubes, built in California after World War Il, accel-
erated protons to speeds several million times faster than the early accelerators.
Later designs, such as the Stanford Linear Accelerator (Figure 24.6B), accelerate

Alternating To vacuum
voltage sources
+/- t
6
Proton
source

A

Figure 24.6 A linear accelerator. A, The voltage of each tubular section is alter-
nated, so that the positively charged particle (a proton here) is repelled from the
section it is leaving and attracted to the section it is entering. As a result, the parti-
cle's speed is continually increased. B, The linear accelerator operated by Stanford
University in California. B

24.3 Nuclear Transmutation: Induced Changes in Nuclei 1061

Alternating voltage source

Path of proton
beam
L Evacuated chamber
Proton source

Target

"Dees"
Figure 24.7 The cyclotron accelerator. When the positively charged particle reaches the gap be-
tween the two D-shaped electrodes ("dees"), it is repelled by one dee and attracted by the other.
The particles move in a spiral path, so the cyclotron can be much smaller than a linear accelerator.

heavier particles, such as B, C, 0, and Ne nuclei, several hundred million times
faster, with correspondingly greater kinetic energies.
The cyclotron (Figure 24.7), invented by E. O. Lawrence in 1930, applies the
principle of the linear accelerator but uses electromagnets to give the particle a
spiral path, thus saving space. The magnets lie within an evacuated chamber above The Powerful Bevatron The bevatron,
and below two "dees," open, D-shaped electrodes that function like the tubes in used to study the physics of high-energy
the linear design. The particle is accelerated as it passes from one dee, which is particle collisions, includes a linear
momentarily positive, to the other, which is momentarily negative. Its speed and section and a synchrotron section. The in-
radius increase until it is deflected toward the target nucleus. The synchrotron uses strument at the Lawrence Berkeley Labo-
a synchronously increasing magnetic field to make the particle's path circular ratory in California increases the kinetic
rather than spiral. 0 energy of the particles by a factor of more
Accelerators have many applications, from producing radioisotopes used in than 6 billion. A beam of 1010 protons
medical applications to studying the fundamental nature of matter. Perhaps their makes more than 4 million revolutions, a
distance of 300,000 miles, in 1.8 s, attain-
most specific application for chemists is the synthesis of transuranium elements,
ing a final speed about 90% of the speed
those with atomic numbers higher than uranium, which is the heaviest naturally
of light! Even more powerful bevatrons
occurring element. Some reactions that were used to form several of these ele- are in use at the Brookhaven National
ments appear in Table 24.6. The transuranium elements include the remaining Laboratory in New York and at CERN,
actinides (Z = 93 to 103), in which the Sf sub level is being filled, and the ele- outside Geneva, Switzerland.
ments in the fourth transition series (Z = 104 to 112), in which the 6d sublevel

Im'm:DI Formation of Some Transuranium Nuclides
Reaction Half-life of Product
2~9pu + ~He ~ 2~~Am + lH + 26n 50.9 h
2~£pU + iHe ~ 2~gCm + 6n 163 days
2~tCm + ~He ~ 2~~Bk + lH + 26n 4.94 days
2§~U + l~C ~ 2~~Cf + 46n 36 h
2§~Es + ~He ~ Ig?Md + 6n 76min
2§§Cf + l~B ~ Ig~Lr + 66n 28 s

Nuclear Reactions and Their Applications

Nuclear Reactions and Their Applications

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