641
Chapter nineteen
NUCLEAR CHEMISTRY
In Chap. 4 we described the experimental basis for the idea that each atom has a small,
very massive nucleus which contains protons and neutrons. Surrounding the nucleus are
one or more electrons which occupy most of the volume of the atom but make only a small
contribution to its mass. Electrons (especially valence electrons) are the only subatomic
particles which are involved in ordinary chemical changes, and we have spent considerable
time describing the rearrangements they undergo when atoms and molecules combine.
However, another category of reactions is possible in which the structures of atomic nuclei
change. In such nuclear reactions electronic structure is incidental—we are primarily
interested in how the protons and neutrons are arranged before and after the reaction.
Nuclear reactions are involved in transmutation of one element into another and in natural
radioactivity, both of which were described briefly in Chap. 4. In this chapter we will
consider nuclear reactions in more detail, exploring their applications to nuclear energy, to
the study of reaction mechanisms, to qualitative and quantitative analysis, and to estimation
of the ages of objects as different as the Dead Sea scrolls and rocks from the moon.
19.1 NATURALLY OCCURRING NUCLEAR REACTIONS
Radioactivity
When the discovery of natural radioactivity was described in Chap. 4, we mentioned the
properties of α particles, β particles, and γ rays, but little
642
attention was paid to the atoms which were left behind when one of these forms of
radiation was emitted. Now we can consider the subject of radioactivity in more detail.
α emission An a particle corresponds to a helium nucleus. It consists of two protons and
two neutrons, and so it has a mass number of 4 and an atomic number (nuclear charge) of 2.
From a chemical point of view we would write it as 42 He 2+ , indicating its lack of two
electrons with the superscript 2+. In writing a nuclear reaction, though, it is unnecessary to
specify the charge, because the presence or absence of electrons around the nucleus is
usually unimportant. For these purposes an α particle is indicated as
4
2
He
4
2
or
α
In certain nuclei a particles are produced by combination of two protons and two neutrons
which are then emitted.
An example of naturally occurring emission of an α particle is the disintegration of one of
U . The equation for this process is
the isotopes of uranium, 238
92
238
92
U 
234
90
Th + 42 He
(19.1)
Note that if we sum the mass numbers on each side of a nuclear equation, such as Eq.
(19.1), the total is the same. That is, 238 on the left equals 234 + 4 on the right. Similarly,
the atomic numbers (subscripts) must also balance (92 on the left and 90 + 2 on the right).
This is a general rule which must be followed in writing any nuclear reaction. The total
number of nucleons (i.e., protons and neutrons) remains unchanged, and electrical charge is
neither created nor destroyed in the process.
When a nucleus emits an a particle, its atomic number is reduced by 2 and it becomes the
nucleus of an element two places earlier in the periodic table. That one element could
transmute into another in this fashion was first demonstrated by Rutherford and Soddy in
1902. It caused a tremendous stir in the scientific circles of the day since it quite clearly
contradicted Dalton’s hypothesis that atoms are immutable. It gave Rutherford, who was
then working at McGill University in Canada, an international reputation.
The type of nucleus that will spontaneously emit an a particle is fairly restricted. The mass
number is usually greater than 209 and the atomic number greater than 82. In addition the
nucleus must have a lower ratio of neutrons to protons than normal. The emission of an a
particle raises the neutron/proton ratio as illustrated by the nuclear equation
210
84
Po 
206
82
Pb + 42 He
(19.2)
Po contains 210 – 84 = 126 neutrons and 84 protons, giving a ratio of
The nucleus of 210
84
126:84 = 1.500. This is increased to 124:82 = 1.512 by the α-emission.
β emission A β particle is an electron which has been emitted from an atomic nucleus. It
has a very small mass and is therefore assigned a mass
643
number of 0. The β particle has a negative electrical charge, and so its nuclear charge is
taken to be –1. Thus it is given the symbol
0
-1
0
-1
or
e
β
in a nuclear equation. Two examples of unstable nuclei which emit β particles are
Th 
234
90
and
14
6
C 
234
91
14
7
Pa + -10 e
0
-1
N+ e
(19.3)
(19.4)
Note that both of these equations accord with the conservation of mass number and atomic
number, showing again that both the total number of nucleons and the total electrical
charge remain unchanged. We can consider a β particle emitted from a nucleus to result
from the transformation of a neutron into a proton and an electron according to the reaction
1
0
n 
1
1
p + -10 e
(19.5)
(Indeed, free neutrons unattached to any nucleus soon decay in this way.) Thus when a
nucleus emits a β particle, the nuclear charge rises by 1 while the mass number is unaltered.
Therefore the disintegration of a nucleus by β decay produces the nucleus of an element
one place further along in the periodic table than the original element.
β decay is a very common form of radioactive disintegration and, unlike α decay, is found
among both heavy and light nuclei. Nuclei which disintegrate in this way usually have a
neutron/proton ratio which is higher than normal. When a β particle is lost, a neutron is
replaced by a proton and the neutron/proton ratio decreases. For example, in the decay
process
206
Pb  206
Bi + -10 e
(19.6)
82
83
the neutron/proton ratio changes from 1.561 to 1.530.
γ radiation γ rays correspond to electromagnetic radiation similar to light waves or
radiowaves except that they have an extremely short wavelength—about a picometer.
Because of the wave-particle duality we can also think of them as particles or photons
having the same velocity as light and an extremely high energy. Since they have zero
charge and are not nucleons, they are denoted in nuclear equations by the symbol 00 γ or,
more simply, γ.
Virtually all nuclear reactions are accompanied by the emission of γ rays. This is because
the occurrence of a nuclear transformation usually leaves the resultant nucleus in an
unstable high-energy state. The nucleus then loses energy in the form of a γ-ray photon as it
adopts a lower-energy more stable form. Usually these two processes succeed each other so
rapidly that they cannot be distinguished. Thus when 238U decays by α emission, it also
emits a γ ray. This is actually a two-stage process. In the first stage a high-energy (or
excited) form of 234Th is produced:
238
92
U 
234
90
Th* + 42 He
(19.7)
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This excited nucleus-then emits a γ ray:
Th* 
234
90
Th + 00 γ
234
90
(19.8)
Usually when a nuclear reaction is written, the γ ray is omitted. Thus Eqs. (19.7) and (19.8)
are usually combined to give
238
92
U 
234
90
Th + 42 He
(19.1)
Radiation and Human Health
Alpha particles, beta particles, gamma rays, and some other types of radiation such as xrays are injurious to humans and other living organisms. A single particle or photon usually
has sufficient energy to break one or more chemical bonds or to ionize a molecule in living
tissue. The free radicals or ions produced in this way are highly reactive chemically. They
can disrupt cell membranes, reduce the effectiveness of enzymes, or even damage genes
and chromosomes. The greatest harm of this type is caused by the heavier, more highly
charged alpha particles, which produce considerable disruption when they collide with
molecules in living tissue. Beta particles are less harmful because of their lesser charge and
mass, and gamma or x-rays have the smallest effect.
When dealing with radioactive materials, it is necessary for humans to shield their bodies
from harmful radiation. In the case of alpha particles even a single sheet of paper serves to
absorb a large fraction. Heavier shielding—on the order of 1 mm of aluminum—is needed
to stop the lighter beta particles, and the uncharged gamma rays or x-rays require 5 cm or
more of a dense metal such as lead to stop them. Thus although alpha particles will do more
damage once inside the human body, one’s skin is a fairly good shield against them. If
breathed in or swallowed, however, alpha emitters are highly poisonous. Outside the body
beta particles are more dangerous than alpha particles, and gamma rays or x-rays, which
can penetrate all the way through one’s tissues to the internal organs, are most harmful of
all.
Radioactive Series
Naturally occurring uranium contains more than 99%
238
92
U , an isotope which decays to
Th by α emission, as shown in Eq. (19.1). The product of this reaction is also
234
90
radioactive, however, and undergoes β decay, as already shown in Eq. (19.3). The
produced in this second reaction also emits a β particle:
234
91
Pa 
234
92
U + -10 e
234
91
Pa
(19.9)
These three reactions [Eqs. (19.1), (19.3), and (19.9)] are only the first of 14 steps. After
Pb is produced. It has a
emission of eight α particles and six β particles, the isotope 206
82
stable nucleus which does not disintegrate further. The complete process may be written as
follows:
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





U 
 23490Th 
 23491 Pa 
 234
U 
 23090Th 
 22688 Ra 
 22288 Rn
92








206
210
210
210
214
214
214
218
Pb 
 84 Po 
 83 Bi 
 82 Pb 
 84 Po 
 83 Bi 
 82 Pb 
 84 Po
82
(19.10a)
238
92
While the net reaction is
238
92
U 
206
82
Pb + 8 42 He + 6 -10 e
(19.10b)
Such a series of successive nuclear reactions is called a radioactive series. Two other
radioactive series similar to the one just described occur in nature. One of these starts with
U and
the isotope 23290Th and involves 10 successive stages, while the other starts with 235
92
involves 11 stages. Each of the three series produces a different stable isotope of lead.
EXAMPLE 19.1 The first four stages in the uranium-actinium series involve the emission
U nucleus, followed successively by the emission of a β particle,
of an α particle from a 235
92
a second α particle, and then a second β particle. Write out equations to describe all four
nuclear reactions.
Solution The emission of an a particle lowers the atomic number by 2 (from 92 to 90).
Since element 90 is thorium, we have
235
92
U 
231
90
Th + 42 He
The emission of a β particle now increases the atomic number by 1 to give an isotope of
element 91, protactinium:
231
Th  231
Pa + -10 e
90
91
The next two stages follow similarly:
231
Pa  227
Ac + 42 He
91
89
and
227
89
Ac 
227
90
Th + -10 e
EXAMPLE 19.2 In the thorium series, 23290Th loses a total of six α particles and four β
particles in a 10-stage process. What isotope is finally produced in this series?
Solution The loss of six α particles and four β particles:
6 42 He + 4 -10 e
involves the total loss of 24 nucleons and 6 × 2 – 4 = 8 positive charges from the 23290Th
nucleus. The eventual result will be an isotope of mass number 232 – 24 = 208 and a
nuclear charge of 90 – 8 = 82. Since element 82 is Pb, we can write
Th 
232
90
208
82
Pb + 6 42 He + 4 -10 e
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19.2 ARTIFICIALLY INDUCED NUCLEAR REACTIONS
In 1919 Rutherford performed the first artificial nuclear reaction. He was able to
demonstrate that when α particles are introduced into a closed sample of N2 gas, an
occasional collision led to the formation of an isotope of O and the release of a proton:
4
2
He +
14
7
N 
17
8
O + 11 H
(19.11)
Since then many thousands of nuclear reactions have been studied, most of them produced
by the bombardment of stable forms of matter with a beam of nucleons or light nuclei as
projectiles. Particles which have been used for this purpose include protons, neutrons,
deuterons ( 21 H ) , α particles, and B, C, N, and O nuclei.
Bombardment with Positive Ions
When the bombarding particle is positively charged, which is usually the case, it must have
a very high kinetic energy to overcome the coulombic repulsion of the nucleus being
bombarded. This is particularly necessary if the nucleus has a high nuclear charge. To give
these charged particles the necessary energy, an accelerator or “atom smasher” such as a
cyclotron must be used. The cyclotron was developed mainly by E. O. Lawrence(1901 to
1958)at the University of California. A schematic diagram of a cyclotron is shown in Fig.
19.1. Two hollow D-shaped plates (dees) are enclosed in an evacuated chamber between
the poles of a powerful electromagnet. The two dees are connected to a source of highfrequency alternating current, so that when one is positive, the other is negative. Ions are
introduced at the center and are accelerated because of their alternate attraction to the leftand right-hand dees. Since the magnetic field would make ions traveling at constant speed
move in a circle, the net result is that they follow a spiral path as they accelerate until they
finally emerge at the outer edge of one of the dees.
Figure 19.1 A cyclotron. The spiral path of the ions is
shown in color.
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Some examples of the kinds of nuclear reactions which are possible with the aid of an
accelerator are as follows:
24
12
7
3
Mg + 11 H 
Li + 21 H 
106
46
8
4
21
11
Na + 42 He
Be + 01n
Pb + He + 
4
2
109
47
(19.12)
(19.13)
1
1
Ag + H
(19.14)
A particularly interesting type of nuclear reaction performed in an accelerator is the
production of the transuranium elements. These elements have atomic numbers greater than
that of uranium (92) and are too unstable to persist for long in nature. The heaviest of them
can be prepared by bombarding nuclei which are already heavy with some of the lighter
nuclei:
238
U + 126 C  246
Cf + 4 01 n
(19.15)
92
98
238
92
252
98
U+
Cf +
14
7
N
247
99
B
257
103
10
5
Es + 5 01n
1
0
Lr + 5 n
(19.16)
(19.17)
Neutron Bombardment
Since a neutron has no charge, it is not repelled by the nucleus it is bombarding. Because of
this, neutrons do not need to be accelerated to high energies before they can undergo a
nuclear reaction. Nuclear reactions involving neutrons are thus easier and cheaper to
perform than those requiring positively charged particles.
Though neutron-bombardment reactions are often carried out in a nuclear reactor (which
will be described later), they can also be very conveniently performed in a small laboratory
Rn
using a neutron source. Usually a neutron source consists of an α emitter such as 222
88
mixed with Be, an element whose nuclei produce neutrons when bombarded by α particles:
9
4
Be + 42 He 
12
6
C + 01 n
(19.18)
This reaction was originally used in 1932 by Sir James Chadwick (1891 to 1974) to
demonstrate the existence of the neutron. (Previous to this it was believed that electrons
were present in the nucleus together with protons.) The neutrons produced by Eq. (19.18)
have a very high energy and are called fast neutrons. For many purposes the neutrons are
more useful if they are first slowed down or moderated by passing them through paraffin
wax or some other substance containing light nuclei in which they can dissipate most of
their energy by collision. The slow neutrons produced by a moderator are then able to
participate in a larger number of neutron-capture reactions of which the following two
are typical:
34
35
S + 01 n  16
S+γ
(19.19)
16
200
80
Hg + 01 n 
201
80
Hg + γ
(19.20)
In such a reaction a different isotope (often an unstable isotope) of the element being
bombarded is produced, with the emission of a γ ray. Radioactive isotopes of virtually all
the elements can be produced in this way.
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An important neutron-capture reaction is that undergone by the most
common isotope of uranium, namely, 238U:
238
92
U + 01 n 
239
92
U+γ
(19.21)
The uranium-239 produced in this way decays by β emission to produce the first and most
important of the transuranium elements, namely, neptunium:
239
92
U 
239
93
N + -10 e
(19.22)
When nuclei are bombarded by fast neutrons, a secondary particle is emitted—usually a
proton or an α particle:
11
5
B + 01n 
27
13
Al + 01 n 
11
4
B + 11 H
(19.23)
24
11
(19.24)
Na + 24 He
Further Modes of Decay
Isotopes produced by nuclear reactions which do not occur in nature (artificial isotopes)
are invariably unstable and radioactive. They exhibit two kinds of decay not found among
naturally occurring radioactive elements. The first is positron emission (also called β+
emission) in which a fundamental particle we have not previously discussed is ejected from
the nucleus. The positron is identical with the electron except that it has a positive rather
than a negative charge. Its symbol is +10 e . An example of positron emission is
11
6
C 
11
5
B+
0
+1
e
(19.25)
Positron emission is common among isotopes having a low neutron-to-proton ratio.
The second new method of decay is called electron capture. The nucleus absorbs one of
the electrons from its own innermost core. An example is the following reaction:
0
-1
ec
e + 74 Be 

7
3
Li
(19.26)
Again this results in an increased neutron/proton ratio.
19.3 NUCLEAR STABILITY
Why is it that certain combinations of nucleons are stable in a nucleus while others are not?
A complete answer to this question cannot yet be given, largely because the exact nature of
the forces holding the nucleons together is still only partially understood. We can, however,
point to several factors which affect nuclear stability. The most obvious is the
neutron/proton ratio. As we have already seen, if this is too high or too low, it makes for an
unstable nucleus.
If we plot the number of neutrons against the number of protons for all known stable (i.e.,
nonradioactive) nuclei, we obtain the result shown in
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Figure 19.2 The number of neutrons plotted against the number of protons for all
the stable nuclei. Note how the neutron/proton ratio increases for the heavier
elements.
Fig. 19.2. All the stable nuclei lie within a definite area called the zone of stability. For
low atomic numbers most stable nuclei have a neutron/proton ratio which is very close to 1.
As the atomic number increases, the zone of stability corresponds to a gradually increasing
neutron/proton
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Bi for instance, the neutron/proton ratio
ratio. In the case of the heaviest stable isotope, 209
83
is 1.518. If an unstable isotope lies to the left of the zone of stability in Fig. 19.2, it is
neutron rich and decays by β emission. If it lies to the right of the zone, it is proton rich and
decays by positron emission or electron capture.
Another factor affecting the stability of a nucleus is whether the number of protons and
neutrons is even or odd. Among the 354 known stable isotopes, 157 (almost half) have an
even number of protons and an even number of neutrons. Only five have an odd number of
both kinds of nucleons. In the universe as a whole (with the exception of hydrogen) we find
that the even-numbered elements are almost always much more abundant than the oddnumbered elements close to them in the periodic table.
Finally there is a particular stability associated with nuclei in which either the number of
protons or the number of neutrons is equal to one of the so-called "magic" numbers 2, 8,
20, 28, 50, 82, and 126. These numbers correspond to the filling of shells in the structure of
the nucleus. These shells are similar in principle but different in detail to those found in
electronic structure. Of particular stability, and also of high abundance in the universe, are
nuclei in which both the-number of protons and the number of neutrons correspond to
Ca , and 208
Pb .
magic numbers. Examples are 42 He , 168 O , 40
20
82
EXAMPLE 19.3 Find which element has the largest number of isotopes, using Fig. 19.2.
Likewise find which is the number of neutrons which occurs most frequently. What do you
notice about the numbers of protons and neutrons in each case?
Solution Tin has 10 isotopes, and its atomic number 50 is a magic number. A total of 7
stable isotopes have 82 neutrons in the nucleus, more than for any other number of
neutrons. Again the number is a magic number.
19.4 THE RATE OF RADIOACTIVE DECAY
So far we have labeled all isotopes which exhibit radioactivity as unstable, but radioactive
isotopes vary considerably in their degree of instability. Some decay so quickly that it is
difficult to detect that they are there at all before they have changed into something else.
Others have hardly decayed at all since the earth was formed.
The process of radioactive decay is governed by the uncertainty principle, so that we can
never say exactly when a particular nucleus is going to disintegrate and emit a particle. We
can, however, give the probability that a nucleus will disintegrate in a given time interval.
For a large number of nuclei we can predict what fraction will disintegrate during that
interval. This fraction will be independent of the amount of isotope but will
651
vary from isotope to isotope depending on its stability. We can also look at the matter from
the opposite point of view, i.e., in terms of how long it will take a given fraction of isotope
to dissociate. Conventionally the tendency for the nuclei of an isotope to decay is measured
by its half-life, symbol t1/2.
This is the time required for exactly half the nuclei to disintegrate. This quantity, too, varies
from isotope to isotope but is independent of the amount of isotope.
I
Figure 19.3 shows how a 1-amol (attomole) sample of 128
53 which has a half-life of 25.0 min,
decays with time. In the first 25 min, half the nuclei disintegrate, leaving behind 0.5 amol.
In the second 25 min, the remainder is reduced by one-half again, i.e., to 0.25 amol. After a
third 25-min period, the remainder is (½)3 amol, after a fourth it is (½)4 amol, and so on. If
x intervals of 25.0 min are allowed to pass, the remaining amount of 128I will be (½)x amol.
This example enables us to see what will happen in the general case. Suppose the initial
amount of an isotope of half-life t1/2 is n0 and the isotope decays to an amount n in time t,
we can measure the time in terms of the number of t1/2 intervals which have elapsed by
defining a variable x such that
x
t
t1/2
Figure 19.3 Radioactive decay of 128I. In the course of each 25-min period, the
amount of the isotope decreases by one-half.
(19.27)
652
Thus after time t our sample will have been reduced to a fraction (½)x of the original
amount. In other words
1
 
n0  2 
n
x
(19.28)
Taking logs we then have
x
1
1
log
=   = x log
= – 0.3010x
2
n0
2
n
Substituting from Eq. (19.27) we thus obtain
log
n
=
n0
0.3010
t1/2
t
(19.29)
EXAMPLE 19.4 What amount of 128I will be left when 3.65 amol of this isotope is
allowed to decay for 15.0 min. The half-life of 128I 25.0 min.
Solution Substituting in Eq. (19.29) we have
log
n
n0
=
0.3010
t1/2
t=
0.3010  15.0 min
25.0 min
= – 0.1806
Thus
n
n0
or
= antilog(– 0.1806) = 10– 0.1806 = 0.6598
n = 0.6598n0 = 0.6598 × 3.65 amol = 2.41 amol
Equation (19.28) describes how the amount of a radioactive isotope decreases with time,
but similar formulas can also be written for the mass m and also for the rate of
disintegration r. This is because both the mass and the rate are proportional to the amount
of isotope. Thus the rate at which an isotope decays is given by
log
r
r0
=
0.3010
t1/2
t
(19.30)
where r0 is the initial rate at time zero.
The decrease over time of the rate of decay of a radioactive isotope can be used to establish
the ages of various objects and thus is important in fields such as archaeology,
paleontology, and geology. The best known of these dating techniques involves the isotope
14
C , a β emitter with a half-life of 5770 years. There is one atom of 146 C for every 7.49 ×
6
1011C atoms in the CO2 of the atmosphere and in all living things. The proportion does not
653
change with time because as fast as 14C nuclei are destroyed by radioactive decay, they
become replenished by the action of cosmic-ray neutrons on N atoms in the upper
atmosphere:
14
N + 01n  146 C + 11 H
(19.31)
7
The carbon produced in this way soon becomes part of a CO2 molecule and enters the
carbon cycle. Thus any sample of carbon derived from a living plant or animal or from the
atmosphere has the same rate of decay—15.3 disintegrations per minute per gram of
carbon.
Once a plant or an animal dies, it is removed from the carbon cycle and the rate of
radioactive decay begins to decrease. By measuring the disintegration rate one can estimate
how long it has been since the sample was re- moved from the carbon cycle.
EXAMPLE 19.5 A sample of carbon derived from one of the Dead Sea scrolls was found
to be decaying at the rate of 12.1 disintegrations per minute per gram of carbon. Estimate
the age of the Dead Sea scrolls.
Solution Since the original rate of decay of the material from which the scrolls were made
was 15.3 disintegrations per minute per gram of carbon, we have r0 = 15.3 min–1 g–1, while
r = 12.1 min–1 g–1. Substituting into Eq. (19.30), we then have
log
log
r
r0
12.1
15.3
=
=
0.3010
t1/2
t
0.3010
5770 years
t
– 0.102 = –5.22 × 10–5 years–1 t
t = 1950 years
There are several dating techniques which can be used to determine the age of rocks. The
simplest of these is perhaps the determination of the ratio of the amount of 238U to the
amount of 206Pb in a given rock. As we have already seen, 238U decays to 206Pb in a series of
14 steps for which the net process is
238
92
U 
206
82
Pb + 8 42 He + 6 -10 e
(19.10b)
The overall rate of this process is governed by its slowest step which has a half-life of 4.5 ×
109 years. The assumption is made that all the 206Pb in the rock derives from the 238U and
that none was present when the rock was initially formed. If this assumption is correct, the
ratio of 238U to 206Pb will decrease with time. By measuring this ratio we can estimate how
long ago the rock was formed.
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EXAMPLE 19.6 Analysis of a rock revealed that it contained 0.753 μg of
μg of
206
82
238
92
U and 0.241
Pb . Calculate the age of the rock.
Solution
Amount of 238U = nU =
0.753 g
238 g mol
Amount of 206Pb = nPb =
Since each mol of
given by
206
1
= 3.16 × 10–3 μmol
0.241 g
206 g mol 1
= 1.17 × 10–3 μmol
Pb was originally a mole of
238
U, the original amount of
238
U, n0, is
n0 = (3.16 + 1.17) × 10–3 μmol = 4.33 × 10–3 μmol
Substituting into Eq. (19.29), we have
log
log
or
n
n0
3.16  103  mol
4.33  10  mol
3
=
=
0.3010
t1/2
t
0.3010
4.5  109 years
t
– 0.137 = – 6.7 × 10–11 years–1 t
t = 2.0 × 109 years
The majority of the age measurements made on earth rocks, and in re- cent years on moon
rocks, yield values in the range of 1 to 4.5 billion years. On this basis the ages of both the
earth and the moon seem to he similar, and the theory that the moon was a fragment of a
previously formed earth becomes difficult to support.
19.5 DETECTION AND MEASUREMENT OF RADIATION
Because radiation is harmful to humans and other organisms, it is very important that we be
able to detect it and measure how much is present. Such measurements are complicated by
two factors. First, we cannot see, hear, smell, taste, or touch radiation, and so special
instruments are required to measure it. Second, as we have already mentioned, different
types of radiation are more dangerous than others, and corrections must be made for the
relative harm done by α particles as opposed to, say, γ rays.
Instruments for Radiation Detection
Perhaps the most common instrument for measuring radiation levels is the Geiger-Müller
counter (the same Geiger who worked with Rutherford to discover the atomic nucleus.) A
schematic diagram of a Geiger-Müller counter is shown in Fig. 19.4. A metal tube
containing Ar gas is sealed at
655
Figure 19.4 A Geiger-Müller tube.
one end with a thin glass or plastic window and contains a central wire well insulated from
it. A potential difference of about 1000 V is applied between the central wire and the tube.
Any incoming α, β or γ ray will ionize some of the Ar atoms. These Ar+ ions are quickly
accelerated to a high velocity by the large potential difference, high enough for them in turn
to start ionizing further Ar atoms. Thus, for every ray that enters the tube, a large number of
ions is formed and a pulse of electrical current is produced. This pulse is amplified and
allowed to drive a digital electronic counter which operates on a principle similar to that of
a digital watch. The number of particles passing through the tube in a given time can thus
be found. Alternatively, the tube can be made to operate a meter indicating the rate at
which radiation is passing into the Geiger-Müller tube.
Another type of detector, much used for γ rays, is the scintillation counter. When a γ ray
penetrates a special crystal or solution, it produces a momentary flash of light (called a
scintillation) which is detected by a photoelectric cell. Again the output can be amplified
and fed into a counter or a meter. A third kind of detector is used to monitor how much
exposure laboratory workers have been subjected to in the course of their work. This is
simply a strip of photographic film. The degree to which this film is darkened is a measure
of the total quantity of radiation to which the worker has been subjected.
Units of Radiation Dose
A variety of units have been designed to measure how much radiation has been absorbed
by a given sample of human or animal tissue. The simplest to understand is the radiationabsorbed dose, abbreviated rad. This corresponds to absorption of 10–5 J of energy per
gram of tissue. A more useful unit is the rem (roentgen-equivalent man), which is the
same as the rad except that it is corrected for the relative harmfulness of each type of
radiation. For example, an α particle having a kinetic energy of 1.6 × 10–22 J can produce
about 10 times as many ions as a γ ray of equal energy. Consequently 1 rad of α radiation
would be corrected to 10 rem, while 1 rad of γ radiation would correspond to 1 rem.
656
Once radiation detectors were developed, it was discovered that there is nowhere that one
can be entirely free of radiation. That is, there is a natural background radiation
impinging on all of us every day of our lives. This comes from natural radioactive isotopes
in our surroundings and from cosmic radiation which enters the earth’s atmosphere from
outer space. The average United States citizen receives just over 0.1 rem per year from
natural background, although this varies from place to place. In Colorado, for example,
background radiation is much higher because of the altitude (less atmosphere to block
cosmic rays) and because of naturally occurring deposits of uranium.
Current estimates indicate that the actual radiation dose received by the average person is
about 80 percent higher than natural background. The major portion of this increase is due
to medical uses—a chest x-ray, for example, contributes about 0.2 rem. Other contributions
are made by radioactive fallout from nuclear bombs (about 4 percent of background), and
miscellaneous sources such as TV sets (about 2 percent).
There is evidence that the effects of small doses of radiation are cumulative, at least to
some degree, and that there is no lower limit to the dose which can cause some damage.
Thus even background radiation may be harmful to some extent, but it is hard to determine
just how harmful because we have no way of turning it off to see how much difference it
makes. In the absence of more accurate information it would seem prudent for each
individual and for a society as a whole to minimize unnecessary radiation, exposures.
19.6 USES OF ARTIFICIAL ISOTOPES IN CHEMISTRY
Tracers
A very large number of isotopes which do not occur naturally can now be made fairly
readily by neutron capture using an atomic reactor or a laboratory neutron source. Many of
these artificial isotopes have proved very useful in chemistry since they provide a way of
identifying atoms from a particular source, a technique known as labeling or tracer study.
This technique is particularly easy to use if the isotope is radioactive. Thus, for example, if
a small quantity of the radioactive isotope 131I is added in the form of iodide ion to a
saturated solution of lead iodide, one soon finds that the solid lead iodide in contact with
the solution, as well as the solution, become radioactive. This clearly demonstrates that the
solution equilibrium
PbI2
Pb2+ + 2I–
(19.32)
is a dynamic process involving the constant interchange of iodide ions between the solution
and the solid.
Tracer studies are also possible with isotopes which are not radioactive. The isotope 18O is
often used in this way, since no convenient radioactive isotope of oxygen is available. In
naturally occurring oxygen the isotope 18O is only 0.2 percent of the total. If extra 18O is
added, its presence can be detected by mass spectrometry. An interesting and important
example of the
657
use of 18O is in the study of photosynthesis. If the water in this reaction is enriched with
18
O, then the isotope is found in the oxygen produced:
6CO2(g) + 6H2O(l) → C6H12O6(s) + 6O2(g)
(19.33)
By contrast, if the carbon dioxide is enriched with 18O, none of this enrichment appears in
the oxygen produced. Another example of the use of 18O comes from inorganic chemistry.
It is the reaction between the sulfite ion and the chlorate ion in aqueous solution:
(19.34a)
By labeling the oxygens in the chlorate ion, it is found that all the 18O lost from the one
species is gained by the other and none of it is transferred to the solvent water. The
mechanism of this reaction must thus be a direct transfer of oxygen and is quite unrelated to
the two half-equations we conventionally use when balancing the redox equation:
2–
2–
SO3 + H2O → SO4 + 2H+ + 2e–
(19.34b)
+
–
2H + 2e +
–
ClO3 →
–
ClO2 +
H2O
Neutron Activation Analysis
An important use of radioisotopes in detecting small amounts of certain elements in a
sample is neutron activation analysis. The sample being analyzed is irradiated by a neutron
source. Nuclei of the element being analyzed capture neutrons, and an unstable nucleus is
formed which emits a γ ray. Since the wavelength of this γ ray is characteristic of the
element, it can be distinguished from other elements in the sample. This method of analysis
has the advantage of being nondestructive. The sample being analyzed is scarcely altered
by being irradiated. Neutron activation is also among the most sensitive of analytical
techniques. As little as a pictogram (10–12 g) of arsenic, for example, can be detected. This
is about 10 000 times more sensitive than Marsh’s test—so often used by the fabled
detective Sherlock Holmes. Neutron activation analysis is used by many modern detectives to find evidence of air and water pollution as well as the types of crimes with
which Holmes was involved.
19.7 MASS-ENERGY RELATIONSHIPS
In a nucleus the protons and the neutrons are held very tightly by forces whose nature is
still imperfectly understood. When the nucleons are very close to each other, these forces
are strong enough to counteract the coulombic repulsion of the protons, but they fall off
very rapidly with distance and are essentially undetectable outside the nucleus. Because the
energies involved in binding the nucleons together are very large, they give rise to an effect
which makes it possible to measure
658
them. According to Einstein’s special theory of relativity, when the energy of a body
increases, so does its mass, and vice versa. If the change in energy is indicated by ΔE and
the change in mass by Δm, these two quantities are related by the equation
ΔE = Δmc2
(19.35)
where c is the velocity of light (2.998 × 108 m s–1).
In ordinary chemical reactions this change in mass with energy is so small as to be
undetectable, but in nuclear reactions we invariably find that products and reactants have
different masses. As a simple example, let us take the dissociation of a deuteron into a
proton and a neutron:
2
D  11 p + 01n
1
The molar mass of a deuteron is found experimentally to be 2.013 55 g mol–1 (see Table
19.1), but if we add the molar masses of a neutron and a proton,
TABLE 19.1 The Molar Masses of Some Selected Nuclei (Electrons Are Not Included in
These Masses).
we obtain a somewhat higher value, namely, (1.007 28 + 1.008 67) g mol–1 = 2.015 95 g
mol–1. The change in mass using the usual delta convention is thus (2.015 95 – 2.013 55) g
mol–1 = 0.002 40 g mol–1. From Eq. (19.35) we then have
ΔE = Δmc2
g

1 kg
× (2.998 × 108 m s–1)2
mol
103 g
= 2.16 × 1011 kg m2 s–2 mol–1
= 216 × 109 J mol–1 = 216 GJ mol–1
= 0.002 40 g mol
Since expansion work or even electronic energies are negligible compared to this change in
nuclear energy, we can equate the change in nuclear energy either to the change in internal
energy or the enthalpy; that is,
ΔE = ΔUm = ΔHm = 216 GJ mol–1
The energy needed to separate a nucleus into its constituent nucleons is called its binding
energy. The binding energy of the 21 D nucleus is thus
659
216 GJ mol–1. Notice how very much larger this is than the bond energy of an average
molecule, which is about 200 or 300 kJ mol–1. Since a gigajoule is 1 million kJ, the
energies involved in holding the nucleons together in a nucleus are something like a million
times larger than those holding the atoms together in a molecule.
Since the number of nucleons in a nucleus is quite variable, it is useful to calculate the
average energy of each nucleon by dividing the total binding energy by the number of
Fe ,
nucleons, A. This gives the binding energy per nucleon. In the case of the nucleus 56
26
for instance, we can easily find from Table 19.1 that Δm for the process
56
26
Fe  26 11 p + 30 01 n
has the value 0.528 72 g mol–1, giving a value for ΔHm, from Eq. (19.35)of 4750 GJ mol–1.
Since A = 56 for this nucleus, the binding energy per nucleon has the value
H m
A
=
4750
56
GJ mol–1 = 848 GJ mol–1
The binding energy of a nucleus tells us not only how much energy must be expended in
pulling the nuclei apart but also how much energy is released when the nucleus is formed
Fe , for instance, we have
from protons and neutrons. In the case of the 56
26
26 11 p + 30 01 n 
56
26
Fe
ΔHm = –4.75 × 103 GJ mol–1
Fe is equal to the negative of the binding energy. In
that is, the energy of formation of 56
26
Fig. 19.5 the energy of formation on a per nucleon basis has been against the mass number
for the most stable isotope of each element. The zero energy axis in this plot corresponds to
the energy of completely separated protons and neutrons, while the points on the graph
correspond to the average energy of a nucleon in the nucleus in question. Obviously, the
lower the energy, the more stable the nucleus.
As we can see from Fig. 19.5, the most stable nuclei are those of mass number close to 60,
Fe nucleus. As the mass number rises above
the nucleus with the lowest energy being the 56
26
60, the nuclei become slightly higher in energy, i.e., less stable. Decreasing the mass
number below 60 also brings us into a region of high-energy nuclei. With the exception of
the 42 He , nucleus, the nuclei of highest energy belong to the very lightest elements.
Figure 19.5 shows us that in principle there are two ways in which we can obtain energy
from the nuclei of the elements. The first of these is by the splitting up or fission of a very
heavy nucleus into two lighter nuclei. In such a case each nucleon will move from a
situation of higher to lower energy and energy will be released. Even more energy will be
released by the fusion of two very light nuclei, each containing only a few nucleons, into a
single heavier nucleus. Though fine in principle, neither of these methods of obtaining
energy is easy to achieve in practice in a controlled way with due respect to the
environment.
660
Figure 19.6 Energy of formation per nucleon (from protons and neutrons) as a function of
mass number.
19.8 NUCLEAR FISSION
The first time that nuclear fission was achieved in the laboratory was by the Italian
physicist Enrico Fermi (1901 to 1954) in 1934. Fermi was among the first to use the
neutron in nuclear reactions, following its discovery by Chadwick in 1932. He hoped, by
bombarding uranium with slow neutrons, to be able to prepare the first transuranium
element. Instead he obtained a product which seemed to be a group II element which he
identified incorrectly as radium. It remained for the experienced German radiochemist Otto
Hahn to correct Fermi’s mistake. (In the meantime Fermi had been awarded the Nobel
Prize.) Somewhat reluctantly, Hahn published a paper early in 1939 showing that the
element produced by the bombardment of uranium was not radium at all but the very much
lighter group II element barium, 36 places earlier in the periodic table! It then became clear
that instead of knocking a small chip off the uranium nucleus as had been expected, the
bombarding neutron had broken the nucleus into two large fragments, one of which was
barium. We now know that the initial step in this process is the formation of an unstable
isotope of uranium which then fissions in a variety of ways, some of which are shown
below:
(19.36)
661
EXAMPLE 19.7 Using Fig. 19.5, make a rough estimate of the energy released by the
fission of 1 g of uranium-235 according to the equation
235
92
U + 01n 
140
56
93
36
Ba +
Kr + 3 01n
Solution From Fig. 19.5 we can make the following estimates of the energies of formation
per nucleon for the four species involved:
ΔHf (140Ba) = – 810 GJ mol–1
ΔHf (93Kr) = – 810 GJ mol–1
ΔHf (235U) = – 730 GJ mol–1
ΔHf ( 01 n ) = 0
Using these quantities in the same way as enthalpies of formation for chemical reactions,
we obtain
ΔHm = [140(– 810) + 93(– 840) – 235(– 730)] GJ mol–1
= – 20 000 GJ mol–1
The enthalpy change per gram is then given by
GJ
1 mol
= – 85 GJ g–1
mol
235 g
Note: This is about the same quantity of heat energy as that produced by burning 3 tons of
bituminous coal!
ΔH = – 20 000
×
Calculations similar to that just performed soon persuaded scientists in 1939 that the fission
of uranium was highly exothermic and could possibly be used in a super bomb. Adolph
Hitler had been in power in Germany for 6 years, and Europe was teetering on the brink of
World War II. The possibility that Nazi Germany might develop such a bomb and use it did
not seem remote, especially to those scientists who had recently fled Nazi and Fascist
Europe and come to the United States. Albert Einstein, himself one of these refugees, was
persuaded to write a letter to President Franklin Roosevelt in August 1939 in which the
alarming possibilities were outlined. Roosevelt heeded Einstein’s advice and established
the so-called Manhattan Project, a super-secret research effort to develop an atomic bomb if
at all possible. After 5 years of intense effort and the expenditure of more money than had
ever been spent on a military-scientific project before, the first bomb was tested in New
Mexico in July 1945. Shortly thereafter two atom bombs were dropped on the Japanese
cities of Hiroshima and Nagasaki, and World War II ended almost immediately.
Some Features of Nuclear Fission
A crucial feature of the fission of uranium without which an atom bomb is impossible is
that fission produces more neutrons than it consumes. As can be seen from Eqs. (19.36),
U nucleus, between two and four neutrons are produced.
for every neutron captured by a 235
92
Suppose now that we have a very large sample of the pure isotope
enters this
235
92
U and a stray neutron
662
sample. As soon as it hits a 235U nucleus, fission will take place and about three neutrons
will be produced. These in turn will fission three more 235U nuclei, producing a total of nine
neutrons. A third repetition will produce 27 neutrons. a fourth 81. and so on. This process
(which is called a chain reaction) escalates very rapidly. Within a few microseconds a very
large number of nuclei fission, with the release of a tremendous amount of energy, and an
atomic explosion results.
There are two reasons why a normal sample of uranium metal does not spontaneously
U
explode in this way. In the first place natural uranium consists mainly of the isotope 235
92
while the fissionable isotope
235
92
U comprises only 0.7 percent of the total. Most of the
U nuclei without any
neutrons produced in a given fission process are captured by 235
92
further production of neutrons. The escalation of the fission process thus becomes
U will not always explode spontaneously.
impossible. However, even a sample of pure 235
92
If it is sufficiently small, many of the neutrons will escape into the surroundings without
causing further fission. The sample must exceed a critical mass before an explosion
results. In an atomic bomb several pieces of fissionable material, all of which are below the
critical mass, are held sufficiently far apart for no chain reaction to occur. When these are
suddenly brought together, an atomic explosion results immediately.
A great deal of the 5 years of the Manhattan Project was spent in separating the 0.7 percent
of 235U from the more abundant 238U. This was done by preparing the gaseous compound
UF6 and allowing it to effuse through a porous screen. (Recall from Sec. 9.4 that the rate of
effusion is inversely proportional to the square root of molar mass.) Each effusion resulted
in a gas which was slightly richer in the lighter isotope. Repeating this process eventually
produced a compound rich enough in 235U for the purposes of bomb manufacture.
Only the first bomb dropped on Japan used uranium. The second bomb used the artificial
element plutonium, produced by the neutron bombardment of 2385U [Eqs. (19.21) and
(19.22)]:
235
U + 01 n  239
Pu + 2 10 p
92
94
Fission of
example,
239
94
Pu occurs in much the same way as for
239
94
Pu + 01 n 
90
38
Sr +
147
56
235
92
U , giving a variety of products; for
Ba + 3 01 n
(19.37)
Again this is a highly exothermic reaction yielding about the same energy per mole (20 000
GJ mol–1) as 235U.
Nuclear Power Plants
Even before the atomic bomb had been produced, scientists and engineers had begun to
think about the possibility of using the energy released by the fission process for the
production of electrical energy. Shortly after World War II confident predictions were
made that human beings would soon depend almost entirely on atomic energy for
electricity. Alas, we are now 30 years into the future from then and no such miracle has oc-
663
curred. In the United States only 4 percent of the electrical energy is currently produced by
this method. The proportion is a little higher in some other countries, notably Great Britain,
but nowhere is nuclear power even on the verge of replacing the fossil fuels. The
unfortunate truth is that producing power from atomic fission has turned out to be much
more expensive than was previously expected. Even in these days of high prices for the
fossil fuels it is still only barely competitive.
A schematic diagram of a typical nuclear reactor is given in Fig. 19.6. The uranium is
present in the form of pellets of the oxide U3O8 enclosed in long steel tubes about 2 cm in
U slightly enriched with the fissionable 235
U . The rate
diameter. The uranium is mainly 238
92
92
of fission can be regulated by inserting or withdrawing control rods made of cadmium,
which is a very efficient neutron absorber. In addition a moderator such as graphite
or water must be present to slow down the neutrons, since slow neutrons are more efficient
at causing fission than fast ones.
The energy released by the fisson of the uranium is carried off by a coolant, usually
superheated steam at about 320°C. This steam cannot be used directly since it becomes
slightly radioactive. Instead it is passed through a heat exchanger so as to produce further
steam which can then be used to power a conventional steam turbine. The whole system is
enclosed in a strong containment vessel (not shown in the figure). This vessel prevents the
spread of radioactivity in case of a serious accident.
Figure 19.6 Schematic diagram of a nuclear power reactor.
664
Nuclear power plants have two advantages over conventional power plants using fossil
fuels. First, for a given energy output they consume much less fuel. Second, they produce
far smaller quantities of toxic effluents. Fossil-fueled plants produce sulfur dioxide, oxides
of nitrogen, and smoke particles, all of which are injurious to health.
Despite the much lower cost for fuel, nuclear power plants are very expensive to build.
This is largely because of their chief disadvantage, the extremely dangerous nature of the
radioactive products of nuclear fission. Fission products consist of a great many neutronrich, unstable nuclei, ranging in atomic number from 25 to 60. Particularly dangerous are
Sr , 137
Cs , and the shorter-lived 131
I
the long-lived isotopes 90
38
55
53 , all of which can be
incorporated into the human body. Extreme precautions must be taken against accidental
release of even traces of these materials into the environment. It should be realized in this
connection that the possibility of a nuclear reactor running out of control and becoming a
U
Hiroshima-type bomb is zero. The fuel used in nuclear reactors is not rich enough in 235
92
for this to occur, and the worst possible accident is complete meltdown of the reactor core.
Such an accident could be very serious because a great many highly radioactive isotopes
would be scattered by the wind.
Even if fission products are handled successfully during normal operation of a nuclear
plant, there still remains the difficulty of their eventual disposal. Although many of the
Sr (25 years) and 137
Cs (30
unstable nuclei produced by fission are short-lived, some, like 90
38
55
years), have quite long half-lives. Accordingly these wastes must be stored for many
hundreds of years before enough nuclei decompose to reduce their radioactivity to a safe
level. At the present time, most of these wastes are stored as solutions in underground tanks
near Richland, Washington. If the number of nuclear plants increases appreciably, the
disposal of these wastes will become very difficult. Originally it was planned to store these
wastes in solid form in underground salt deposits, but no entirely satisfactory site has yet
been found.
Breeder Reactors
U is only 0.7 percent of naturally occurring uranium, its supply is fairly limited
Because 235
92
and could well only last for about 50 years of full-scale use. The other 99 percent of the
uranium can also be utilized if it is first converted into plutonium by neutron bombardment:
235
92
As we have already seen,
235
92
239
94
U + 01 n 
239
94
Pu + 2 10 p
Pu is also fissionable, and so it could be used in a nuclear
reactor as well as U .
The production of plutonium can be carried out in a breeder reactor which not only
produces energy like other reactors but is designed to allow some of the fast neutrons to
U , producing plutonium at the same time. More fuel is then produced than
bombard the 235
92
is consumed.
665
Breeder reactors present additional safety hazards to those already outlined. They operate at
higher temperatures and use very reactive liquid metals such as sodium in their cooling
systems, and so the possibility of a serious accident is higher. In addition the large
quantities of plutonium which would be produced in a breeder economy would have to be
carefully safeguarded. Plutonium is an α emitter and is very dangerous if taken internally.
Its half-life is 24 000 years, and so it will remain in the environment for a long time if
Pu can be separated chemically (not by the much more expensive
dispersed. Moreover, 239
94
U ) from fission products and used to make bombs.
gaseous diffusion used to concentrate 235
92
Such a material will obviously be attractive to terrorist groups, as well as to countries
which are not currently capable of producing their own atomic weapons.
19.9 NUCLEAR FUSION
In addition to fission, a second possible method for obtaining energy from nuclear reactions
lies in the fusing together of two light nuclei to form a heavier nucleus. As we have already
seen in discussing Fig. 19.5, such a process results in nucleons which are more firmly
bonded to each other and hence lower in potential energy. This is particularly true if 42 He is
formed, because this nucleus is very stable. Such a reaction occurs between the nuclei of
the two heavy isotopes of hydrogen, deuterium and tritium:
2
1
D + 31T 
4
2
He + 01 n
(19.38)
For this reaction Δm = – 0.018 88 g mol–1 so that ΔHm = – 1700 GJ mol–1. Although very
large quantities of energy are released by a reaction like Eq. (19.38) such a reaction is very
difficult to achieve in practice. This is because of the very high activation energy, about 30
GJ mol–1, which must be overcome to bring the nuclei close enough to fuse together. This
barrier is created by coulombic repulsion between the positively charged nuclei. The only
place where scientists have succeeded in producing fusion reactions on a large scale is in a
hydrogen bomb. Here the necessary activation energy is achieved by exploding a fission
bomb to heat the reactants to a temperature of about 108 K. Attempts to carry out fusion in
a more controlled way have met with only limited success. At the very high temperatures
required, all molecules dissociate and most atoms ionize. A new state of matter called a
plasma is formed. It is neither solid, liquid, or gas and behaves much like the universal
solvent of the alchemists by converting any solid material which it contacts into vapor.
Two techniques for producing a controlled fusion reaction are currently being explored.
The first is to restrict the plasma by means of a strong magnetic field rather than the walls
of a container. This has met with some success but has not yet been able to contain a
plasma long enough for usable energy to be obtained. The second technique involves the
sudden compression and heating of pellets of deuterium and tritium by means of a sharply
focused laser beam. Again, only a limited success has been obtained.
666
Though these attempts at a controlled fusion reaction have so far been only partially
successful, they are nevertheless worth pursuing. Because of the much readier availability
of lighter isotopes necessary for fusion as opposed to the much rarer heavier isotopes
required for fission, controlled nuclear fusion would offer the human race an essentially
limitless supply of energy. There would still be some environmental difficulties with the
production of isotopes such as tritium, but these would be nowhere near the seriousness of
the problem caused by the production of the witches brew of radioactive isotopes in a
fission reactor. It must be confessed, though, that at the present rate of progress, the
prospect of limitless clean energy from fusion seems unlikely in the next decade or two.
SUMMARY
Nuclear reactions involve rearrangements of the protons and neutrons within atomic nuclei.
During naturally occurring nuclear reactions α particles, β particles, and γ rays are emitted,
often in a radioactive series of successive reactions. Nuclear reactions may also be induced
by bombarding nuclei with positive ions or neutrons. Artificial isotopes produced in this
way may decay by positron emission or electron capture as well as by α , β or γ emission.
Stability of nuclei depends on the neutron/proton ratio (usually between 1 and 1.6) and
magic numbers of protons and neutrons.
Radioactive decay obeys a first-order rate law, and its rate is often reported in terms of
half-life, the time necessary for half the radioactive nuclei to decompose. Known half-lives
U may be used to establish the ages of objects containing
of isotopes such as 146 C and 238
92
these elements, provided accurate measurements can be made of the quantity of radiation
emitted. Geiger-Müller counters or scintillation counters are often used for such
measurements. Other important applications of radioactive isotopes include tracer studies,
where a particular type of atom can be labeled and followed throughout a reaction, and
neutron activation analysis, which can determine extremely low concentrations of many
elements.
The relative stability of a nucleus is given by the energy of formation per nuclear particle.
This may be determined from the difference between the molar mass of the nucleus and the
sum of the molar masses of its constituent protons and neutrons. Both fission, breaking
apart of a heavy nucleus, and fusion, combining of two light nuclei, can result in release of
U or 239
Pu , and these isotopes have been used in
energy. Fission usually involves 238
92
94
nuclear explosives and nuclear power plants. Fission products are highly radioactive.
Because of the considerable damage done to living tissue by the ability of α, β and γ
radiation to break bonds and form ions, emission of radioactive materials must be carefully
controlled and fission power plants are quite expensive to construct. Although it promises
much larger quantities of free energy and fewer harmful by-products than fission, nuclear
fusion bas not yet been shown to be feasible for use in power plants. So far its only
application has been in hydrogen bombs.