Table of Contents
Related Titles
Title page
Copyright page
Preface
Volume 1
1: Fundamental Concepts
1.1 The Atom
1.2 Atomic Processes
1.3 Discovery of the Atomic Nucleus
1.4 Nuclear Decay Types
1.5 Some Physical Concepts Needed in Nuclear Chemistry
2: Radioactivity in Nature
2.1 Discovery of Radioactivity
2.2 Radioactive Substances in Nature
3: Radioelements and Radioisotopes and Their Atomic Masses
3.1 Periodic Table of the Elements
3.2 Isotopes and the Chart of Nuclides
3.3 Nuclide Masses and Binding Energies
3.4 Evidence for Shell Structure in Nuclei
3.5 Precision Mass Spectrometry
4: Other Physical Properties of Nuclei
4.1 Nuclear Radii
4.2 Nuclear Angular Momenta
4.3 Magnetic Dipole Moments
4.4 Electric Quadrupole Moments
4.5 Statistics and Parity
4.6 Excited States
5: The Nuclear Force and Nuclear Structure
5.1 Nuclear Forces
5.2 Charge Independence and Isospin
5.3 Nuclear Matter
5.4 Fermi Gas Model
5.5 Shell Model
5.6 Collective Motion in Nuclei
5.7 Nilsson Model
5.8 The Pairing Force and Quasi-Particles
5.9 Macroscopic–Microscopic Model
5.10 Interacting Boson Approximation
5.11 Further Collective Excitations: Coulomb Excitation, High-Spin States, Giant Resonances
6: Decay Modes
6.1 Nuclear Instability and Nuclear Spectroscopy
6.2 Alpha Decay
6.3 Cluster Radioactivity
6.4 Proton Radioactivity
6.5 Spontaneous Fission
6.6 Beta Decay
6.7 Electromagnetic Transitions
7: Radioactive Decay Kinetics
7.1 Law and Energy of Radioactive Decay
7.2 Radioactive Equilibria
7.3 Secular Radioactive Equilibrium
7.4 Transient Radioactive Equilibrium
7.5 Half-life of Mother Nuclide Shorter than Half-life of Daughter Nuclide
7.6 Similar Half-lives
7.7 Branching Decay
7.8 Successive Transformations
8: Nuclear Radiation
8.1 General Properties
8.2 Heavy Charged Particles (A ≥ 1)
8.3 Beta Radiation
8.4 Gamma Radiation
8.5 Neutrons
8.6 Short-lived Elementary Particles in Atoms and Molecules
9: Measurement of Nuclear Radiation
9.1 Activity and Counting Rate
9.2 Gas-Filled Detectors
9.3 Scintillation Detectors
9.4 Semiconductor Detectors
9.5 Choice of Detectors
9.6 Spectrometry
9.7 Determination of Absolute Disintegration Rates
9.8 Use of Coincidence and Anticoincidence Circuits
9.9 Low-Level Counting
9.10 Neutron Detection and Measurement
9.11 Track Detectors
9.12 Detectors Used in Health Physics
10: Statistical Considerations in Radioactivity Measurements
10.1 Distribution of Random Variables
10.2 Probability and Probability Distributions
10.3 Maximum Likelihood
10.4 Experimental Applications
10.5 Statistics of Pulse-Height Distributions
10.6 Setting Upper Limits When No Counts Are Observed
11: Techniques in Nuclear Chemistry
11.1 Special Aspects of the Chemistry of Radionuclides
11.2 Target Preparation
11.3 Measuring Beam Intensity and Fluxes
11.4 Neutron Spectrum in Nuclear Reactors
11.5 Production of Radionuclides
11.6 Use of Recoil Momenta
11.7 Preparation of Samples for Activity Measurements
11.8 Determination of Half-Lives
11.9 Decay-Scheme Studies
11.10 In-Beam Nuclear Reaction Studies
Volume 2
12: Nuclear Reactions
12.1 Collision Kinematics
12.2 Coulomb Trajectories
12.3 Cross-sections
12.4 Elastic Scattering
12.5 Elastic Scattering and Reaction Cross-section
12.6 Optical Model
12.7 Nuclear Reactions and Models
12.8 Nuclear Reactions Revisited with Heavy Ions
13: Chemical Effects of Nuclear Transmutations
13.1 General Aspects
13.2 Recoil Effects
13.3 Excitation Effects
13.4 Gases and Liquids
13.5 Solids
13.6 Szilard–Chalmers Reactions
13.7 Recoil Labeling and Self-labeling
14: Influence of Chemical Bonding on Nuclear Properties
14.1 Survey
14.2 Dependence of Half-Lives on Chemical Bonding
14.3 Dependence of Radiation Emission on the Chemical Environment
14.4 Mössbauer Spectrometry
15: Nuclear Energy, Nuclear Reactors, Nuclear Fuel, and Fuel Cycles
15.1 Energy Production by Nuclear Fission
15.2 Nuclear Fuel and Fuel Cycles
15.3 Production of Uranium and Uranium Compounds
15.4 Fuel Elements
15.5 Nuclear Reactors, Moderators, and Coolants
15.6 The Chernobyl Accident
15.7 Reprocessing
15.8 Radioactive Waste
15.9 The Natural Reactors at Oklo
15.10 Controlled Thermonuclear Reactors
15.11 Nuclear Explosives
16: Sources of Nuclear Bombarding Particles
16.1 Neutron Sources
16.2 Neutron Generators
16.3 Research Reactors
16.4 Charged-Particle Accelerators
17: Radioelements
17.1 Natural and Artificial Radioelements
17.2 Technetium and Promethium
17.3 Production of Transuranic Elements
17.4 Cross-sections
17.5 Nuclear Structure of Superheavy Elements
17.6 Spectroscopy of Actinides and Transactinides
17.7 Properties of the Actinides
17.8 Chemical Properties of the Transactinides
18: Radionuclides in Geo- and Cosmochemistry
18.1 Natural Abundances of the Elements and Isotope Variations
18.2 General Aspects of Cosmochemistry
18.3 Early Stages of the Universe
18.4 Synthesis of the Elements in the Stars
18.5 The Solar Neutrino Problem
18.6 Interstellar Matter and Cosmic Radiation
19: Dating by Nuclear Methods
19.1 General Aspect
19.2 Cosmogenic Radionuclides
19.3 Terrestrial Mother/Daughter Nuclide Pairs
19.4 Natural Decay Series
19.5 Ratios of Stable Isotopes
19.6 Radioactive Disequilibria
19.7 Fission Tracks
20: Radioanalysis
20.1 General Aspects
20.2 Analysis on the Basis of Inherent Radioactivity
20.3 Neutron Activation Analysis (NAA)
20.4 Activation by Charged Particles
20.5 Activation by Photons
20.6 Special Features of Activation Analysis
20.7 Isotope Dilution Analysis
20.8 Radiometric Methods
20.9 Other Analytical Applications of Radiotracers
20.10 Absorption and Scattering of Radiation
20.11 Radionuclides as Radiation Sources in X-ray Fluorescence Analysis (XFA)
20.12 Analysis with Ion Beams
20.13 Radioisotope Mass Spectrometry
21: Radiotracers in Chemistry
21.1 General Aspects
21.2 Chemical Equilibria and Chemical Bonding
21.3 Reaction Mechanisms in Homogeneous Systems
21.4 Reaction Mechanisms in Heterogeneous Systems
21.5 Diffusion and Transport Processes
21.6 Emanation Techniques
22: Radionuclides in the Life Sciences
22.1 Survey
22.2 Application in Ecological Studies
22.3 Radioanalysis in the Life Sciences
22.4 Application in Physiological and Metabolic Studies
22.5 Radionuclides Used in Nuclear Medicine
22.6 Single-Photon Emission Computed Tomography (SPECT)
22.7 Positron Emission Tomography (PET)
22.8 Labeled Compounds
23: Technical and Industrial Applications of Radionuclides and Nuclear Radiation
23.1 Radiotracer Techniques
23.2 Absorption and Scattering of Radiation
23.3 Radiation-induced Reactions
23.4 Energy Production by Nuclear Radiation
24: Radionuclides in the Geosphere and the Biosphere
24.1 Sources of Radioactivity
24.2 Mobility of Radionuclides in the Geosphere
24.3 Reactions of Radionuclides with the Components of Natural Waters
24.4 Interactions of Radionuclides with Solid Components of the Geosphere
24.5 Radionuclides in the Biosphere
24.6 Speciation Techniques with Relevance for Nuclear Safeguards, Verification, and Applications
25: Dosimetry and Radiation Protection
25.1 Dosimetry
25.2 External Radiation Sources
25.3 Internal Radiation Sources
25.4 Radiation Effects in Cell
25.5 Radiation Effects in Humans, Animals, and Plants
25.6 Non-occupational Radiation Exposure
25.7 Safety Recommendations
25.8 Safety Regulations
25.9 Monitoring of the Environment
Appendix
Glossary
Physical Constants
Conversion Factors
Relevant Journals
Index
Related Titles
The Author
Prof. Dr. Jens-Volker Kratz
Institut für Kernchemie
Universität Mainz
Fritz-Strassmann-Weg 2
55128 Mainz
Germany
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Preface
This textbook aims at a complete and concise description of the present knowledge of nuclear and radiochemistry and applications in various fields of the natural sciences. It is based on teaching courses and research spanning several decades. The book is mainly addressed to advanced undergraduate students and to graduate students of chemistry. Students and scientists working in physics, geology, mineralogy, biology, medicine, and other fields will also find useful information about the principles and applications of nuclear and radiochemistry.
Traditionally, nuclear chemistry has been deeply tied to nuclear physics, cooperatively called nuclear science. At the same time, a wide field of applications of nuclear and radiochemistry in other sciences has developed. Therefore, it was considered important to bring together in one textbook a detailed presentation of the physical fundamentals as well as applied aspects of nuclear chemistry ranging from nuclear structure, nuclear masses, nuclear reactions, the production of radionuclides and labeled compounds, the chemistry of the radioelements, the study of radionuclides in the environment, all the way to the nuclear and radiochemistry needed in nuclear technology. Applications also include the use of radionuclides in analytical chemistry, in geo- and cosmochemistry, dating by nuclear methods, and the use of radionuclides in the life sciences and medicine.
For further reading, the relevant literature is listed abundantly at the end of each chapter. Generally, it is arranged in chronological order, beginning with the literature of historical relevance, followed by more recent work subdivided according to the subject matter into general and more specialized aspects.
After the passing of Professor Karl Heinrich Lieser, the younger author (JVK) was approached by the Lieser family and by the publisher and was motivated to prepare a generally updated third edition of this textbook. The concept and structure of the book remain largely unchanged; however, new developments and results have been incorporated, including the most recent references. These updates concern the physical properties of atomic nuclei, the nuclear force and nuclear structure, techniques in nuclear chemistry, nuclear reactions, statistical considerations in radioactivity measurements, the actinides and transactinides, radionuclide mass spectrometry, and modern methods of speciation of radionuclides in the environment. These have been taken from teaching courses held at the Johannes Gutenberg University over the last 30 years.
It is my pleasure to thank Mrs. Petra Sach-Muth for help with the software “wiley-vch.dot” and Mr. Jürgen Hubrath for scanning and impoving a large number of new figures.
Jens-Volker Kratz
Mainz, April 2012
1
Fundamental Concepts
Nuclear and radiochemistry cover a wide spectrum of areas such as (i) studies of the chemical and physical properties of the heaviest human-made elements; (ii) studies of nuclear structure, nuclear reactions, and radioactive decay, (iii) studies of nuclear processes in the Universe, such as geochronology and cosmochemistry; and (iv) applications of radioactivity in a vast variety of fields such as radioanalysis, chemistry, life sciences, and industrial applications, and in the geo- and biosphere. Nuclear chemistry has ties to all traditional areas of chemistry. Nuclear chemists are involved in the preparation of radiopharmaceuticals for use in medicine. Radiometric techniques play an important role in analytical chemistry and are often used as references validating other analytical techniques. The study of the actinide and transactinide elements has traditionally involved nuclear chemists studying the limits of nuclear stability and the periodicity of the periodic table of the elements. The physical concepts at the heart of nuclear chemistry have their roots in nuclear physics. Thus nuclear physics and nuclear chemistry overlap and are cooperatively called nuclear science. However, there are distinctions between these related fields. Besides the close ties to chemistry mentioned above, nuclear chemists are studying nuclear problems in different ways than nuclear physicists. Nuclear physics tends to look into the fundamental interactions between subatomic particles and fundamental symmetries. Nuclear chemists have focused on more complex phenomena where statistical properties are important. Nuclear chemists are more involved in applications of nuclear phenomena. For example, the nuclear fuel cycle or the migration of radionuclides in the environment are so inherently chemical that they involve nuclear chemists almost exclusively. The other term, radiochemistry, refers to the chemical applications of radioactivity and of related phenomena. Radiochemists are nuclear chemists but not all nuclear chemists are radiochemists. There are many nuclear chemists who use purely instrumental, physical techniques for their research and thus their work is not radiochemistry.
The atom is the smallest unit a chemical element can be divided into without losing its chemical properties. The radii of atoms are on the order of 10−10 m (Å). The atomic nucleus, see Figure 1.1, is a very small object with a radius on the order of 1–10 · 10−15 m (femtometer, fm, called fermi) in the center of the atom and contains almost the entire mass of the atom. It contains Z protons, where Z is the atomic number of the element. Being the number of protons, Z is thus the number of positive charges in the nucleus. The nucleus also contains N neutrons, where N is the neutron number. Neutrons are uncharged particles with masses almost identical to the proton mass. Electrons surround the nucleus. Electrons are small negatively charged particles with a mass of 1/1836 of the proton mass. The electrons are bound electrostatically to the positively charged nucleus. In a neutral atom, the number of electrons equals the number of protons in the nucleus. The chemistry of the element is controlled by Z. From quantum mechanics, we know that only certain discrete energies and angular momenta of the electrons are allowed. These quantized states are schematically depicted in Figure 1.1. Later, in Chapter 5, we will see also that nucleons occupy orbits with discrete energies and angular momenta. However, the sizes and energies of atomic and nuclear processes are very different, allowing us to consider them separately.
Figure 1.1 Schematic representation of the relative sizes of the atom and the nucleus.
In the inelastic collision of two atoms, we can anticipate (i) excitation of one or both atoms involving a change in electron configuration; or (ii) ionization of one or both atoms, that is, removal of one or more electrons from the atom to form a positively charged ion. For this process to occur, an atomic electron must receive an energy exceeding its binding energy. This energy far exceeds the kinetic energies of gaseous atoms at room temperature. Thus, the atoms must have high kinetic energies as a result of nuclear decay or acceleration to eject electrons from other atoms in atomic collisions. When an electron in an outer atomic electron shell drops down to fill a vacancy in an inner electron shell, electromagnetic radiation called X-rays is emitted. In Figure 1.2, an L-shell electron is shown filling a K-shell vacancy. In the transition, a characteristic K X-ray is emitted. The energy of the X-rays is equal to the difference in the binding energies of the electrons in the two shells, which depends on the atomic number of the element. Specifically, X-rays due to transitions from the L shell to the K shell are called Kα X-rays, while X-rays due to transitions from the M to K shells are termed Kβ X-rays. Refining further, Kα1 and Kα2 designate transitions from different subshells of the L shell, that is, 2p3/2 (LIII) and 2p1/2 (LII). X-rays for transitions from M to L are Lα X-rays. For each transition, the change in orbital angular momentum Δℓ and total angular momentum Δj must be Δℓ = ±1 and Δj = 0, ±1.
Figure 1.2 Scheme showing X-ray emission when a vacancy in an inner electron shell caused by nuclear decay is filled. An L-shell electron is shown filling a K-shell vacancy associated with K X-ray emission.
For a hydrogen-like atom, the Bohr model predicts that the transition energy ΔE is
(1.1) 
where R∞ is the Rydberg constant, h the Planck constant, c the speed of light, and n the principal quantum number of the electron. The X-ray energy Ex = −ΔE, after inserting the physical constants, is
(1.2) 
For Kα X-rays from hydrogen-like atoms
(1.3) 
and for Lα transitions
(1.4) 
In a realistic atom, Z must be replaced by Zeffective to take care of the screening of the nuclear charge by other electrons. Henry Moseley showed that the frequencies, v, of the Kα X-rays scale as
(1.5) 
and those of the Lα X-rays scale as
(1.6) 
Thus, Moseley showed that the X-ray energies, hv, depend on the square of an altered, effective atomic number due to screening. The relative intensities of different X-rays depend on the chemical state of the atom, its oxidation state, complexation with ligands, and generally on local electron density. The relative intensities are, therefore, useful in chemical speciation studies. As will be discussed in Chapter 6, radioactive decays can be accompanied by X-ray production and the latter may be used to identify the decaying nucleus.
Before the discovery of radioactivity, elements were considered as unchangeable substances. In 1897, J.J. Thomson discovered the electron and concluded that the atom must have a structure. As the mass of the electron is roughly 1/2000 of the mass of hydrogen, he concluded that most of the mass of the atom must be contained in the positively charged constituents. It was assumed that negative and positive charges are evenly distributed over the atomic volume.
In 1911, Ernest Rutherford studied the scattering of α particles in thin metal foils. He found that backscattering to θ > 90° was more frequent than expected for multiple scattering from homogeneously charged atoms. This led Rutherford to postulate the existence of an atomic nucleus having mass and positive charges concentrated in a very small volume. The nucleus was supposed to be surrounded by electrons at the atomic diameter and the electrons do not contribute to the α-particle scattering. He postulated the following ansatz: the nuclear charge is Ze; that of the α particle is Zα = 2e. The scattering force is the Coulomb force. The nucleus is at rest in the collision and the path of an α particle in the field of the nucleus is a hyperbola with the nucleus at the external focus. From these simplifying geometric properties and from the conservation of momentum and energy, Rutherford derived his famous scattering formula which relates the number n(θ) of α particles scattered into a unit area S at a distance r from the target foil F, see Figure 1.3, to the scattering angle θ
(1.7) 
with no being the number of incident α particles, t the thickness of the target foil, N the number of target nuclei per unit volume, and Mα and υα the mass and initial velocity of the α particle.
Figure 1.3 Schematic representation of the Rutherford scattering experiment. A collimated beam of α particles (no number of ingoing α particles with velocity vα and rest mass Mα) hits a gold foil F (thickness t, N number of target nuclei per cubic centimeter) and is scattered to the polar angle θ under which a scintillator S at distance r from the target detects n(θ) scattered particles.
Precision measurements by Hans Geiger and Ernest Marsden soon verified that, for sufficiently heavy scatterers, the number of scattered particles detected per unit area was indeed inversely proportional to the square of the α-particle energy and to the fourth power of the sine of half the scattering angle. In principle for all, but notably only for light target nuclei, Eq. (1.7) must be modified because the target nucleus is not at rest. This can be accommodated by inserting the center of mass energy instead of the laboratory energy and by using the reduced mass instead of the rest mass. Figure 1.4 shows the apparatus used by Geiger and Marsden. It resembled an exsiccator that could be evacuated. The upper part contained the α-particle source (in German Emanationsröhrchen, R) in a lead brick. The collimated beam of α particles passed a gold foil F. The α particles that, after scattering in F, interacted with the scintillator S were observed through the microscope M. The microscope together with the scintillator could be moved to different scattering angles θ by turning the flange (Schliff, Sch). Figure 1.5 shows the results obtained by Geiger and Marsden. They agree in an impressive way over five orders of magnitude with the theoretical dependence (1/sin4(θ/2)) for pure Coulomb scattering. This way, it was possible to study systematically the magnitude of the nuclear charge in the atoms of given elements through scattering experiments since the scattered intensity depends on the square of the nuclear charge. It was by the method of α-particle scattering that nuclear charges were determined and this led to the suggestion that the atomic number Z of an element was identical to the nuclear charge. Further understanding of atomic structure developed rapidly through the study of X-rays and optical spectra, culminating in Niels Bohr's theory of 1913 and Erwin Schrödinger's and Werner Heisenberg's quantum-mechanical description of the atom in 1926.
Figure 1.4 Experimental setup by Geiger and Marsden for the observation of Rutherford scattering of α particles in a gold foil F. (Figure from the original work by Geiger and Marsden [1].) The radioactive source R is contained in a lead housing. The scattered α particles are interacting with the scintillator S that is observed by a microscope M. The microscope together with the scintillator could be turned to variable scattering angles θ by turning the flange.
Figure 1.5 Intensity of scattered α particles measured by Geiger and Marsden as a function of scattering angle θ. The solid line represents a 1/sin4(θ/2) function representing the theoretical dependence for pure Coulomb scattering.
Radioactive decay involves the spontaneous emission of radiation by an unstable nucleus. While this subject will be discussed in detail in Chapter 6, we present here a general introduction. In Table 1.1, we summarize the characteristics of the various decay types. Three basic decay modes were discovered by Rutherford starting in 1899: α decay, β decay, and γ radiation. He found that α particles are completely absorbed in thin metal foils, for example, 15 μm of Al. β particles were found to be largely absorbed only in Al a hundred times thicker. An absorption equation I = I0 e−μd was found where μ is a mass absorption coefficient (cm−1) depending on Z of the absorber and d was the thickness in cm. γ radiation was found to be almost not absorbed (in aluminum) and a mass absorption coefficient depending on Z5 was associated with it. Therefore, today, thick bricks of lead are commonly used in radiochemical laboratories for shielding purposes. Recognition of the character of the α and β rays as high-speed charged particles came largely from magnetic and electrostatic deflection experiments in which β particles were seen to be electrons. From the deflection of α particles, the ratio of charge to mass was found to be half that of the hydrogen ion. The suggestion that α particles were 4He2+ ions was immediately made. This was proven in 1903 by William Ramsay in an experiment in which α rays were allowed to pass through a very thin glass wall into an evacuated glass vessel. Within a few days, sufficient helium gas was accumulated in the glass vessel and was detected spectroscopically. γ radiation was found not to be deflected in the magnetic field and was recognized to be electromagnetic radiation. The difference to the atomic X-ray radiation, however, was not clear at that time.
Table 1.1 Characteristics of radioactive decay modes.
Nuclear β decay occurs in three ways: β−, β+, and electron capture (EC). In these decays, a nuclear neutron or proton changes into a nuclear proton or neutron, respectively, with the simultaneous emission of an antineutrino or an electron neutrino and an electron or positron. In EC, an orbital electron is captured by the nucleus changing a proton into a neutron with the emission of a monoenergetic neutrino. Due to the creation of a hole in the electron shell, the subsequent emission of X-rays or Auger electrons occurs. The mass number A remains constant in these decays while the atomic number Z is increased by 1 unit in β− decay and decreased by 1 unit in β+ decay and EC. In β− and β+ decay, the decay energy is shared between the emitted β particle, the (anti)neutrino, and the recoiling daughter nucleus.
Nuclear electromagnetic decay occurs in two ways: γ emission and internal conversion (IC). A nucleus in an excited state decays by the emission of a high-energy photon or the same excited nucleus transfers its decay energy radiationless to an orbital electron that is ejected from the atom. As in EC, the creation of a hole in the electron shell causes accompanying processes to occur, such as X-ray emission. There is no change in the number of the nucleons.
In 1940, K.A. Petrzhak and G.N. Flerov discovered spontaneous fission of 238U when they spread out a thin layer of uranium in a large area ionization chamber operated in a Moscow underground train station (to shield against cosmic radiation), observing large ionization bursts much larger than the pulse heights of the abundantly emitted α particles. A spontaneous fission half-life of 1016 years was estimated. It was concluded that the gain in binding energy delivers the decay energy when a nucleus with A nucleons splits into two fission fragments of roughly A/2.
In 1981, the emission of monoenergetic protons was discovered by S. Hofmann et al. at the GSI Helmholtz Center for Heavy Ion Research, Darmstadt. This proton radioactivity is now a widespread decay mode of very neutron-deficient nuclei. In 1984, H.J. Rose and G.A. Jones discovered cluster radioactivity in the decay of 223Ra, which emits, with a probability of 8.5 · 10−10 relative to the α particle emission, 14C clusters and decays into 209Pb. Heavier clusters are emitted from heavier nuclei with decreasing probabilities: for example, 238Pu decays by emission of 28Mg into 210Pb and by emission of 32Si into 206Hg with probabilities of 5.6 · 10−17 and 1.4 · 10−16 relative to the α-particle emission.
In 1989 Rutherford was the first scientist to observe the laws of radioactive decay and growth of a radioactive gas emanating from a thorium salt, radon. He used an electroscope, see Figure 1.6, for these radioactivity measurements. In the electroscope, the pointer G, a gold wire, deflected from the central metal bar when the upper part of the condenser was electrically charged relative to the housing. The condenser is discharged by ionizing radiation leading to a decrease in the deflection of the pointer G with a constant speed being a measure of the “saturation current,” the activity. Figure 1.7 shows schematically the two experiments that Rutherford conducted with 55 s 220Rn. In version a, the gas inlet and outlet valves in the lower part of the housing are closed. The 228Th source is placed inside the electroscope and is covered so that only the 220Rn emanating from the thorium salt can diffuse into the free volume and discharge the condenser, giving rise to a constant activity; see the activity vs. time diagram to the right. At a given time indicated by the arrow, the gas inlet and outlet valves are opened and the lower part of the electroscope is flushed with gas, thus removing the 220Rn from the electroscope and causing the activity to fall to zero. Upon closing the valves, new 220Rn grows from the 228Th such that the activity discharging the condenser increases until the old saturation activity is reached. This can be repeated over and over again, showing each time the same characteristic time dependence. In version b, the 228Th source is placed in a box outside the electroscope and the activity is zero. On opening the valves and flushing 220Rn into the electroscope with a carrier gas and closing the valves shortly thereafter, the 220Rn decays with a characteristic time dependence. This can also be repeated over and over again. In the lower right part of Figure 1.7, the logarithm of the activity is plotted vs. time giving a linear decrease with time
(1.8) 
where A(t) is the activity A vs. time t, A0 is the activity at time zero, and λ is the decay constant. In this way, the radioactive decay law
(1.9) 
was discovered. The unit of activity is 1 decay s−1 = 1 becquerel = 1 Bq. The decay constant, λ, is characteristic for each nuclide and is related to the nuclear half-life, t1/2, by
(1.10) 
Figure 1.6 Electroscope for the measurement of radioactivity. The gold wire G strives against the strut when the upper plate of the condenser is electrically charged relative to the housing. S is an insulator. For charging the condenser, a high voltage is applied to position A. Ionizing radiation is discharging the condenser, visible by a decrease in the deflection of the gold wire from the central metal bar with a constant velocity.
Figure 1.7 Rutherford observed the growth (a) and decay (b) of a radioactive gas (55 s 220Rn) emanating from a Th source (1.9 y 228Th).
The activity is equal to the number of nuclei present, N, multiplied by the decay constant λ, that is, A = λN. Therefore, the number of radioactive nuclei present will also decrease exponentially as
(1.11) 
Some important physical concepts need to be reviewed here because we will make use of them in later discussions.
All interactions in nature are the result of four fundamental forces, see Table 1.2. The weakest force is gravity. It is most significant when the interacting objects are massive, such as stars. The next stronger force is the weak interaction which acts in nuclear β decay. The electromagnetic force is next in strength while the strong interaction is more than a hundred times stronger than the electromagnetic force. The ranges associated with the four forces are given in Table 1.2 along with their strengths relative to the strong force and with the respective force carriers or exchange particles. Among these, gravitons have not yet been observed but are believed to be responsible for gravity, which is not a part of the Standard Model of particle physics, see Section 1.5.6. In Chapter 6, we will see that Glashow, Salam, and Weinberg introduced a unified theoretical treatment of electromagnetic and weak interactions, the electroweak interaction, in which the photon and the massive vector bosons W± and Z0 emerge from one theory. We note in passing that the free neutron undergoes interactions with all four forces at the same time, see Chapter 8.
Table 1.2 Fundamental forces in nature.
A force is a vector that describes the rate of change of a momentum with time
(1.12) 
For the motion of a particle, the orbital angular momentum of the particle, l, with mass m, relative to the center of mass, is
(1.13) 
l is a vector of magnitude mυr for circular motion. For motion past a stationary point, the magnitude is mυb where b is the impact parameter. The relationship between a force F and the potential energy V is generally
(1.14) 
Thus, for example, the Coulomb force, FC, for two charges Z1e and Z2e separated by the distance, r, is
(1.15) 
where, for convenience, we set e2 = 1.439 98 MeV fm.
When a particle moves with a velocity approaching the speed of light, according to the special theory of relativity by A. Einstein, the mass of the particle changes with speed according to
(1.16) 
where m′ and m0 are the masses of the particle in motion and at rest and γ is the Lorentz factor
(1.17) 
and
where β is υ / c, the velocity of the particle relative to the speed of light. The total energy of a relativistic particle is
(1.18) 
this being the kinetic energy, T, plus the rest mass energy equivalent m0c2, where
(1.19) 
For a particle at rest, the total energy is
(1.20) 
For a massless particle such as the photon,
(1.21) 
where p is the momentum of the photon. The momentum of a relativistic particle is
(1.22) 
These equations demonstrate why the units MeV/c2 for mass and MeV/c for momentum are necessary in nuclear calculations.
To give an example, we calculate the velocity, momentum, and total energy of an 40Ar ion with a kinetic energy of 1 GeV/nucleon. The total kinetic energy is 40 × 1 GeV/nucleon = 40 GeV = 40 000 MeV. The rest mass m0c2 is approximately 40 atomic mass units (40 u) or (40)(931.5) MeV, see Eq. (3.1), or 37 260 MeV. Thus, γ = T/m0c2 + 1 = 1 + 40 000/37 260 = 2.07. With Eq. (1.17), we obtain β = 0.88. So the velocity is 0.88c or (0.88)(3 · 108 m s−1) = 2.6 · 108 m s−1. We modify Eq. (1.22) to pc = mc / (1 − β)1/2 and obtain (40)(931.5)(0.88)(2.07) = 67.7 GeV, that is, p = 67.7 GeV/c. The total energy, Eq. (1.18), is (2.07)(40)(931.5) = 77.3 GeV.
The space–time coordinates x,y,z,t in a stationary laboratory system are, in the special theory of relativity, related to the space–time coordinates in a system moving along the x axis, x′,y′,z′,t′, by
(1.23) 
This transformation from the stationary to the moving frame is the Lorentz transformation. The inverse Lorentz transformation is obtained by reversing the sign of υ giving
(1.24) 
For γ > 1, time is slowed down for the scientist in the laboratory, and the distance in the x direction is contracted. An example for the relevance of these equations in nuclear chemistry is the decay of rapidly moving particles such as muons in cosmic rays. At rest, the muon has a lifetime of 2.2 μs. At relativistic energies such as in cosmic rays, the lifetime is orders of magnitude longer. Due to this time dilatation, muons can reach the surface of the Earth.
A rule of thumb for the decision of whether the classical expressions or the relativistic expressions are to be used is γ ≥ 1.1.
The well-known wave–particle duality says that there is no distinction between wave and particle descriptions of atomic matter; that is, associated with each particle, there is an equivalent description in which the particle is assigned a wavelength, the de Broglie wavelength,
(1.25) 
or in rationalized units
(1.26) 
with ħ = h / 2π. The relativistic equivalent is
(1.27) 
Figure 1.8 shows de Broglie wavelengths for a sample of particles (electron, pion, proton, and neutron, deuteron, α particle) as a function of kinetic energy. They are largest for the lightest particles at lowest energies. The horizontal bar indicates the order of magnitude where 
becomes larger than the maximum impact parameter R for light-particle-induced reactions and from where the wavelength of the projectile influences the nuclear reaction cross-section, see Chapter 12.
Figure 1.8 De Broglie wavelengths vs. particle kinetic energy for a few particles.
One can also associate a wavelength to photons
(1.28) 
where ν is the frequency associated with the wavelength λ. A practical form of Eq. (1.28) is
(1.29) 
Treating photons as particles is useful if they are emitted or absorbed by a nucleus. Here, we have
(1.30) 
The Heisenberg uncertainty principle states that there are limits in our knowledge of the location of a particle and its momentum, that is,
(1.31) 
where Δpi Δi are the uncertainties in the ith component of the momentum and the location on the ith coordinate, while ΔE is the uncertainty in the total energy of the particle and Δt is its lifetime. These limits are not due to the limited resolution of our instruments; they are fundamental even with perfect instrumentation.
We will encounter a typical application in β decay, in Chapter 6, when it comes to counting the number of ways that the decay energy can be divided between the electron and the neutrino. There, with Eq. (1.31), we will see that the location and momentum of the electron and neutrino are somewhere within the volume of a spherical shell in phase space where the volume of the unit cell is h3. The number of states of the electron with momentum between pe and pe + dpe is the volume of a spherical shell in momentum space 
In addition, it must be found in space in a volume V. Together, this gives the phase volume 
. The number of possibilities for the electron to find itself within this phase volume is obtained by normalizing the latter to the volume of the unit cell h3, such that
(1.32) 
Similarly for the neutrino, the number of states of the free neutrino with momentum between pv and pv + dpv in a volume V is
(1.33) 
and the total number of states dn = dNe dNv is
(1.34) 
Equation (1.34) will be used in Chapter 6 to deduce the density of final states dn/dE0 where n is the number of states per unit energy interval, the so-called statistical or phase space factor, which determines the shape of the electron momentum distribution.
Figure 1.9 depicts matter as consisting of six types, or “flavors,” of quarks – called up, down, charm, strange, bottom, and top – and six light particles, the leptons, electron, muon, and tau and their three neutrino partners. The 12 particles are divided into three families of increasing mass, each family containing two quarks and two leptons. Their properties are listed in Table 1.3. Each particle also has an antiparticle of opposite electric charge. Our familiar protons and neutrons comprise three quarks: two ups and a down, and two downs and an up, respectively. The Standard Model also includes three of the four fundamental forces: the electromagnetic force and the weak and strong interactions. These are carried by exchange particles called intermediate vector bosons, that is, the photon, the W and Z bosons, and the exchange boson of the strong force, the gluon.
Figure 1.9 Fermions (quarks and leptons) and intermediate vector bosons in the Standard Model. The bosons are the force carriers of the four fundamental interactions.
Table 1.3 Quarks and leptons and their properties. For each of these particles, there exists an antiparticle.a)
Particles can be classified as fermions and bosons. Fermions have antisymmetric wave functions and half-integer spins and obey the Pauli principle. Examples for fermions are neutrons, protons, and electrons. Bosons have symmetric wave functions and integer spins. They need not obey the Pauli principle. Examples are photons and the other gage bosons. Particle groups like fermions can be further divided into leptons and hadrons such as the proton and the neutron, the nucleons. Hadrons interact via the strong interaction while leptons do not. Both particle types can interact via other forces such as the electromagnetic force. The neutrino partners of the leptons are electrically neutral and have very small rest masses close to zero. Their masses are a vital subject of current research, see Chapter 18. In nuclear processes involving leptons, their number must be conserved. For example, in the decay of the free neutron
the number of leptons on the left is zero, so the number of leptons on the right must be zero as well. We see that this is true if we assign a lepton number L = 1 to the electron and L = −1 to the 
being an antiparticle. For the reaction
which was instrumental in the discovery of the antineutrino by F. Reines and C. Cowan in 1959, L = −1 on both sides, and lepton conservation is fulfilled as well. As for leptons, there is a conservation law for baryons. To each baryon, we assign a baryon number B = +1 and B = −1 to each antibaryon. The total baryon number must be conserved. Take for example the reaction
On both sides, we have B = 2 because the π+ is a meson with B = 0. Since three quarks/antiquarks binding together make baryons/antibaryons, binding a quark with an antiquark forms mesons. The π+ and π− (
, 
) mesons are important particles in nuclear chemistry. Mesons have integer spins and are bosons. Some mesons and baryons are listed in Table 1.4. All mesons are unstable with lifetimes up to about 10−8 s. The baryons are also unstable, with the exception of the neutron (lifetime 885.7 s) and the proton, which is considered to be stable.
Table 1.4 Examples for hadrons.
A set of symmetries that are a sensitive probe of the Standard Model describe what happens if certain particle properties are reflected as though in a mirror. There is a charge mirror (C) changing particles into antiparticles of opposite charge, a parity mirror (P) changing the spin or handedness of a particle, and a time mirror (T) reversing a particle interaction, like rewinding a video. Surprisingly, these mirrors do not work perfectly. β particles emitted in the decay of 60Co always spin in the same direction even if the spin of the cobalt nucleus is reversed. Cracks in the C and P mirrors (CP violation) also appear in the decay of exotic mesons – the kaon and the B meson. Connected to CP and T violation is the existence of a permanent electric dipole moments (EDMs) in particles such as the neutron and atoms. EDMs are forbidden by P, T, and CP symmetries, but might be essential to explain the predominance of matter over antimatter in the Universe. Laboratories worldwide are actively searching for these EDMs. This is typical of high-precision measurements using nuclear particles at lowest energies to search for physics beyond the Standard Model. This way, nuclear chemists are actively involved in furthering our knowledge of fundamental interactions and symmetries.
In Section 1.5.1, we introduced the force carriers, which are all bosons. In Section 1.5.5, we dealt with the Heisenberg uncertainty principle. Together these will allow us now to understand how force carriers work. For illustration, let us consider the electromagnetic force between two positively charged particles. The latter is caused by photons passing between them. One tends to think that the emission of a photon should change the energy of the emitter, but exchange of a force carrier does not. The solution is that the uncertainty principle allows the emission of virtual particles if such emission and absorption occur within a time Δt that is less than that allowed by the uncertainty principle, Eq. (1.31) saying that Δt = ћ/ΔE where ΔE is the extent to which energy conservation is violated. We will come back to this in Chapter 6.
Reference
General and Historical
1 Geiger, H. and Marsden, E. (1913) The laws of deflexion of α particles through large angles. Philos. Mag., 25, 604.
Further Reading
General and Historical
Rutherford, E. and Soddy, F. (1902) The cause and nature of radioactivity I, II. Philos. Mag., 4, 370, 569.
Rutherford, E. and Soddy, F. (1903) Radioactive change. Philos. Mag., 5, 576.
Geiger, H. and Marsden, E. (1909) Diffuse reflection of the α particle. Proc. R. Soc., 82, 495.
Rutherford, E. (1911) The scattering of α and β particles by matter and the structure of the atom. Philos. Mag., 21, 669.
Moseley, H.G. (1913) The high-frequency spectra of the elements I. Philos. Mag., 26, 1024.
Moseley, H.G. (1914) The high-frequency spectra of the elements II. Philos. Mag., 27, 703.
Evans, R. (1955) The Atomic Nucleus, McGraw-Hill, New York.
Romer, A. (1964) The Discovery of Radioactivity and Transmutation, Dover, New York.
Harvey, B.G. (1965) Nuclear Chemistry, Prentice Hall, Englewood Cliffs, NJ.
Harvey, B.G. (1969) Introduction to Nuclear Physics and Chemistry, 2nd edn, Prentice Hall, Englewood Cliffs, NJ.
Romer, A. (1970) Radiochemistry and the Discovery of Isotopes, Dover, New York.
Harvey, B.G. and Evans, R. (1971) The Atomic Nucleus, McGraw-Hill, New York.
Friedlander, G., Kennedy, J., Macias, E.S., and Miller, J.M. (1981) Nuclear and Radiochemistry, 3rd edn, John Wiley & Sons, Inc., New York.
Seaborg, G.T. and Loveland, W. (1982) Nuclear Chemistry, Hutchinson-Ross, Stroudsberg, PA.
Ehmann, W.D. and Vance, D.E. (1991) Radiochemistry and Nuclear Methods of Analysis, John Wiley & Sons, Inc., New York.
Loveland, W. (1992) Nuclear chemistry, in Encyclopedia of Physical Science and Technology, vol. 11, Academic Press, Orlando, FL.
Adloff, J.P., Lieser, K.H., and Stöcklin, G. (eds.) (1995) One hundred years after the discovery of radioactivity. Radiochim. Acta, 70/71 (special issue).
Choppin, G.R., Liljenzin, J.O., and Rydberg, J. (2001) Radiochemistry and Nuclear Chemistry, 3rd edn, Butterworth–Heinemann, Oxford.
Fényes, T. (2011) Basic properties of the atomic nucleus, in Handbook of Nuclear Chemistry, vol. 1, 2nd edn (eds. A. Vértes, S. Nagy, Z. Klencsár, R.G. Lovas, and F. Rösch), Springer, Berlin, p. 39.
More Specialized
Weinberg, S. (1967) A model of leptons. Phys. Rev. Lett., 19, 1264.
Salam, A. (1968) in Elementary Particle Theory (ed. N. Svartholm), Almquist and Wiksell, Stockholm, p. 367.
Marmier, P. and Sheldon, E. (1969) Physics of Nuclei and Particles, vols. I and II, Academic Press, New York.
Glashow, S.L., Iliopoulos, J., and Maiani, L. (1970) Weak interactions with lepton-hadron symmetry. Phys. Rev., D2, 1285.
Weinberg, S. (1972) Mixing angle in renormalizable theories of weak and electromagnetic interactions. Phys. Rev., D5, 1962.
Segre, E. (1977) Nuclei and Particles, 2nd edn, Benjamin, Reading, MA.
Musiol, G., Ranft, J., Reif, R., and Seeliger, D. (1988) Kern- und Elementarteilchenphysik, VCH Verlagsgesellschaft, Weinheim.
Frauenfelder, H. and Henley, E.M. (1991) Subatomic Physics, 2nd edn, Prentice Hall, Englewood Cliffs, NJ.
Donoghue, J.F. (1994) Dynamics of the Standard Model, Cambridge University Press, Cambridge.
Weinberg, S. (1995, 2005) The Quantum Theory of Fields, Cambridge University Press, Cambridge.
Heyde, K. (1999) Basic Ideas and Concepts in Nuclear Physics, IOP Publishing, Bristol.
Amsler, C. et al. (Particle Data Group) (2008) The review of particle physics. Phys. Lett., B667, 1.
Horváth, D. (2011) The standard model of elementary particles, in Handbook of Nuclear Chemistry, vol. 1, 2nd edn (eds. A. Vértes, S. Nagy, Z. Klencsár, R.G. Lovas, and F. Rösch), Springer, Berlin, p. 457.
2
Radioactivity in Nature