Platinum 194 superscripts and subscripts

Modern Nuclear Chemistry

Modern Nuclear Chemistry

Second Edition

Walter D. Loveland Oregon State University

David J. Morrissey Michigan State University

Glenn T. Seaborg University of California, Berkeley

Copyright © 2017 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data

Names: Loveland, Walter D. | Morrissey, David J. | Seaborg, Glenn T. (Glenn Theodore), 1912–1999.

Title: Modern nuclear chemistry / Walter D. Loveland, David J. Morrissey, Glenn T. Seaborg. Description: Second edition. | Hoboken, NJ : John Wiley & Sons, Inc., 2017. |

Includes bibliographical references and index. Identifiers: LCCN 2016045901| ISBN 9780470906736 (cloth) | ISBN 9781119328483 (epub) Subjects: LCSH: Nuclear chemistry–Textbooks. | Chemistry, Physical and

theoretical–Textbooks. Classification: LCC QD601.3 .L68 2017 | DDC 541/.38–dc23 LC record available at https://lccn.loc.gov/2016045901

Cover Image: Courtesy of the author Cover Design: Wiley

Set in 10/12pt Warnock by SPi Global, Pondicherry, India

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

v

Contents

Preface to the Second Edition xv Preface to the First Edition xvii

1 Introductory Concepts 1 1.1 Introduction 1 1.2 The Excitement and Relevance of Nuclear Chemistry 2 1.3 The Atom 3 1.4 Atomic Processes 4 1.4.1 Ionization 5 1.4.2 X-Ray Emission 5 1.5 The Nucleus: Nomenclature 7 1.6 Properties of the Nucleus 8 1.7 Survey of Nuclear Decay Types 9 1.8 Modern Physical Concepts Needed in Nuclear Chemistry 12 1.8.1 Elementary Mechanics 13 1.8.2 Relativistic Mechanics 14 1.8.3 de Broglie Wavelength: Wave–Particle Duality 16 1.8.4 Heisenberg Uncertainty Principle 18 1.8.5 Units and Conversion Factors 19

Problems 19 Bibliography 21

2 Nuclear Properties 25 2.1 Nuclear Masses 25 2.2 Terminology 28 2.3 Binding Energy Per Nucleon 29 2.4 Separation Energy Systematics 31 2.5 Abundance Systematics 32 2.6 Semiempirical Mass Equation 33 2.7 Nuclear Sizes and Shapes 39 2.8 Quantum Mechanical Properties 43

vi Contents

2.8.1 Nuclear Angular Momentum 43 2.9 Electric and Magnetic Moments 45 2.9.1 Magnetic Dipole Moment 45 2.9.2 Electric Quadrupole Moment 48

Problems 51 Bibliography 55

3 Radioactive Decay Kinetics 57 3.1 Basic Decay Equations 57 3.2 Mixture of Two Independently Decaying Radionuclides 65 3.3 Radioactive Decay Equilibrium 66 3.4 Branching Decay 76 3.5 Radiation Dosage 77 3.6 Natural Radioactivity 79 3.6.1 General Information 79 3.6.2 Primordial Nuclei and the Uranium Decay Series 79 3.6.3 Cosmogenic Nuclei 81 3.6.4 Anthropogenic Nuclei 83 3.6.5 Health Effects of Natural Radiation 83 3.7 Radionuclide Dating 84

Problems 90 Bibliography 92

4 Nuclear Medicine 93 4.1 Introduction 93 4.2 Radiopharmaceuticals 94 4.3 Imaging 96 4.4 99Tcm 98 4.5 PET 101 4.6 Other Imaging Techniques 103 4.7 Some Random Observations about the Physics of Imaging 104 4.8 Therapy 108

Problems 110 Bibliography 112

5 Particle Physics and the Nuclear Force 113 5.1 Particle Physics 113 5.2 The Nuclear Force 117 5.3 Characteristics of the Strong Force 119 5.4 Charge Independence of Nuclear Forces 120

Problems 124 Bibliography 124

Contents vii

6 Nuclear Structure 125 6.1 Introduction 125 6.2 Nuclear Potentials 127 6.3 Schematic Shell Model 129 6.4 Independent Particle Model 141 6.5 Collective Model 143 6.6 Nilsson Model 149 6.7 Fermi Gas Model 152

Problems 161 Bibliography 164

7 𝛂-Decay 167 7.1 Introduction 167 7.2 Energetics of α Decay 169 7.3 Theory of α Decay 173 7.4 Hindrance Factors 182 7.5 Heavy Particle Radioactivity 183 7.6 Proton Radioactivity 185

Problems 186 Bibliography 188

8 𝛃-Decay 191 8.1 Introduction 191 8.2 Neutrino Hypothesis 192 8.3 Derivation of the Spectral Shape 196 8.4 Kurie Plots 199 8.5 β Decay Rate Constant 200 8.6 Electron Capture Decay 206 8.7 Parity Nonconservation 207 8.8 Neutrinos Again 208 8.9 β-Delayed Radioactivities 209 8.10 Double β Decay 211

Problems 213 Bibliography 214

9 𝛄-Ray Decay 217 9.1 Introduction 217 9.2 Energetics of γ-Ray Decay 218 9.3 Classification of Decay Types 220 9.4 Electromagnetic Transition Rates 223 9.5 Internal Conversion 229 9.6 Angular Correlations 232 9.7 Mössbauer Effect 238

viii Contents

Problems 244 Bibliography 245

10 Nuclear Reactions 247 10.1 Introduction 247 10.2 Energetics of Nuclear Reactions 248 10.3 Reaction Types and Mechanisms 252 10.4 Nuclear Reaction Cross Sections 253 10.5 Reaction Observables 264 10.6 Rutherford Scattering 264 10.7 Elastic (Diffractive) Scattering 268 10.8 Aside on the Optical Model 270 10.9 Direct Reactions 271 10.10 Compound Nuclear Reactions 273 10.11 Photonuclear Reactions 279 10.12 Heavy-Ion Reactions 281 10.12.1 Coulomb Excitation 284 10.12.2 Elastic Scattering 284 10.12.3 Fusion Reactions 284 10.12.4 Incomplete Fusion 288 10.12.5 Deep-Inelastic Scattering 289 10.13 High-Energy Nuclear Reactions 291 10.13.1 Spallation/Fragmentation Reactions 291 10.13.2 Reactions Induced by Radioactive Projectiles 295 10.13.3 Multifragmentation 296 10.13.4 Quark–Gluon Plasma 298

Problems 298 Bibliography 302

11 Fission 305 11.1 Introduction 305 11.2 Probability of Fission 308 11.2.1 Liquid Drop Model 308 11.2.2 Shell Corrections 310 11.2.3 Spontaneous Fission 312 11.2.4 Spontaneously Fissioning Isomers 315 11.2.5 The Transition Nucleus 316 11.3 Dynamical Properties of Fission Fragments 323 11.4 Fission Product Distributions 327 11.4.1 Total Kinetic Energy (TKE) Release 327 11.4.2 Fission Product Mass Distribution 327 11.4.3 Fission Product Charge Distributions 330 11.5 Excitation Energy of Fission Fragments 334

Contents ix

Problems 337 Bibliography 338

12 Nuclear Astrophysics 339 12.1 Introduction 339 12.2 Elemental and Isotopic Abundances 340 12.3 Primordial Nucleosynthesis 343 12.3.1 Stellar Evolution 347 12.4 Thermonuclear Reaction Rates 351 12.5 Stellar Nucleosynthesis 353 12.5.1 Introduction 353 12.5.2 Hydrogen Burning 353 12.5.3 Helium Burning 357 12.5.4 Synthesis of Nuclei with A < 60 359 12.5.5 Synthesis of Nuclei with A > 60 360 12.6 Solar Neutrino Problem 366 12.6.1 Introduction 366 12.6.2 Expected Solar Neutrino Sources, Energies, and Fluxes 367 12.6.3 Detection of Solar Neutrinos 369 12.6.4 The Solar Neutrino Problem 371 12.6.5 Solution to the Problem: Neutrino Oscillations 371 12.7 Synthesis of Li, Be, and B 373

Problems 375 Bibliography 376

13 Reactors and Accelerators 379 13.1 Introduction 379 13.2 Nuclear Reactors 380 13.2.1 Neutron-Induced Reaction 380 13.2.2 Neutron-Induced Fission 383 13.2.3 Neutron Inventory 384 13.2.4 Light Water Reactors 386 13.2.5 The Oklo Phenomenon 391 13.3 Neutron Sources 392 13.4 Neutron Generators 392 13.5 Accelerators 393 13.5.1 Ion Sources 394 13.5.2 Electrostatic Machines 396 13.5.3 Linear Accelerators 400 13.5.4 Cyclotrons, Synchrotrons, and Rings 403 13.6 Charged-Particle Beam Transport and Analysis 410 13.7 Radioactive Ion Beams 415 13.8 Nuclear Weapons 421

x Contents

Problems 425 Bibliography 427

14 The Transuranium Elements 429 14.1 Introduction 429 14.2 Limits of Stability 429 14.3 Element Synthesis 434 14.4 History of Transuranium Element Discovery 437 14.5 Superheavy Elements 449 14.6 Chemistry of the Transuranium Elements 453 14.7 Environmental Chemistry of the Transuranium Elements 461

Problems 468 Bibliography 469

15 Nuclear Reactor Chemistry 473 15.1 Introduction 473 15.2 Fission Product Chemistry 475 15.3 Radiochemistry of Uranium 478 15.3.1 Uranium Isotopes 478 15.3.2 Metallic Uranium 478 15.3.3 Uranium Compounds 478 15.3.4 Uranium Solution Chemistry 479 15.4 The Nuclear Fuel Cycle: The Front End 480 15.4.1 Mining and Milling 481 15.4.2 Refining and Chemical Conversion 483 15.4.3 Isotopic Enhancement 484 15.4.4 Fuel Fabrication 487 15.5 The Nuclear Fuel Cycle: The Back End 488 15.5.1 Properties of Spent Fuel 488 15.5.2 Fuel Reprocessing 490 15.6 Radioactive Waste Disposal 493 15.6.1 Classifications of Radioactive Waste 493 15.6.2 Waste Amounts and Associated Hazards 494 15.6.3 Storage and Disposal of Nuclear Waste 496 15.6.4 Spent Nuclear Fuel 497 15.6.5 HLW 498 15.6.6 Transuranic Waste 499 15.6.7 Low-Level Waste 499 15.6.8 Mill Tailings 500 15.6.9 Partitioning of Waste 500 15.6.10 Transmutation of Waste 501 15.7 Chemistry of Operating Reactors 504 15.7.1 Radiation Chemistry of Coolants 504

Contents xi

15.7.2 Corrosion 505 15.7.3 Coolant Activities 505

Problems 506 Bibliography 507

16 Interaction of Radiation with Matter 509 16.1 Introduction 509 16.2 Heavy Charged Particles 512 16.2.1 Stopping Power 512 16.2.2 Range 521 16.3 Electrons 526 16.4 Electromagnetic Radiation 532 16.4.1 Photoelectric Effect 534 16.4.2 Compton Scattering 536 16.4.3 Pair Production 537 16.5 Neutrons 540 16.6 Radiation Exposure and Dosimetry 544

Problems 548 Bibliography 550

17 Radiation Detectors 553 17.1 Introduction 553 17.1.1 Gas Ionization 554 17.1.2 Ionization in a Solid (Semiconductor Detectors) 554 17.1.3 Solid Scintillators 555 17.1.4 Liquid Scintillators 555 17.1.5 Nuclear Emulsions 555 17.2 Detectors Based on Collecting Ionization 556 17.2.1 Gas Ionization Detectors 557 17.2.2 Semiconductor Detectors (Solid State Ionization Chambers) 567 17.3 Scintillation Detectors 578 17.4 Nuclear Track Detectors 584 17.5 Neutron Detectors 585 17.6 Nuclear Electronics and Data Collection 587 17.7 Nuclear Statistics 589 17.7.1 Distributions of Data and Uncertainty 591 17.7.2 Rejection of Abnormal Data 597 17.7.3 Setting Upper Limits When No Counts Are Observed 598

Problems 599 Bibliography 600

18 Nuclear Analytical Methods 603 18.1 Introduction 603 18.2 Activation Analysis 603

xii Contents

18.2.1 Basic Description of the Method 603 18.2.2 Advantages and Disadvantages of Activation Analysis 605 18.2.3 Practical Considerations in Activation Analysis 607 18.2.4 Applications of Activation Analysis 611 18.3 PIXE 612 18.4 Rutherford Backscattering 615 18.5 Accelerator Mass Spectrometry (AMS) 619 18.6 Other Mass Spectrometric Techniques 620

Problems 621 Bibliography 623

19 Radiochemical Techniques 625 19.1 Introduction 625 19.2 Unique Aspects of Radiochemistry 626 19.3 Availability of Radioactive Material 630 19.4 Targetry 632 19.5 Measuring Beam Intensity and Fluxes 637 19.6 Recoils, Evaporation Residues, and Heavy Residues 639 19.7 Radiochemical Separation Techniques 644 19.7.1 Precipitation 644 19.7.2 Solvent Extraction 645 19.7.3 Ion Exchange 648 19.7.4 Extraction Chromatography 650 19.7.5 Rapid Radiochemical Separations 652 19.8 Low-Level Measurement Techniques 653 19.8.1 Blanks 654 19.8.2 Low-Level Counting: General Principles 654 19.8.3 Low-Level Counting: Details 655 19.8.4 Limits of Detection 658

Problems 659 Bibliography 660

20 Nuclear Forensics 663 20.1 Introduction 663 20.1.1 Basic Principles of Forensic Analysis 666 20.2 Chronometry 670 20.3 Nuclear Weapons and Their Debris 672 20.3.1 RDD or Dirty Bombs 672 20.3.2 Nuclear Explosions 674 20.4 Deducing Sources and Routes of Transmission 678

Problems 680 Bibliography 681

Contents xiii

Appendix A: Fundamental Constants and Conversion Factors 683

Appendix B: Nuclear Wallet Cards 687

Appendix C: Periodic Table of the Elements 711

Appendix D: Alphabetical List of the Elements 713

Appendix E: Elements of Quantum Mechanics 715

Index 737

xv

Preface to the Second Edition

In this second edition of Modern Nuclear Chemistry, we have added new chapters on nuclear medicine, particle physics, and nuclear forensics. We have edited and updated all the chapters in the first edition reflecting the substantial progress that has been made in the past 12 years. We have dropped the chapter on radiotracer methods. We have tried to remove all the typographical errors in the first edition, without, we hope, introducing new errors. We continue to be grateful to the many colleagues and students who have taught us about a wide range of nuclear chemistry. In addition to our colleagues acknowledged in the first edition of this book, we gratefully acknowledge the helpful comments of J. Cerny and L.G. Sobotka on various portions of the book.

Walter D. Loveland Corvallis, OR March, 2016

David J. Morrissey East Lansing, MI

March, 2016

xvii

Preface to the First Edition

There are many fine textbooks of nuclear physics and chemistry in print at this time. So the question can be raised as to why we would write another textbook, especially one focusing on the smaller discipline of nuclear chemistry. When we began this project over five years ago, we felt that we were a unique juncture in nuclear chemistry and technology and that, immodestly, we had a unique perspective to offer to students.

Much of the mainstream of nuclear chemistry is now deeply tied to nuclear physics, in a cooperative endeavor called “nuclear science.” At the same time, there is a large, growing, and vital community of people who use the applica- tions of nuclear chemistry to tackle wide-ranging set of problems in the phys- ical, biological, and environmental sciences, medicine, engineering, and so on. We thought it was important to bring together, in a single volume, a rigorous, detailed perspective on both the “pure” and “applied” aspects of nuclear chem- istry. As such, one might find more detail about any particular subject than one might like. We hope this encourages instructors to summarize the textbook material and present it in a manner most suitable to a particular audience. The amount of material contained in this book is too much for a one quarter or one semester course and a bit too little for a yearlong course. Instructors can pick and choose which material seems most suitable for their course.

We have attempted to present nuclear chemistry and the associated applica- tions at a level suitable for an advanced undergraduate or beginning graduate student. We have assumed that a student has prior or concurrent instruction in physical chemistry or modern physics and has some skills in handling differen- tial equations. We have attempted to sprinkle solved problems throughout the text, as we believe that one learns by working problems. The end-of-the-chapter homework problems are largely examination questions used at Oregon State University. They should be considered to be integral part of the textbook as they are intended to illustrate or amplify the main points of each chapter. We have taken some pains to use quantum mechanics in a schematic way, that is, to use the conclusions of such considerations without using or demanding a rigorous, complete approach. The use of hand-waving quantum mechanics, we

xviii Preface to the First Edition

believe, is appropriate for our general audience. We summarize, in the appen- dices, some salient features of quantum mechanics that may be useful for those students with limited backgrounds.

Our aim is to convey the essence of the ideas and the blend of theory and experiment that characterizes nuclear and radiochemistry. We have included some more advanced material for those who would like a deeper immersion in the subject. Our hope is that the reader can use this book for an introductory treatment of the subject of interest and can use the end-of-chapter bibliogra- phy as a guide to more advanced and detailed presentations. We also hope the practicing scientist might see this volume as a quick refresher course for the rudiments of relatively unfamiliar aspects of nuclear and radiochemistry and as an information booth for directions for more detailed inquiries.

It is with the deep sense of loss and sadness that the junior authors (WDL, DJM) note the passing of our dear friend, colleague, and coauthor, Prof. Glenn T. Seaborg, before the completion of this work. Glenn participated in planning and development of the textbook, wrote some of the text, and reviewed much of the rest. We deeply miss his guidance and his perspective as we have brought this project to conclusion. We regret not paying closer attention to his urging that we work harder and faster as he would remark to us, “You know I’m not going to live forever.” We hope that the thoughts and ideas that he taught us are reflected in these pages.

We gratefully acknowledge the many colleagues and students who have taught us about nuclear chemistry and other things. Special thanks are due to Darrah Thomas and the late Tom Sugihara for pointing out better ways to discuss some material. We acknowledge the efforts of Einar Hageb who used an early version of this book in his classes and gave us important feedback. We gratefully acknowledge the helpful comments of D. Peterson, P. Mantica, A. Paulenova, and R.A. Schmitt on various portions of the book. One of us (WDL) wishes to acknowledge the hospitality of the National Superconducting Cyclotron Laboratory at Michigan State University for their hospitality in the fall of 1999 during which time a portion of this book was written.

Walter D. Loveland Corvallis, OR October, 2004

David J. Morrissey East Lansing, MI

October, 2004

1

1

Introductory Concepts

1.1 Introduction

Nuclear chemistry consists of a four-pronged endeavor made up of (a) studies of the chemical and physical properties of the heaviest elements where detec- tion of radioactive decay is an essential part of the work, (b) studies of nuclear properties such as structure, reactions, and radioactive decay by people trained as chemists, (c) studies of macroscopic phenomena (such as geochronology or astrophysics) where nuclear processes are intimately involved, and (d) application of measurement techniques based on nuclear phenomena (such as activation analysis or radiotracers) to study scientific problems in a variety of fields. The principal activity or “mainstream” of nuclear chemistry involves those activities listed under (b).

As a branch of chemistry, the activities of nuclear chemists frequently span several traditional areas of chemistry such as organic, analytical, inorganic, and physical chemistry. Nuclear chemistry has ties to all branches of chemistry. For example, nuclear chemists are frequently involved with the synthesis and preparation of radiolabeled molecules for use in research or medicine. Nuclear analytical techniques are an important part of the arsenal of the modern analyt- ical chemist. The study of the actinide and transactinide elements has involved the joint efforts of nuclear and inorganic chemists in extending knowledge of the periodic table. Certainly the physical concepts and reasoning at the heart of modern nuclear chemistry are familiar to physical chemists. In this book we will touch on many of these interdisciplinary topics and attempt to bring in familiar chemical concepts.

A frequently asked question is “what are the differences between nuclear physics and nuclear chemistry?” Clearly, the two endeavors overlap to a large extent, and in recognition of this overlap, they are collectively referred to by the catchall phrase “nuclear science.” But we believe that there are fundamental, important distinctions between these two fields. Besides the continuing close ties to traditional chemistry cited previously, nuclear chemists tend to study nuclear problems in different ways than nuclear physicists. Much of nuclear

Modern Nuclear Chemistry, Second Edition. Walter D. Loveland, David J. Morrissey, and Glenn T. Seaborg. © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc.

2 Introductory Concepts

physics is focused on detailed studies of the fundamental interactions oper- ating between subatomic particles and the basic symmetries governing their behavior. Nuclear chemists, by contrast, have tended to focus on studies of more complex phenomena where “statistical behavior” is important. Nuclear chemists are more likely to be involved in applications of nuclear phenomena than nuclear physicists, although there is clearly a considerable overlap in their efforts. Some problems, such as the study of the nuclear fuel cycle in reactors or the migration of nuclides in the environment, are so inherently chemical that they involve chemists almost exclusively.

One term that is frequently associated with nuclear chemistry is radio- chemistry. The term radiochemistry refers to the chemical manipulation of radioactivity and associated phenomena. All radiochemists are, by definition, nuclear chemists, but not all nuclear chemists are radiochemists. Many nuclear chemists use purely nonchemical and therefore physical techniques to study nuclear phenomena, and thus, their work is not radiochemistry.

1.2 The Excitement and Relevance of Nuclear Chemistry

What do nuclear chemists do? Why do they do it? Who are the nuclear chemists? What is exciting and relevant about nuclear chemistry? The answers to these questions and many more similar questions are what we will discuss in this book.

Nuclear chemists ask questions about the sizes of things like nuclei and their constituents. But because nuclear reactions are what makes the stars shine, the laboratory for many nuclear chemists is the universe with attention focusing on supernova and neutron stars (the largest known “nuclei”). The size scale for the nuclear chemistry laboratory ranges from zeptometers (10−21 m) to zettameters (1021 m). Nuclear chemists are always trying to make/discover new things about the natural world. From using radioactivity to measure the temperature of the planet Earth to tracing the flow of groundwater or the circulation patterns of the oceans, nuclear chemists explore the natural world. What makes the stars shine or how do they shine? A nuclear chemist, Ray Davis, won the 2002 Nobel Prize in Physics for his pioneering work on the neutrinos emitted by the sun (see Chapter 12).

Speaking of Nobel Prizes, the junior authors (WDL, DJM) would be remiss not to mention that our coauthor (GTS) won the 1951 Nobel Prize in Chem- istry for his discoveries in the chemistry of the transuranium elements. In total, nuclear chemists and physicists have discovered 26 new elements, expanding the fundamental building blocks of nature by about 30%. The expansion of the nuclear landscape from the 3000 known nuclei to the 7000 possibly bound

1.3 The Atom 3

nuclei remains an agenda item for nuclear science. Understanding why only about 228 of these nuclei are stable is also important.

Understanding the sizes and shapes of nuclei remains an important item. Shapes such as spherical, oblate, prolate, and hexadecapole are all observed; sometimes there are coexisting shapes even in the decay products of a single nucleus, such as 190Po, which decays to spherical, oblate and prolate-shaped products. Some nuclei like 11Li appear to have spatially extended structures due to weak binding that make them huge.

The applications of nuclear chemistry to the world around us enrich our lives in countless ways. One of these ways is the application of nuclear chemistry to the diagnosis and treatment of disease (nuclear medicine). Over 400 million nuclear medicine procedures are performed each year for the diagnosis of dis- ease. The most widely used (over 10 million procedures/year) radionuclide is 99Tcm, which was discovered by one of us (GTS). Positron emission tomogra- phy (PET) is used in over 1.5 million procedures/year in the United States. In PET, compounds of short-lived 𝛽+ emitters, like 18F, are injected into a patient, concentrating in particular organs. When the positron emitters decay, the 𝛽+ particles contact ordinary electrons, annihilating to produce two 0.511 MeV photons moving in opposite directions. When enough of these photon pairs are detected, one can form an image of the location of the decay. Studies of these images can be used to understand the location of tumors, brain functions, and so on. Targeted radiopharmaceuticals can be used to deliver a radiation dose to a specific location in the body.

Nuclear chemistry plays a role in our national security. In the United States, 300 portal monitors detect the possible entry of clandestine nuclear material. Several of these monitors employ advanced technologies to combat sophis- ticated schemes to shield the clandestine material. In the event of a nuclear radioactivity release, such as what occurred at the Fukushima reactor complex in Japan, simple ray spectroscopy of exposed air filters has proven to be useful.

Nuclear power remains an important source of electricity for several coun- tries. Nuclear chemists play key roles in waste remediation from nuclear power plants and providing solutions for nuclear fuel cycle issues. As chemists, they are also able to contribute to studies of material damage in reactor components.

There is a significant demand for people trained as nuclear chemists and radiochemists. In the United States, the demand for trained nuclear chemists at the PhD level exceeds the supply by a factor of 10 and has done so for decades.

1.3 The Atom

Before beginning a discussion of nuclei and their properties, we need to under- stand the environment in which most nuclei exist, that is, in the center of atoms. In elementary chemistry, we learn that the atom is the smallest unit a chemical

4 Introductory Concepts

3 × 10–10 m 5 × 10–15 m

Figure 1.1 Schematic representation of the relative sizes of a lithium atom and its nucleus. The nucleus is too small to be represented in the image of the atom even with the smallest printable dot. (See insert for color representation of the figure.)

element can be divided into that retains its chemical properties. As we know from our study of chemistry, the radii of atoms are ∼ 1 to 5 × 10−10 m, that is, 1–5 Å. At the center of each atom, we find the nucleus, a small object (r ≈ 1 to 10 × 10−15 m) that contains almost all the mass of the atom (Fig. 1.1). The atomic nucleus contains Z protons where Z is the atomic number of the ele- ment under study. Z is equal to the number of protons and thus the number of positive charges in the nucleus. The chemistry of the element is controlled by Z in that all nuclei with the same Z will have similar chemical behavior. The nucleus also contains N neutrons where N is the neutron number. Neutrons are uncharged particles with masses approximately equal to the mass of a pro- ton ( ≈1 u). The protons have a positive charge equal to that of an electron. The overall charge of a nucleus is +Z electronic charge units.

Most of the atom is empty space in which the electrons surround the nucleus. (Electrons are small, negatively charged particles with a charge of−1 electronic charge units and a mass of about 1∕1840 of the proton mass.) The negatively charged electrons are bound by an electrostatic (Coulombic) attraction to the positively charged nucleus. In a neutral atom, the number of electrons in the atom equals the number of protons in the nucleus.

Quantum mechanics tells us that only certain discrete values of E, the total electron energy, and J , the angular momentum of the electrons, are allowed. These discrete states have been depicted in the familiar semiclassical picture of the atom (Fig. 1.1) as a tiny nucleus with electrons rotating about it in discrete orbits. In this book, we will examine nuclear structure and will develop a similar semiclassical picture of the nucleus that will allow us to understand and predict a large range of nuclear phenomena.

1.4 Atomic Processes

The sizes and energy scales of atomic and nuclear processes are very different. These differences allow us to consider them separately.

1.4 Atomic Processes 5

1.4.1 Ionization

Suppose one atom collides with another atom. If the collision is inelastic, (the kinetic energies of the colliding nuclei are not conserved), one of two things may happen. They are (a) excitation of one or both atoms to an excited state involving a change in electron configuration or (b) ionization of atoms, that is, removal of one or more of the atom’s electrons to form a positively charged ion. For ionization to occur, an atomic electron must receive an energy that is at least equivalent to its binding energy, which, for the innermost or K electrons, is (Zeffective/137)2(255.5) keV, where Zeffective is the effective nuclear charge felt by the electron (and includes the effects of screening of the nuclear charge by other electrons). This effective nuclear charge for K electrons can be approximated by the expression (Z – 0.3). As one can see from these expressions, the energy nec- essary to cause ionization far exceeds the kinetic energies of gaseous atoms at room temperature. Thus, atoms must be moving with high speeds (as the result of nuclear decay processes or acceleration) to eject tightly bound electrons from other atoms.

1.4.2 X-Ray Emission

The term X-ray refers to the electromagnetic radiation produced when an elec- tron in an outer atomic electron shell drops down to fill a vacancy in an inner atomic electron shell (Fig. 1.2), such as going from the M shell to fill a vacancy in the L shell. The electron loses potential energy in this transition (in going to a more tightly bound shell) and radiates this energy in the form of X-rays. (X-rays are not to be confused with generally more energetic 𝛾-rays that result from transitions made by the neutrons and protons in the nucleus of the atom,

Figure 1.2 Schematic representation to show X-ray emission to fill vacancy caused by nuclear decay. An L shell electron (A) is shown filling a K shell vacancy (B). In doing so, it emits a characteristic K X-ray.

A

B

K L M

K X-ray emission

6 Introductory Concepts

not in the atomic electron shells.) The energy of the X-ray is given by the differ- ence in the binding energies of the electrons in the two shells, which, in turn, depends on the atomic number of the element. Thus X-ray energies can be used to determine the atomic number of the elemental constituents of a material and are also regarded as conclusive proof of the identification of a new chemical element.

In X-ray terminology, X-rays due to transitions from the L to K shell are called K

𝛼 X-rays; X-rays due to transitions from the M to K shells are called K

𝛽 X-rays.

In a further refinement, the terms K 𝛼1 and K𝛼2 refer to X-rays originating in

different subshells (2p3∕2, 2p1∕2) of the L shell. X-rays from M to L transitions are L

𝛼 and so on. For each transition, the changes in orbital angular momentum,

Δ𝓁, and total angular momentum, Δj, are required to be

Δ𝓁 = ±1 (1.1)

Δj = 0,±1 (1.2)

The simple Bohr model of the hydrogen-like atom (one electron only) predicts that the X-ray energy or the transition energy, ΔE, is given as

ΔE = Einitial − Efinal = R∞hcZ2 (

1 n2initial

− 1 n2final

) (1.3)

where R∞, h, c, and n denote the Rydberg constant, the Planck constant, the speed of light, and the principal quantum number for the orbital electron, respectively. Since the X-ray energy, Ex, is actually – ΔE, we can write (after substituting values for the physical constants)

Ex = 13.6Z2 (

1 n2final

− 1 n2initial

) eV (1.4)

where Ex is given in units of electron volts (eV). For K

𝛼 X-rays from ions with only one electron,

EKx = 13.6 ( 1

12 − 1

22 )

Z2 eV (1.5)

while for L 𝛼

X-rays, we have

ELx = 13.6 ( 1

22 − 1

32 )

Z2 eV (1.6)

In reality, many electrons will surround the nucleus, and we must replace Z by Zeffective to reflect the screening of the nuclear charge by these other electrons. This correction was done by Moseley who showed that the frequencies, 𝜈, of the K

𝛼 series X-rays could be expressed as

𝜈 1∕2 = const(Z − 1) (1.7)

1.5 The Nucleus: Nomenclature 7

while for L 𝛼

series X-rays,

𝜈 1∕2 = const(Z − 7.4) (1.8)

Moseley thus demonstrated the X-ray energies (= h𝜈) depend on the square of some altered form (due to screening) of the atomic number. Also, the rela- tive intensities of the K

𝛼1, K𝛼2, etc X-rays will be proportional to the number of possible ways to make the transition. Thus, we expect the K

𝛼1/K𝛼2 intensity ratio to be ∼2 as the maximum number of electrons in the 2p3∕2 level is 4 while the maximum number of electrons in the 2p1∕2 level is 2. The relative intensi- ties of different X-rays depend on the chemical state of the atom, its oxidation state, bonding with ligands, and other factors that affect the local electron den- sity. These relative intensities are, thus, useful in chemical speciation studies. We should also note, as discussed extensively in Chapters 7–9, that X-ray pro- duction can accompany radioactive decay. Radioactive decay modes, such as electron capture (EC) or internal conversion (IC), directly result in vacancies in the atomic electron shells. The resulting X-rays are signatures that can be used to characterize the decay modes and/or the decaying species.

1.5 The Nucleus: Nomenclature

A nucleus is said to be composed of nucleons. There are two “kinds” of nucleons, the neutrons and the protons. A nucleus with a given number of protons and neutrons is called a nuclide. The atomic number Z is the number of protons in the nucleus, while N , the neutron number, is used to designate the number of neutrons in the nucleus. The total number of nucleons in the nucleus is A, the mass number. Obviously A = N + Z. Note that A, the number of nucleons in the nucleus, is an integer, while the actual mass of that nucleus, m, is not an integer.

Nuclides with the same number of protons in the nucleus but with differing numbers of neutrons are called isotopes. (This word comes from the Greek iso + topos, meaning “same place” and referring to the position in the periodic table.) Isotopes have very similar chemical behavior because they have the same elec- tron configurations. Nuclides with the same number of neutrons in the nucleus, N , but differing numbers of protons, Z, are referred to as isotones. Isotones have some nuclear properties that are similar in analogy to the similar chemi- cal properties of isotopes. Nuclides with the same mass number, A, but differing numbers of neutrons and protons are referred to as isobars. Isobars are impor- tant in radioactive decay processes. Finally, the term isomer refers to a nuclide in an excited nuclear state that has a measurable lifetime (>10−9 s). These labels are straightforward, but one of them is frequently misused, that is, the term isotope. For example, radioactive nuclei (radionuclides) are often incorrectly

8 Introductory Concepts

referred to as radioisotopes, even though the nuclides being referenced do not have the same atomic numbers.

The convention for designating a given nuclide (with Z protons, N neutrons) is to write AZChemical SymbolN with the relative positions indicating a specific feature of the nuclide. Thus, the nucleus with 6 protons and 8 neutrons is 14 6 C8 or completely equivalently,

14C. (The older literature used the form N Z Chemical Symbol

A, so 14C was designated as C14. This nomenclature is generally extinct.) Note that sometimes the atomic charge of the entity containing the nuclide is denoted as an upper right-hand superscript. Thus a doubly ionized atom containing a Li nucleus with 3 protons and 4 neutrons and only one electron is designated as 7Li2+.

Sample Problem 1.1: Labels Consider the following nuclei: 60mCo, 14C, 14N, 12C, 13N. Which are iso- topes? isotones? isobars? isomers?

Solution 60mCo is the isomer, 14C and 12C are isotopes of carbon, 13N and 14N are isotopes of nitrogen, 14C and 14N are isobars (A = 14), while 12C and 13N are isotones (N = 6).

1.6 Properties of the Nucleus

We can now make an estimate of two important quantities, the size and the density of a typical nucleus. We can say

𝜌 ≡ Density = Mass Volume

≈ A (amu)4 3 𝜋R3

(1.9)

if we assume that the mass of each nucleon is about 1 u and the nucleus can be represented as a sphere. It turns out (Chapter 2) that a rule to describe the radii of stable nuclei is that radius R is

R = 1.2 × 10−13A1∕3 cm (1.10)

Thus we have

𝜌 = (A (u))

( 1.66 × 10−24 (g/u)

) 4 3 𝜋

( 1.2 × 10−13A1∕3 cm

)3 (1.11) where we have used the value of 1.66 × 10−24 g for 1 u (Appendix A). Before evaluating the density 𝜌 numerically, we note that the A factor cancels in the expression, leading us to conclude that all nuclei have approximately the

1.7 Survey of Nuclear Decay Types 9

same density. This is similar to the situation with different sized drops of a pure liquid. All of the molecules in a drop interact with each other with the same short-ranged forces, and the overall drop size grows with the number of molecules. Evaluating this expression and converting to convenient units, we have

𝜌 ≈ 200, 000 metric tons/mm3

A cube of nuclear matter that is 1 mm on a side contains a mass of 200,000 tonnes. WOW! Now we can realize what all the excitement about the nuclear phenomena is about. Think of the tremendous forces that are needed to hold matter together with this density. Relatively small changes in nuclei (via decay or reactions) can release large amounts of energy. (From the point of view of the student doing calculations with nuclear problems, a more useful expression of the nuclear density is 0.17 nucleons/fm3.)

1.7 Survey of Nuclear Decay Types

Nuclei can emit radiation spontaneously. The general process is called radioac- tive decay. While this subject will be discussed in detail in Chapters 3, 7, 8, and 9, we need to know a few general ideas about these processes right away (which we can summarize in the following).

Radioactive decay usually involves one of three basic types of decay, 𝛼-decay, 𝛽-decay, or 𝛾-decay in which an unstable nuclide spontaneously changes into a more stable form and emits some radiation. In Table 1.1, we summarize the basic features of these decay types.

The fact that there were three basic decay processes (and their names) was discovered by Rutherford. He showed that all three processes occur in a sam- ple of decaying natural uranium (and its daughters). The emitted radiations were designated 𝛼, 𝛽, and 𝛾 to denote the penetrating power of the different radiation types. Further research has shown that in 𝛼-decay, a heavy nucleus spontaneously emits an 4He nucleus (an 𝛼- particle). The emitted 𝛼-particles are monoenergetic, and as a result of the decay, the parent nucleus loses two protons and two neutrons and is transformed into a new nuclide. All nuclei with Z > 83 are unstable with respect to this decay mode.

Nuclear 𝛽 decay occurs in three ways, 𝛽−, 𝛽+, and EC. In these decays, a nuclear neutron (proton) changes into a nuclear proton (neutron) with the ejec- tion of neutrinos (small neutral particles) and electrons (or positrons). (In EC, an orbital electron is captured by the nucleus, changing a proton into a neu- tron with the emission of a neutrino.) The total number of nucleons in the nucleus, A, does not change in these decays, only the relative number of neu- trons and protons. In a sense, this process can “correct” or “adjust” an imbalance between the number of neutrons, and protons in a nucleus. In 𝛽+ and 𝛽− decays,

Table 1.1 Characteristics of Radioactive Decay.

Typical

Decay Emitted Energy of

Type Particle 𝚫𝚫Z 𝚫𝚫N 𝚫𝚫A Emitted Particle Example Occurrence

𝛼𝛼 4He2+ −2 −2 −4 4≤ E

𝛼𝛼 ≤ 10 MeV 238U→234Th+𝛼𝛼 Z >83

𝛽𝛽 − Energetic e−, 𝜈𝜈e +1 −1 0 0≤ E𝛽𝛽 ≤ 2 MeV 14C→14N+𝛽𝛽−+𝜈𝜈e N∕Z > (N∕Z)stable

𝛽𝛽 + Energetic e+, 𝜈𝜈e −1 +1 0 0 ≤ E𝛽𝛽 ≤ 2 MeV 22Na→22Ne+𝛽𝛽++𝜈𝜈e N∕Z < (N∕Z)stable; light nuclei

EC 𝜈𝜈e −1 +1 0 0 ≤ E𝜈𝜈 ≤2 MeV e−+207Bi→207Pb+𝜈𝜈e N∕Z < (N∕Z)stable; heavy nuclei 𝛾𝛾 Photon 0 0 0 0.1 ≤ E

𝛾𝛾 ≤ 2 MeV 60Ni∗ →60Ni+𝛾𝛾 Any excited nucleus

IC Electron 0 0 0 0.1 ≤ Ee ≤ 2 MeV 125Sbm →125Sb+e− Cases where 𝛾𝛾-ray emission is inhibited

1.7 Survey of Nuclear Decay Types 11

the decay energy is shared between the emitted electrons, the neutrinos, and the recoiling daughter nucleus. Thus, the energy spectrum of the emitted elec- trons and neutrinos is continuous ranging from zero to the decay energy. In EC decay, essentially all the decay energy is carried away by the emitted neutrino. Neutron-rich nuclei decay by 𝛽− decay while proton-rich nuclei decay by 𝛽+ or EC decay. 𝛽+ decay is favored in the light nuclei and requires the decay energy to be > 1.02 MeV (for reasons to be discussed later), while EC decay is found mostly in the heavier nuclei.

Nuclear electromagnetic decay occurs in two ways, 𝛾-decay and IC. In 𝛾-ray decay a nucleus in an excited state decays by the emission of a photon. In IC the same excited nucleus transfers its energy radiationlessly to an orbital electron that is ejected from the atom. In both types of decay, only the excitation energy of the nucleus is reduced with no change in the number of any of the nucleons.

Sample Problem 1.2: Balancing equations The conservation of the number of nucleons in the nucleus and conser- vation of charge during radioactive decay (Table 1.1) makes it relatively easy to write and balance nuclear decay equations. For example, consider

• The 𝛽− decay of 90Sr • The 𝛼 decay of 232Th • The 𝛽+ decay of 62Cu • The EC decay of 256Md

Solution These decay equations can be written, using Table 1.1, as

• 9038Sr → 90 39Y

+ + 𝛽− + 𝜈e

• 23290 Th → 228 88 Ra +

4 2 He

• 6229Cu → 62 28Ni

− + 𝛽+ + 𝜈e

• e− + 256101Md + →

256 100Fm + 𝜈e

Besides its qualitative description, radioactive decay has an important quan- titative description. Radioactive decay can be described as a first-order reac- tion, that is, the number of decays is proportional to the number of decaying nuclei present. It is described by the integrated rate law

N = N0e−𝜆t (1.12)

where N is the number of nuclei present at time t while N0 is the number of nuclei present at time t = 0. The decay constant 𝜆, a characteristic of each nucleus, is related to the half-life t1∕2 by

12 Introductory Concepts

𝜆 = ln 2 t 1

2

(1.13)

The half-life is the time required for the number of nuclei present to decrease by a factor of 2. The number of decays that occur in a radioactive sample in a given amount of time is called the activity A of the sample. The activity is equal to the number of nuclei present, N , multiplied by the probability of decay per nucleus, 𝜆, that is, A = 𝜆 N . Therefore, the activity will also decrease exponentially with time, that is,

A = A0e−𝜆t (1.14)

where A is the number of disintegrations per unit time at time t and A0 is the activity at time t = 0. The half-lives of nuclei with respect to each decay mode are often used to identify the nuclei.

Sample Problem 1.3 14C decays to 14N by 𝛽− decay with a half-life of 5730 years. If a 1 g sam- ple of carbon contains 15.0 dis/min, what will be its activity after 10,000 years?

Solution

• A = A0e−𝜆t

• 𝜆 = ln 2 5730 years

= 1.210 × 10−4∕year

• A = (15 dis/min) e−(1.210 × 10−4)(10,000) = 4.5 dis/min

All living things maintain a constant level of 14C per gram of carbon through exchange with their surroundings. When they die, this exchange stops, and the amount of 14C present decreases exponentially with time. A measurement of the 14C content of a dead object can be used to determine the age of the object. This process and other geologically important decay processes are discussed in Chapter 3.

1.8 Modern Physical Concepts Needed in Nuclear Chemistry

While we shall strive to describe nuclear chemistry without using extensive mathematics and physics, there are several important concepts from modern physics that we need to review because we will use these concepts in our dis- cussions.

1.8 Modern Physical Concepts Needed in Nuclear Chemistry 13

1.8.1 Elementary Mechanics

Let us recall a few elementary relationships from classical physics that we shall use. Force can be represented as a vector, F, which describes the rate of change of the momentum with time:

F = dp dt

(1.15)

where the momentum p = m𝑣 and where m is the mass and 𝑣 is the velocity of the particle. Neglecting relativistic effects (Section 1.8.2) that are important for particles whose velocity approaches the speed of light, we can say that the kinetic energy of a moving body T is given as

T = 1 2

m𝑣2 (1.16)

For the situation depicted in Figure 1.3 for the motion of a particle past a fixed point, we can say that the orbital angular momentum of the particle, 𝓁, with mass m with respect to the point Q is

l = r × p (1.17) The quantity 𝓁 is a vector whose magnitude is m𝑣r for circular motion. For motion past a stationary point, the magnitude is m𝑣b where b is the distance of closest approach called the impact parameter.

Let us also recall the relationship between the magnitude of a force F(r) that depends on the distance between two objects, r, and the potential energy, V (r), that is,

F = −𝜕V dr

(1.18)

Figure 1.3 A particle of mass, m, moving with a velocity, 𝑣, has a linear momentum p = m𝑣. Relative to point O, the particle has an angular momentum of 𝓵 = r× p, where r is a vector connecting point O and the particle. At the point of closest approach, r is equal to impact parameter b. O

x

y

z

I = r × p

p m

P θ

r

14 Introductory Concepts

Thus, if the Coulomb potential energy between two charged objects is given as

V = +kq1q2

r12 (1.19)

where r12 is the distance separating charges q1 and q2 (and where k is a con- stant), we can say t the magnitude of the Coulomb force, FC , is

FC = −𝜕V

dr =

kq1q2 r212

(1.20)

Since forces are usually represented as vectors, it is more convenient when dis- cussing nuclear interactions to refer to the scalar, potential energy. From the previous discussion, we should always remember that a discussion of potential energy V (r) is also a discussion of force F(r).

1.8.2 Relativistic Mechanics

As Einstein demonstrated, when a particle moves with a velocity approach- ing that of light, the classical relations (Section 1.8.1) describing its motion in a stationary system are no longer valid. Nuclear processes frequently involve par- ticles with such high velocities. Thus we need to understand the basic elements of relativistic mechanics. According to the special theory of relativity, the mass of a moving particle changes with speed according to the equation

m∗ = 𝛾m0 (1.21)

where m∗ and m0 are the mass of a particle in motion and at rest, respectively. The Lorentz factor, 𝛾 , is given as

𝛾 = ( 1 − 𝛽2