ModernNuclearChemistry - download.e-bookshelf.de...Contents vii 6 NuclearStructure 125 6.1 Introduction 125 6.2 NuclearPotentials 127 6.3 SchematicShellModel 129 6.4 IndependentParticleModel

Modern Nuclear Chemistry

Modern Nuclear Chemistry

Second Edition

Walter D. LovelandOregon State University

David J. MorrisseyMichigan State University

Glenn T. SeaborgUniversity 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. (GlennTheodore), 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–dc23LC record available at https://lccn.loc.gov/2016045901

Cover Image: Courtesy of the authorCover 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 xvPreface to the First Edition xvii

1 Introductory Concepts 11.1 Introduction 11.2 The Excitement and Relevance of Nuclear Chemistry 21.3 The Atom 31.4 Atomic Processes 41.4.1 Ionization 51.4.2 X-Ray Emission 51.5 The Nucleus: Nomenclature 71.6 Properties of the Nucleus 81.7 Survey of Nuclear Decay Types 91.8 Modern Physical Concepts Needed in Nuclear Chemistry 121.8.1 Elementary Mechanics 131.8.2 Relativistic Mechanics 141.8.3 de Broglie Wavelength: Wave–Particle Duality 161.8.4 Heisenberg Uncertainty Principle 181.8.5 Units and Conversion Factors 19

Problems 19Bibliography 21

2 Nuclear Properties 252.1 Nuclear Masses 252.2 Terminology 282.3 Binding Energy Per Nucleon 292.4 Separation Energy Systematics 312.5 Abundance Systematics 322.6 Semiempirical Mass Equation 332.7 Nuclear Sizes and Shapes 392.8 Quantum Mechanical Properties 43

vi Contents

2.8.1 Nuclear Angular Momentum 432.9 Electric and Magnetic Moments 452.9.1 Magnetic Dipole Moment 452.9.2 Electric Quadrupole Moment 48


3 Radioactive Decay Kinetics 573.1 Basic Decay Equations 573.2 Mixture of Two Independently Decaying Radionuclides 653.3 Radioactive Decay Equilibrium 663.4 Branching Decay 763.5 Radiation Dosage 773.6 Natural Radioactivity 793.6.1 General Information 793.6.2 Primordial Nuclei and the Uranium Decay Series 793.6.3 Cosmogenic Nuclei 813.6.4 Anthropogenic Nuclei 833.6.5 Health Effects of Natural Radiation 833.7 Radionuclide Dating 84


4 Nuclear Medicine 934.1 Introduction 934.2 Radiopharmaceuticals 944.3 Imaging 964.4 99Tcm 984.5 PET 1014.6 Other Imaging Techniques 1034.7 Some Random Observations about the Physics of Imaging 1044.8 Therapy 108


5 Particle Physics and the Nuclear Force 1135.1 Particle Physics 1135.2 The Nuclear Force 1175.3 Characteristics of the Strong Force 1195.4 Charge Independence of Nuclear Forces 120


Contents vii

6 Nuclear Structure 1256.1 Introduction 1256.2 Nuclear Potentials 1276.3 Schematic Shell Model 1296.4 Independent Particle Model 1416.5 Collective Model 1436.6 Nilsson Model 1496.7 Fermi Gas Model 152


7 𝛂-Decay 1677.1 Introduction 1677.2 Energetics of α Decay 1697.3 Theory of α Decay 1737.4 Hindrance Factors 1827.5 Heavy Particle Radioactivity 1837.6 Proton Radioactivity 185


8 𝛃-Decay 1918.1 Introduction 1918.2 Neutrino Hypothesis 1928.3 Derivation of the Spectral Shape 1968.4 Kurie Plots 1998.5 β Decay Rate Constant 2008.6 Electron Capture Decay 2068.7 Parity Nonconservation 2078.8 Neutrinos Again 2088.9 β-Delayed Radioactivities 2098.10 Double β Decay 211


9 𝛄-Ray Decay 2179.1 Introduction 2179.2 Energetics of γ-Ray Decay 2189.3 Classification of Decay Types 2209.4 Electromagnetic Transition Rates 2239.5 Internal Conversion 2299.6 Angular Correlations 2329.7 Mössbauer Effect 238

viii Contents


10 Nuclear Reactions 24710.1 Introduction 24710.2 Energetics of Nuclear Reactions 24810.3 Reaction Types and Mechanisms 25210.4 Nuclear Reaction Cross Sections 25310.5 Reaction Observables 26410.6 Rutherford Scattering 26410.7 Elastic (Diffractive) Scattering 26810.8 Aside on the Optical Model 27010.9 Direct Reactions 27110.10 Compound Nuclear Reactions 27310.11 Photonuclear Reactions 27910.12 Heavy-Ion Reactions 28110.12.1 Coulomb Excitation 28410.12.2 Elastic Scattering 28410.12.3 Fusion Reactions 28410.12.4 Incomplete Fusion 28810.12.5 Deep-Inelastic Scattering 28910.13 High-Energy Nuclear Reactions 29110.13.1 Spallation/Fragmentation Reactions 29110.13.2 Reactions Induced by Radioactive Projectiles 29510.13.3 Multifragmentation 29610.13.4 Quark–Gluon Plasma 298


11 Fission 30511.1 Introduction 30511.2 Probability of Fission 30811.2.1 Liquid Drop Model 30811.2.2 Shell Corrections 31011.2.3 Spontaneous Fission 31211.2.4 Spontaneously Fissioning Isomers 31511.2.5 The Transition Nucleus 31611.3 Dynamical Properties of Fission Fragments 32311.4 Fission Product Distributions 32711.4.1 Total Kinetic Energy (TKE) Release 32711.4.2 Fission Product Mass Distribution 32711.4.3 Fission Product Charge Distributions 33011.5 Excitation Energy of Fission Fragments 334

Contents ix


12 Nuclear Astrophysics 33912.1 Introduction 33912.2 Elemental and Isotopic Abundances 34012.3 Primordial Nucleosynthesis 34312.3.1 Stellar Evolution 34712.4 Thermonuclear Reaction Rates 35112.5 Stellar Nucleosynthesis 35312.5.1 Introduction 35312.5.2 Hydrogen Burning 35312.5.3 Helium Burning 35712.5.4 Synthesis of Nuclei with A < 60 35912.5.5 Synthesis of Nuclei with A > 60 36012.6 Solar Neutrino Problem 36612.6.1 Introduction 36612.6.2 Expected Solar Neutrino Sources, Energies, and Fluxes 36712.6.3 Detection of Solar Neutrinos 36912.6.4 The Solar Neutrino Problem 37112.6.5 Solution to the Problem: Neutrino Oscillations 37112.7 Synthesis of Li, Be, and B 373


13 Reactors and Accelerators 37913.1 Introduction 37913.2 Nuclear Reactors 38013.2.1 Neutron-Induced Reaction 38013.2.2 Neutron-Induced Fission 38313.2.3 Neutron Inventory 38413.2.4 Light Water Reactors 38613.2.5 The Oklo Phenomenon 39113.3 Neutron Sources 39213.4 Neutron Generators 39213.5 Accelerators 39313.5.1 Ion Sources 39413.5.2 Electrostatic Machines 39613.5.3 Linear Accelerators 40013.5.4 Cyclotrons, Synchrotrons, and Rings 40313.6 Charged-Particle Beam Transport and Analysis 41013.7 Radioactive Ion Beams 41513.8 Nuclear Weapons 421

x Contents


14 The Transuranium Elements 42914.1 Introduction 42914.2 Limits of Stability 42914.3 Element Synthesis 43414.4 History of Transuranium Element Discovery 43714.5 Superheavy Elements 44914.6 Chemistry of the Transuranium Elements 45314.7 Environmental Chemistry of the Transuranium Elements 461


15 Nuclear Reactor Chemistry 47315.1 Introduction 47315.2 Fission Product Chemistry 47515.3 Radiochemistry of Uranium 47815.3.1 Uranium Isotopes 47815.3.2 Metallic Uranium 47815.3.3 Uranium Compounds 47815.3.4 Uranium Solution Chemistry 47915.4 The Nuclear Fuel Cycle: The Front End 48015.4.1 Mining and Milling 48115.4.2 Refining and Chemical Conversion 48315.4.3 Isotopic Enhancement 48415.4.4 Fuel Fabrication 48715.5 The Nuclear Fuel Cycle: The Back End 48815.5.1 Properties of Spent Fuel 48815.5.2 Fuel Reprocessing 49015.6 Radioactive Waste Disposal 49315.6.1 Classifications of Radioactive Waste 49315.6.2 Waste Amounts and Associated Hazards 49415.6.3 Storage and Disposal of Nuclear Waste 49615.6.4 Spent Nuclear Fuel 49715.6.5 HLW 49815.6.6 Transuranic Waste 49915.6.7 Low-Level Waste 49915.6.8 Mill Tailings 50015.6.9 Partitioning of Waste 50015.6.10 Transmutation of Waste 50115.7 Chemistry of Operating Reactors 50415.7.1 Radiation Chemistry of Coolants 504

Contents xi

15.7.2 Corrosion 50515.7.3 Coolant Activities 505


16 Interaction of Radiation with Matter 50916.1 Introduction 50916.2 Heavy Charged Particles 51216.2.1 Stopping Power 51216.2.2 Range 52116.3 Electrons 52616.4 Electromagnetic Radiation 53216.4.1 Photoelectric Effect 53416.4.2 Compton Scattering 53616.4.3 Pair Production 53716.5 Neutrons 54016.6 Radiation Exposure and Dosimetry 544


17 Radiation Detectors 55317.1 Introduction 55317.1.1 Gas Ionization 55417.1.2 Ionization in a Solid (Semiconductor Detectors) 55417.1.3 Solid Scintillators 55517.1.4 Liquid Scintillators 55517.1.5 Nuclear Emulsions 55517.2 Detectors Based on Collecting Ionization 55617.2.1 Gas Ionization Detectors 55717.2.2 Semiconductor Detectors (Solid State Ionization Chambers) 56717.3 Scintillation Detectors 57817.4 Nuclear Track Detectors 58417.5 Neutron Detectors 58517.6 Nuclear Electronics and Data Collection 58717.7 Nuclear Statistics 58917.7.1 Distributions of Data and Uncertainty 59117.7.2 Rejection of Abnormal Data 59717.7.3 Setting Upper Limits When No Counts Are Observed 598


18 Nuclear Analytical Methods 60318.1 Introduction 60318.2 Activation Analysis 603

xii Contents

18.2.1 Basic Description of the Method 60318.2.2 Advantages and Disadvantages of Activation Analysis 60518.2.3 Practical Considerations in Activation Analysis 60718.2.4 Applications of Activation Analysis 61118.3 PIXE 61218.4 Rutherford Backscattering 61518.5 Accelerator Mass Spectrometry (AMS) 61918.6 Other Mass Spectrometric Techniques 620


19 Radiochemical Techniques 62519.1 Introduction 62519.2 Unique Aspects of Radiochemistry 62619.3 Availability of Radioactive Material 63019.4 Targetry 63219.5 Measuring Beam Intensity and Fluxes 63719.6 Recoils, Evaporation Residues, and Heavy Residues 63919.7 Radiochemical Separation Techniques 64419.7.1 Precipitation 64419.7.2 Solvent Extraction 64519.7.3 Ion Exchange 64819.7.4 Extraction Chromatography 65019.7.5 Rapid Radiochemical Separations 65219.8 Low-Level Measurement Techniques 65319.8.1 Blanks 65419.8.2 Low-Level Counting: General Principles 65419.8.3 Low-Level Counting: Details 65519.8.4 Limits of Detection 658


20 Nuclear Forensics 66320.1 Introduction 66320.1.1 Basic Principles of Forensic Analysis 66620.2 Chronometry 67020.3 Nuclear Weapons and Their Debris 67220.3.1 RDD or Dirty Bombs 67220.3.2 Nuclear Explosions 67420.4 Deducing Sources and Routes of Transmission 678


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 newchapters on nuclear medicine, particle physics, and nuclear forensics. We haveedited and updated all the chapters in the first edition reflecting the substantialprogress that has been made in the past 12 years. We have dropped the chapteron radiotracer methods. We have tried to remove all the typographical errorsin the first edition, without, we hope, introducing new errors. We continue tobe grateful to the many colleagues and students who have taught us about awide range of nuclear chemistry. In addition to our colleagues acknowledged inthe first edition of this book, we gratefully acknowledge the helpful commentsof J. Cerny and L.G. Sobotka on various portions of the book.

Walter D. LovelandCorvallis, ORMarch, 2016

David J. MorrisseyEast Lansing, MI

March, 2016

xvii

Preface to the First Edition

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

Much of the mainstream of nuclear chemistry is now deeply tied to nuclearphysics, 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 onemight like. We hope this encourages instructors to summarize the textbookmaterial and present it in a manner most suitable to a particular audience. Theamount of material contained in this book is too much for a one quarter or onesemester course and a bit too little for a yearlong course. Instructors can pickand 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 graduatestudent. We have assumed that a student has prior or concurrent instruction inphysical chemistry or modern physics and has some skills in handling differen-tial equations. We have attempted to sprinkle solved problems throughout thetext, as we believe that one learns by working problems. The end-of-the-chapterhomework problems are largely examination questions used at Oregon StateUniversity. They should be considered to be integral part of the textbook asthey are intended to illustrate or amplify the main points of each chapter. Wehave taken some pains to use quantum mechanics in a schematic way, that is,to use the conclusions of such considerations without using or demanding arigorous, 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 thosestudents with limited backgrounds.

Our aim is to convey the essence of the ideas and the blend of theory andexperiment that characterizes nuclear and radiochemistry. We have includedsome more advanced material for those who would like a deeper immersion inthe subject. Our hope is that the reader can use this book for an introductorytreatment 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 thepracticing scientist might see this volume as a quick refresher course for therudiments of relatively unfamiliar aspects of nuclear and radiochemistry andas 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. GlennT. Seaborg, before the completion of this work. Glenn participated in planningand development of the textbook, wrote some of the text, and reviewed muchof the rest. We deeply miss his guidance and his perspective as we have broughtthis project to conclusion. We regret not paying closer attention to his urgingthat we work harder and faster as he would remark to us, “You know I’m notgoing to live forever.” We hope that the thoughts and ideas that he taught us arereflected in these pages.

We gratefully acknowledge the many colleagues and students who havetaught us about nuclear chemistry and other things. Special thanks are dueto Darrah Thomas and the late Tom Sugihara for pointing out better ways todiscuss some material. We acknowledge the efforts of Einar Hageb who usedan 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 SuperconductingCyclotron Laboratory at Michigan State University for their hospitality in thefall of 1999 during which time a portion of this book was written.

Walter D. LovelandCorvallis, OROctober, 2004

David J. MorrisseyEast Lansing, MI

October, 2004

1

1

Introductory Concepts

1.1 Introduction

Nuclear chemistry consists of a four-pronged endeavor made up of (a) studiesof 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 nuclearproperties such as structure, reactions, and radioactive decay by people trainedas chemists, (c) studies of macroscopic phenomena (such as geochronologyor astrophysics) where nuclear processes are intimately involved, and (d)application of measurement techniques based on nuclear phenomena (suchas activation analysis or radiotracers) to study scientific problems in a varietyof fields. The principal activity or “mainstream” of nuclear chemistry involvesthose activities listed under (b).

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

A frequently asked question is “what are the differences between nuclearphysics and nuclear chemistry?” Clearly, the two endeavors overlap to a largeextent, and in recognition of this overlap, they are collectively referred to bythe catchall phrase “nuclear science.” But we believe that there are fundamental,important distinctions between these two fields. Besides the continuing closeties to traditional chemistry cited previously, nuclear chemists tend to studynuclear 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 theirbehavior. Nuclear chemists, by contrast, have tended to focus on studies ofmore complex phenomena where “statistical behavior” is important. Nuclearchemists are more likely to be involved in applications of nuclear phenomenathan nuclear physicists, although there is clearly a considerable overlap in theirefforts. Some problems, such as the study of the nuclear fuel cycle in reactors orthe migration of nuclides in the environment, are so inherently chemical thatthey involve chemists almost exclusively.

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

1.2 The Excitement and Relevance ofNuclear Chemistry

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

Nuclear chemists ask questions about the sizes of things like nuclei and theirconstituents. But because nuclear reactions are what makes the stars shine, thelaboratory for many nuclear chemists is the universe with attention focusing onsupernova and neutron stars (the largest known “nuclei”). The size scale for thenuclear chemistry laboratory ranges from zeptometers (10−21 m) to zettameters(1021 m). Nuclear chemists are always trying to make/discover new things aboutthe natural world. From using radioactivity to measure the temperature of theplanet Earth to tracing the flow of groundwater or the circulation patterns ofthe oceans, nuclear chemists explore the natural world. What makes the starsshine or how do they shine? A nuclear chemist, Ray Davis, won the 2002 NobelPrize 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 remissnot 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, expandingthe fundamental building blocks of nature by about 30%. The expansion of thenuclear 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 onlyabout 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 singlenucleus, such as 190Po, which decays to spherical, oblate and prolate-shapedproducts. Some nuclei like 11Li appear to have spatially extended structuresdue to weak binding that make them huge.

The applications of nuclear chemistry to the world around us enrich our livesin countless ways. One of these ways is the application of nuclear chemistryto the diagnosis and treatment of disease (nuclear medicine). Over 400 millionnuclear medicine procedures are performed each year for the diagnosis of dis-ease. The most widely used (over 10 million procedures/year) radionuclide is99Tcm, 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. InPET, 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 MeVphotons moving in opposite directions. When enough of these photon pairs aredetected, one can form an image of the location of the decay. Studies of theseimages can be used to understand the location of tumors, brain functions, andso on. Targeted radiopharmaceuticals can be used to deliver a radiation dose toa 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 nuclearradioactivity release, such as what occurred at the Fukushima reactor complexin 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 powerplants and providing solutions for nuclear fuel cycle issues. As chemists, theyare also able to contribute to studies of material damage in reactor components.

There is a significant demand for people trained as nuclear chemists andradiochemists. In the United States, the demand for trained nuclear chemists atthe 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


3 × 10–10 m 5 × 10–15 m

Figure 1.1 Schematicrepresentation of the relativesizes of a lithium atom and itsnucleus. The nucleus is toosmall to be represented in theimage of the atom even withthe smallest printable dot.(See insert for colorrepresentation of the figure.)

element can be divided into that retains its chemical properties. As we knowfrom 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 ≈ 1to 10 × 10−15 m) that contains almost all the mass of the atom (Fig. 1.1). Theatomic 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 numberof positive charges in the nucleus. The chemistry of the element is controlledby Z in that all nuclei with the same Z will have similar chemical behavior. Thenucleus also contains N neutrons where N is the neutron number. Neutronsare 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. Theoverall 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 electroniccharge units and a mass of about 1∕1840 of the proton mass.) The negativelycharged electrons are bound by an electrostatic (Coulombic) attraction to thepositively charged nucleus. In a neutral atom, the number of electrons in theatom equals the number of protons in the nucleus.

Quantum mechanics tells us that only certain discrete values of E, the totalelectron energy, and J , the angular momentum of the electrons, are allowed.These discrete states have been depicted in the familiar semiclassical picture ofthe atom (Fig. 1.1) as a tiny nucleus with electrons rotating about it in discreteorbits. In this book, we will examine nuclear structure and will develop a similarsemiclassical picture of the nucleus that will allow us to understand and predicta 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, (thekinetic energies of the colliding nuclei are not conserved), one of two thingsmay happen. They are (a) excitation of one or both atoms to an excited stateinvolving a change in electron configuration or (b) ionization of atoms, thatis, removal of one or more of the atom’s electrons to form a positively chargedion. For ionization to occur, an atomic electron must receive an energy that is atleast 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 bythe electron (and includes the effects of screening of the nuclear charge by otherelectrons). This effective nuclear charge for K electrons can be approximated bythe 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 atroom temperature. Thus, atoms must be moving with high speeds (as the resultof nuclear decay processes or acceleration) to eject tightly bound electrons fromother 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 inneratomic electron shell (Fig. 1.2), such as going from the M shell to fill a vacancyin the L shell. The electron loses potential energy in this transition (in goingto 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 resultfrom transitions made by the neutrons and protons in the nucleus of the atom,

Figure 1.2 Schematicrepresentation to showX-ray emission to fill vacancycaused by nuclear decay. AnL shell electron (A) is shownfilling a K shell vacancy (B).In doing so, it emits acharacteristic K X-ray.

A

B

K L M

K X-rayemission


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 usedto determine the atomic number of the elemental constituents of a material andare also regarded as conclusive proof of the identification of a new chemicalelement.

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

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

𝛽X-rays.

In a further refinement, the terms K𝛼1 and K

𝛼2 refer to X-rays originating indifferent subshells (2p3∕2, 2p1∕2) of the L shell. X-rays from M to L transitionsare L

𝛼and 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) predictsthat the X-ray energy or the transition energy, ΔE, is given as

ΔE = Einitial − Efinal = R∞hcZ2

(1

n2initial

− 1n2

final

)(1.3)

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

Ex = 13.6Z2

(1

n2final

− 1n2

initial

)eV (1.4)

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

𝛼X-rays from ions with only one electron,

EKx = 13.6

( 112 −

122

)Z2 eV (1.5)

while for L𝛼

X-rays, we have

ELx = 13.6

( 122 −

132

)Z2 eV (1.6)

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

𝛼series X-rays could be expressed as

𝜈1∕2 = const(Z − 1) (1.7)

1.5 The Nucleus: Nomenclature 7

while for L𝛼

series X-rays,

𝜈1∕2 = const(Z − 7.4) (1.8)

Moseley thus demonstrated the X-ray energies (= h𝜈) depend on the squareof 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 K𝛼1/K

𝛼2 intensityratio to be ∼2 as the maximum number of electrons in the 2p3∕2 level is 4 whilethe 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 oxidationstate, 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 aselectron capture (EC) or internal conversion (IC), directly result in vacanciesin the atomic electron shells. The resulting X-rays are signatures that can beused 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 andneutrons is called a nuclide. The atomic number Z is the number of protons inthe nucleus, while N , the neutron number, is used to designate the number ofneutrons in the nucleus. The total number of nucleons in the nucleus is A, themass number. Obviously A = N + Z. Note that A, the number of nucleons inthe nucleus, is an integer, while the actual mass of that nucleus, m, is not aninteger.

Nuclides with the same number of protons in the nucleus but with differingnumbers 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. Isotoneshave some nuclear properties that are similar in analogy to the similar chemi-cal properties of isotopes. Nuclides with the same mass number, A, but differingnumbers 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 inan excited nuclear state that has a measurable lifetime (>10−9 s). These labelsare straightforward, but one of them is frequently misused, that is, the termisotope. For example, radioactive nuclei (radionuclides) are often incorrectly


referred to as radioisotopes, even though the nuclides being referenced do nothave the same atomic numbers.

The convention for designating a given nuclide (with Z protons, N neutrons)is to write A

ZChemical SymbolN

with the relative positions indicating a specificfeature of the nuclide. Thus, the nucleus with 6 protons and 8 neutrons is146 C8 or completely equivalently, 14C. (The older literature used the formNZ Chemical SymbolA, so 14C was designated as C14. This nomenclatureis generally extinct.) Note that sometimes the atomic charge of the entitycontaining the nuclide is denoted as an upper right-hand superscript. Thus adoubly ionized atom containing a Li nucleus with 3 protons and 4 neutronsand only one electron is designated as 7Li2+.

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

Solution60mCo is the isomer, 14C and 12C are isotopes of carbon, 13N and 14N areisotopes of nitrogen, 14C and 14N are isobars (A = 14), while 12C and 13Nare isotones (N = 6).

1.6 Properties of the Nucleus

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

𝜌 ≡ Density = MassVolume

≈ A (amu)43𝜋R3

(1.9)

if we assume that the mass of each nucleon is about 1 u and the nucleus can berepresented as a sphere. It turns out (Chapter 2) that a rule to describe the radiiof 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)

)43𝜋

(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). Beforeevaluating the density 𝜌 numerically, we note that the A factor cancels inthe 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 apure liquid. All of the molecules in a drop interact with each other with thesame short-ranged forces, and the overall drop size grows with the numberof 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 200,000tonnes. WOW! Now we can realize what all the excitement about the nuclearphenomena is about. Think of the tremendous forces that are needed to holdmatter together with this density. Relatively small changes in nuclei (via decayor reactions) can release large amounts of energy. (From the point of view of thestudent doing calculations with nuclear problems, a more useful expression ofthe 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, and9, we need to know a few general ideas about these processes right away (whichwe 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 intoa more stable form and emits some radiation. In Table 1.1, we summarize thebasic features of these decay types.

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

Nuclear 𝛽 decay occurs in three ways, 𝛽−, 𝛽+, and EC. In these decays, anuclear 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 thenucleus, 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 imbalancebetween the number of neutrons, and protons in a nucleus. In 𝛽

+ and 𝛽− decays,

Characteristics of Radioactive Decay.

Typical

Energy of

𝚫𝚫Z 𝚫𝚫N 𝚫𝚫A Emitted Particle Example Occurrence

−2 −2 −4 4≤ E𝛼𝛼≤ 10 MeV 238U→234Th+𝛼𝛼 Z >83

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

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

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

Photon 0 0 0 0.1 ≤ E𝛾𝛾≤ 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

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ModernNuclearChemistry - download.e-bookshelf.de...Contents vii 6 NuclearStructure 125 6.1 Introduction 125 6.2 NuclearPotentials 127 6.3 SchematicShellModel 129 6.4 IndependentParticleModel