PRINCIPLES OFINORGANICCHEMISTRY

PRINCIPLES OFINORGANICCHEMISTRY

Brian W. Pfennig

Copyright © 2015 by John Wiley & Sons, Inc. All rights reserved

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Library of Congress Cataloging-in-Publication Data:

Pfennig, Brian William.Principles of inorganic chemistry / Brian W. Pfennig.

pages cmIncludes bibliographical references and index.ISBN 978-1-118-85910-0 (cloth)

1. Chemistry, Inorganic–Textbooks. 2. Chemistry, Inorganic–Study and teaching (Higher) 3. Chemistry,Inorganic–Study and teaching (Graduate) I. Title.QD151.3.P46 2015546–dc23

2014043250

Cover image :Courtesy of the authorTypeset in 10/12pt GillSans by Laserwords Private Limited, Chennai, India.

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

1 2015

Contents

Preface xi

Acknowledgements xv

Chapter 1 | The Composition of Matter 11.1 Early Descriptions of Matter 11.2 Visualizing Atoms 61.3 The Periodic Table 81.4 The Standard Model 9Exercises 12Bibliography 13

Chapter 2 | The Structure of the Nucleus 152.1 The Nucleus 152.2 Nuclear Binding Energies 162.3 Nuclear Reactions: Fusion and Fission 172.4 Radioactive Decay and the Band of Stability 222.5 The Shell Model of the Nucleus 272.6 The Origin of the Elements 30Exercises 38Bibliography 39

Chapter 3 | A Brief Review of Quantum Theory 413.1 The Wavelike Properties of Light 413.2 Problems with the Classical Model of the Atom 483.3 The Bohr Model of the Atom 553.4 Implications of Wave-Particle Duality 583.5 Postulates of Quantum Mechanics 643.6 The Schrödinger Equation 673.7 The Particle in a Box Problem 703.8 The Harmonic Oscillator Problem 75Exercises 78Bibliography 79

Chapter 4 | Atomic Structure 814.1 The Hydrogen Atom 81

4.1.1 The Radial Wave Functions 824.1.2 The Angular Wave Functions 86

4.2 Polyelectronic Atoms 914.3 Electron Spin and the Pauli Principle 934.4 Electron Configurations and the Periodic Table 964.5 Atomic Term Symbols 98

vi CONTENTS

4.5.1 Extracting Term Symbols Using Russell–Saunders Coupling 1004.5.2 Extracting Term Symbols Using jj Coupling 1024.5.3 Correlation Between RS (LS) Coupling and jj Coupling 104

4.6 Shielding and Effective Nuclear Charge 105Exercises 107Bibliography 108

Chapter 5 | Periodic Properties of the Elements 1095.1 The Modern Periodic Table 1095.2 Radius 1115.3 Ionization Energy 1185.4 Electron Affinity 1215.5 The Uniqueness Principle 1225.6 Diagonal Properties 1245.7 The Metal–Nonmetal Line 1255.8 Standard Reduction Potentials 1265.9 The Inert-Pair Effect 1295.10 Relativistic Effects 1305.11 Electronegativity 133Exercises 136Bibliography 137

Chapter 6 | An Introduction to Chemical Bonding 1396.1 The Bonding in Molecular Hydrogen 1396.2 Lewis Structures 1406.3 Covalent Bond Lengths and Bond Dissociation Energies 1446.4 Resonance 1466.5 Polar Covalent Bonding 149Exercises 153Bibliography 154

Chapter 7 | Molecular Geometry 1557.1 The VSEPR Model 1557.2 The Ligand Close-Packing Model 1707.3 A Comparison of the VSEPR and LCP Models 175Exercises 176Bibliography 177

Chapter 8 | Molecular Symmetry 1798.1 Symmetry Elements and Symmetry Operations 179

8.1.1 Identity, E 1808.1.2 Proper Rotation, Cn 1818.1.3 Reflection, 𝜎 1828.1.4 Inversion, i 1838.1.5 Improper Rotation, Sn 183

8.2 Symmetry Groups 1868.3 Molecular Point Groups 1918.4 Representations 1958.5 Character Tables 2028.6 Direct Products 2098.7 Reducible Representations 214Exercises 222Bibliography 224

CONTENTS vii

Chapter 9 | Vibrational Spectroscopy 2279.1 Overview of Vibrational Spectroscopy 2279.2 Selection Rules for IR and Raman-Active Vibrational Modes 2319.3 Determining the Symmetries of the Normal Modes of Vibration 2359.4 Generating Symmetry Coordinates Using the Projection Operator Method 2439.5 Resonance Raman Spectroscopy 252Exercises 256Bibliography 258

Chapter 10 | Covalent Bonding 25910.1 Valence Bond Theory 25910.2 Molecular Orbital Theory: Diatomics 27810.3 Molecular Orbital Theory: Polyatomics 29210.4 Molecular Orbital Theory: pi Orbitals 30510.5 Molecular Orbital Theory: More Complex Examples 31710.6 Borane and Carborane Cluster Compounds 325Exercises 334Bibliography 336

Chapter 11 | Metallic Bonding 33911.1 Crystalline Lattices 33911.2 X-Ray Diffraction 34511.3 Closest-Packed Structures 35011.4 The Free Electron Model of Metallic Bonding 35511.5 Band Theory of Solids 36011.6 Conductivity in Solids 37411.7 Connections Between Solids and Discrete Molecules 383Exercises 384Bibliography 388

Chapter 12 | Ionic Bonding 39112.1 Common Types of Ionic Solids 39112.2 Lattice Enthalpies and the Born–Haber Cycle 39812.3 Ionic Radii and Pauling’s Rules 40412.4 The Silicates 41712.5 Zeolites 42212.6 Defects in Crystals 423Exercises 426Bibliography 428

Chapter 13 | Structure and Bonding 43113.1 A Reexamination of Crystalline Solids 43113.2 Intermediate Types of Bonding in Solids 43413.3 Quantum Theory of Atoms in Molecules (QTAIM) 443Exercises 449Bibliography 452

Chapter 14 | Structure and Reactivity 45314.1 An Overview of Chemical Reactivity 45314.2 Acid–Base Reactions 45514.3 Frontier Molecular Orbital Theory 467

viii CONTENTS

14.4 Oxidation–Reduction Reactions 47314.5 A Generalized View of Molecular Reactivity 475Exercises 480Bibliography 481

Chapter 15 | An Introduction to Coordination Compounds 48315.1 A Historical Overview of Coordination Chemistry 48315.2 Types of Ligands and Nomenclature 48715.3 Stability Constants 49015.4 Coordination Numbers and Geometries 49215.5 Isomerism 49815.6 The Magnetic Properties of Coordination Compounds 501Exercises 506Bibliography 508

Chapter 16 | Structure, Bonding, and Spectroscopy of Coordination Compounds 50916.1 Valence Bond Model 50916.2 Crystal Field Theory 51216.3 Ligand Field Theory 52516.4 The Angular Overlap Method 53416.5 Molecular Term Symbols 541

16.5.1 Scenario 1—All the Orbitals are Completely Occupied 54616.5.2 Scenario 2—There is a Single Unpaired Electron in One of the Orbitals 54616.5.3 Scenario 3—There are Two Unpaired Electrons in Two Different Orbitals 54616.5.4 Scenario 4—A Degenerate Orbital is Lacking a Single Electron 54716.5.5 Scenario 5—There are Two Electrons in a Degenerate Orbital 54716.5.6 Scenario 6—There are Three Electrons in a Triply Degenerate Orbital 547

16.6 Tanabe–Sugano Diagrams 54916.7 Electronic Spectroscopy of Coordination Compounds 55416.8 The Jahn–Teller Effect 564Exercises 566Bibliography 570

Chapter 17 | Reactions of Coordination Compounds 57317.1 Kinetics Overview 57317.2 Octahedral Substitution Reactions 577

17.2.1 Associative (A) Mechanism 57817.2.2 Interchange (I) Mechanism 57917.2.3 Dissociative (D) Mechanism 580

17.3 Square Planar Substitution Reactions 58517.4 Electron Transfer Reactions 59317.5 Inorganic Photochemistry 606

17.5.1 Photochemistry of Chromium(III) Ammine Compounds 60717.5.2 Light-Induced Excited State Spin Trapping in Iron(II) Compounds 61117.5.3 MLCT Photochemistry in Pentaammineruthenium(II) Compounds 61517.5.4 Photochemistry and Photophysics of Ruthenium(II) Polypyridyl Compounds 617

Exercises 622Bibliography 624

Chapter 18 | Structure and Bonding in Organometallic Compounds 62718.1 Introduction to Organometallic Chemistry 62718.2 Electron Counting and the 18-Electron Rule 628

CONTENTS ix

18.3 Carbonyl Ligands 63118.4 Nitrosyl Ligands 63518.5 Hydride and Dihydrogen Ligands 63818.6 Phosphine Ligands 64018.7 Ethylene and Related Ligands 64118.8 Cyclopentadiene and Related Ligands 64518.9 Carbenes, Carbynes, and Carbidos 648Exercises 651Bibliography 654

Chapter 19 | Reactions of Organometallic Compounds 65519.1 Some General Principles 65519.2 Organometallic Reactions Involving Changes at the Metal 656

19.2.1 Ligand Substitution Reactions 65619.2.2 Oxidative Addition and Reductive Elimination 658

19.3 Organometallic Reactions Involving Changes at the Ligand 66419.3.1 Insertion and Elimination Reactions 66419.3.2 Nucleophilic Attack on the Ligands 66719.3.3 Electrophilic Attack on the Ligands 669

19.4 Metathesis Reactions 67019.4.1 𝜋-Bond Metathesis 67019.4.2 Ziegler–Natta Polymerization of Alkenes 67119.4.3 𝜎-Bond Metathesis 671

19.5 Commercial Catalytic Processes 67419.5.1 Catalytic Hydrogenation 67419.5.2 Hydroformylation 67419.5.3 Wacker–Smidt Process 67619.5.4 Monsanto Acetic Acid Process 677

19.6 Organometallic Photochemistry 67819.6.1 Photosubstitution of CO 67819.6.2 Photoinduced Cleavage of Metal–Metal Bonds 68019.6.3 Photochemistry of Metallocenes 682

19.7 The Isolobal Analogy and Metal–Metal Bonding in Organometallic Clusters 683Exercises 689Bibliography 691

Appendix: A Derivation of the Classical Wave Equation 693Bibliography 694

Appendix: B Character Tables 695Bibliography 708

Appendix: C Direct Product Tables 709Bibliography 713

Appendix: D Correlation Tables 715Bibliography 721

Appendix: E The 230 Space Groups 723Bibliography 728

Index 729

Preface

This book was written as a result of the perceived need of mine and several othercolleagues for a more advanced physical inorganic text with a strong emphasis ongroup theory and its applications. Many of the inorganic textbooks on the market areeither disjointed—with one chapter completely unrelated to the next—or encyclo-pedic, so that the student of inorganic chemistry is left to wonder if the only way tomaster the field is to memorize a large body of facts. While there is certainly somemerit to a descriptive approach, this text will focus on a more principles-based ped-agogy, teaching students how to rationalize the structure and reactivity of inorganiccompounds—rather than relying on rote memorization.

After many years of teaching the inorganic course without a suitable text, Idecided to write my own. Beginning in the summer of 2006, I drew on a variety ofdifferent sources and tried to pull together bits and pieces from different texts andreference books, finishing a first draft (containing 10 chapters) in August, 2007. I usedthis version of the text as supplementary reading for a few years before taking up thetask of writing again in earnest in 2012, subdividing and expanding the upon original10 chapters to the current 19, adding references and more colorful illustrations, andincluding problems at the ends of each chapter.

The book was written with my students in mind. I am a teacher first and a scien-tist second. I make no claims about my limited knowledge of this incredibly expansivefield. My main contribution has been to collect material from various sources and toorganize and present it in a pedagogically coherent manner so that my students canunderstand and appreciate the principles underlying such a diverse and interestingsubject as inorganic chemistry.

The book is organized in a logical progression. Chapter 1 provides a basicintroduction to the composition of matter and the experiments that led to thedevelopment of the periodic table. Chapter 2 then examines the structure andreactivity of the nucleus. Chapter 3 follows with a basic primer on wave-particleduality and some of the fundamentals of quantum mechanics. Chapter 4 discussesthe solutions to the Schrödinger equation for the hydrogen atom, the Pauli principle,the shapes of the orbitals, polyelectronic wave functions, shielding, and the quan-tum mechanical basis for the underlying structure of the periodic table. Chapter 5concludes this section of the text by examining the various periodic trends thatinfluence the physical and chemical properties of the elements. Chapter 6 thenbegins a series of chapters relating to chemical bonding by reviewing the basicsof Lewis structures, resonance, and formal charge. Chapter 7 is devoted to themolecular geometries of molecules and includes not only a more extensive treat-ment of the VSEPR model than most other textbooks but it also presents the ligandclose-packing model as a complementary model for the prediction of moleculargeometries. Symmetry and group theory are introduced in detail in Chapter 8 andwill reappear as a recurring theme throughout the remainder of the text. Unlikemost inorganic textbooks on the market, ample coverage is given to representa-tions of groups, reducing representations, direct products, the projection operator,and applications of group theory. Chapter 9 focuses on one of the applications ofgroup theory to the vibrational spectroscopy of molecules, showing how symmetrycoordinates can be used to approximate the normal modes of vibration of smallmolecules. The selection rules for IR and Raman spectroscopy are discussed and

xii PREFACE

the chapter closes with a brief introduction to resonance Raman spectroscopy. Thenext three chapters focus on the three different types of chemical bonding: covalent,metallic, and ionic bonding. Chapter 10 examines the valence bond and molecularorbital models, which expands upon the application of group theory to chemicalproblems. Chapter 11 then delves into metallic bonding, beginning with a primer oncrystallography before exploring the free electron model and band theory of solids.Chapter 12 is focused on ionic bonding—lattice enthalpies, the Born–Haber cycle,and Pauling’s rules for the rationalization of ionic solids. It also has extensive cover-age of the silicates and zeolites. The structure of solids is reviewed in greater detailin Chapter 13, which explores the interface between the different types of chemi-cal bonding in both solids and discrete molecules. Switching gears for a while fromstructure and bonding to chemical reactivity, Chapter 14 introduces the two majortypes of chemical reactions: acid–base reactions and oxidation–reduction reactions.In addition to the usual coverage of hard–soft acid–base theory, this chapter alsoexamines a more general overview of chemical reactivity that is based on the dif-ferent topologies of the MOs involved in chemical transformations. This chapteralso serves as a bridge to the transition metals. Chapter 15 presents an introduc-tion to coordination compounds and their thermodynamic and magnetic properties.Chapter 16 examines the structure, bonding, and electronic spectroscopy of coor-dination compounds, making extensive use of group theory. Chapter 17 investigatesthe reactions of coordination compounds in detail, including a section on inorganicphotochemistry. Finally, the text closes with two chapters on organometallic chem-istry: Chapter 18 looks at the different types of bonding in organometallics from anMO point of view, while Chapter 19 presents of a survey of organometallic reactionmechanisms, catalysis, and organometallic photochemistry and then concludes withconnections to main group chemistry using the isolobal analogy. Throughout thetextbook, there is a continual building on earlier material, especially as it relates togroup theory and MOT, which serve as the underlying themes for the majority ofthe book.

This text was originally written for undergraduate students taking an advancedinorganic chemistry course at the undergraduate level, although it is equally suit-able as a graduate-level text. I have written the book with the more capable andintellectually curious students in my undergraduate courses in mind. The prose israther informal and directly challenges the student to examine each new experi-mental observation in the context of previously introduced principles of inorganicchemistry. Students should appreciate the ample number of solved sample problemsinterwoven throughout the body of the text and the clear, annotated figures andillustrations. The end-of-chapter problems are designed to invoke an active wranglingwith the material and to force students to examine the data from several differentpoints of view. While the text is very physical in emphasis, it is not overly math-ematical and thorough derivations are provided for the more important physicalrelationships. It is my hope that students will not only enjoy using this textbook intheir classes but will read and reread it again as a valuable reference book throughoutthe remainder of their chemical careers.

While this book provides a thorough introduction to physical inorganic chem-istry, the field is too vast to include every possible topic; and it is therefore somewhatlimited in its scope. The usual group by group descriptive chemistry of the elements,for example, is completely lacking, as are chapters on bioinorganic chemistry orinorganic materials chemistry. However, it is my belief that what it lacks in breadthis more than compensated for by its depth and pedagogical organization. Nonethe-less, I eagerly welcome any comments, criticisms, and corrections and have opened a

PREFACE xiii

dedicated e-mail account for just such a purpose at pfennigtext@hotmail.com. I lookforward to hearing your suggestions.

BRIAN W. PFENNIGLancaster, PAJune, 2014

Acknowledgments

This book would not have been possible without the generous contributions ofothers. I am especially indebted to my teachers and mentors over the years whoalways inspired in me a curiosity for the wonders of science, including Al Bieber,Dave Smith, Bill Birdsall, Jim Scheirer, Andy Bocarsly, Mark Thompson, Jeff Schwartz,Tom Spiro, Don McClure, Bob Cava, and Tom Meyer. In addition, I thank some ofthe many colleagues who have contributed to my knowledge of inorganic chemistry,including Ranjit Kumble, Jim McCusker, Dave Thompson, Claude Yoder, Jim Spencer,Rick Schaeffer, John Chesick, Marianne Begemann, Andrew Price, and Amanda Reig.I also thank Reid Wickham at Pearson (Prentice-Hall) for her encouragement andadvice with respect to getting published and to Anita Lekwhani at John Wiley &Sons, Inc. for giving me that chance. Thank you all for believing in me and for yourencouragement.

There is little original content in this inorganic text that cannot be found else-where. My only real contribution has been to crystallize the content of many otherauthors and to organize it in a way that hopefully makes sense to the student. Ihave therefore drawn heavily on the following inorganic texts: Inorganic Chemistry(Miessler and Tarr), Inorganic Chemistry (Huheey, Keiter, and Keiter), Chemical Appli-cations of Group Theory (Cotton), Molecular Symmetry and Group Theory (Carter),Symmetry and Spectroscopy (Harris and Bertulucci), Problems in Molecular Orbital The-ory (Albright and Burdett), Chemical Bonding and Molecular Geometry (Gillespie andHargittai), Ligand Field Theory (Figgis and Hitchman), Physical Chemistry (McQuarrieand Simon), Elements of Quantum Theory (Bockhoff), Introduction to Crystallography(Sands), and Organometallic Chemistry (Spessard and Miessler).

In addition, I am grateful to a number of people who have assisted me in thepreparation of my manuscript, especially to the many people who have reviewedsample chapters of the textbook or who have generously provided permission touse their figures. I am especially indebted to Lori Blatt at Blatt Communications forproducing many of the amazing illustrations in the text and to Aubrey Paris for herinvaluable assistance with proofing the final manuscript.

I would be remiss if I failed to acknowledge the contributions of my students,both past and present, in giving me the inspiration and perseverance necessary towrite a volume of this magnitude. I am especially indebted to the intellectual inter-actions I have had with Dave Watson, Jamie Cohen, Jenny Lockard, Mike Norris,Aaron Peters, and Aubrey Paris over the years. Lastly, I would like to acknowledgethe most important people in my life, without whose undying support and toleranceI would never have been able to complete this work—my family. I am especiallygrateful to my wonderful parents who instilled in me the values of a good education,hard work, and integrity; to my wife Jessica for her unwavering faith in me; and tomy incredibly talented daughter Rachel, who more than anyone has suffered fromlack of my attention as I struggled to complete this work.

The Compositionof Matter 1

“Everything existing in the universe is the fruit of chance and necessity.”—Democritus

1.1 EARLY DESCRIPTIONS OF MATTER

Chemistry has been defined as the study of matter and its interconversions. Thus, in asense, chemistry is a study of the physical world in which we live. But how much dowe really know about the fundamental structure of matter and its relationship to thelarger macroscopic world? I have in my rock collection, which I have had since I was aboy, a sample of the mineral cinnabar, which is several centimeters across and weighsabout 10 g. Cinnabar is a reddish granular solid with a density about eight times thatof water and the chemical composition mercuric sulfide. Now suppose that someprimal instinct suddenly overcame me and I were inclined to demolish this precioustalisman from my childhood. I could take a hammer to it and smash it into a billionlittle pieces. Choosing the smallest of these chunks, I could further disintegrate thematerial in a mortar and pestle, grinding it into ever finer and finer grains until I wasleft with nothing but a red powder (in fact, this powder is known as vermilion andhas been used as a red pigment in artwork dating back to the fourteenth century).Having satisfied my destructive tendencies, I would nonetheless still have exactly thesame material that I started with—that is, it would have precisely the same chemicaland physical properties as the original. I might therefore wonder to myself if there issome inherent limitation as to how finely I can divide the substance or if this is simplylimited by the tools at my disposal. With the proper equipment, would I be able tocontinue dividing the compound into smaller and smaller pieces until ultimately Iobtained the unit cell, or smallest basic building block of the crystalline structure ofHgS, as shown in Figure 1.1? For that matter (no pun intended), is there a way forme to separate out the two different types of atoms in the substance?

If matter is defined as anything that has mass and is perceptible to the senses, atwhat point does it become impossible (or at the very least impractical) for me tocontinue to measure the mass of the individual grains or for them to no longer beperceptible to my senses (even if placed under an optical microscope)? The ancientphilosopher Democritus (ca 460–370 BC) was one of the first to propose that matteris constructed of tiny indivisible particles known as atomos (or atoms), the differentvarieties (sizes, shapes, masses, etc.) of which form the fundamental building blocksof the natural world. In other words, there should be some lower limit as to how

Principles of Inorganic Chemistry, First Edition. Brian W. Pfennig.© 2015 John Wiley & Sons, Inc. Published 2015 by John Wiley & Sons, Inc.

2 1 THE COMPOSITION OF MATTER

FIGURE 1.1Three examples of the samechemical material ranging fromthe macroscopic to the atomicscale: (a) the mineral cinnabar,(b) vermilion powder, and (c) theunit cell of mercuric sulfide.[Vermilion pigment photocourtesy of KremerPigments, Inc.]

(a)

(b)

(c)

finely I can continue to carve up my little chunk of cinnabar. As far back as the MiddleAges, the alchemists learned that one could decompose a sample of HgS by heatingit up in a crucible. At temperatures above 580 ∘C, the heat drives off the sulfur andleaves behind a pool of silvery liquid mercury. Eventually, I could break the moleculeitself apart into its individual atoms, but then I could go no further.

1.1 EARLY DESCRIPTIONS OF MATTER 3

Or could I? In the late 1800s, scientists discovered that if they constructed a hol-low glass tube with an anode in one end and a cathode in the other and pumped outas much of the air as they could, an electrical discharge between the two electrodescould produce a faint glow within the tube. Later, cathode ray tubes, as they becameto be known, were more sophisticated and contained a phosphorescent coating inone end of the tube. William Crookes demonstrated that the rays were emittedfrom the cathode and that they traveled in straight lines and could not bend aroundobjects in their path. A while later, Julius Plücker was able to show that a magnetapplied to the exterior of the cathode ray tube could change the position of thephosphorescence. Physicists knew that the cathode ray carried a negative charge (inphysics, the cathode is the negatively charged electrode and because the beam origi-nated from the cathode, it must therefore be negatively charged). However, they didnot know whether the charge and the ray could be separated from one another. In1897, Joseph J. Thomson finally resolved the issue by demonstrating that both thebeam and the charged particles could be bent by an electrical field that was appliedperpendicular to the path of the beam, as shown in Figure 1.2. By systematically vary-ing the electric field strength and measuring the angle of deflection, Thomson wasable to determine the charge-to-mass (e/m) ratio of the particles, which he calledcorpuscles and which are now known as electrons. Thomson measured the e/m ratioas −1.76 × 108 C/g, a value that was at least a thousand times larger than the oneexpected on the basis of the known atomic weights of even the lightest of atoms,indicating that the negatively charged electrons must be much smaller in size than atypical atom. In other words, the atom was not indivisible, and could itself be bro-ken down into smaller components, with the electron being one of these subatomicparticles. As a result of his discovery, Thomson proposed the so-called plum pud-ding model of the atom, where the atom consisted of one or more of these tinyelectrons distributed in a sea of positive charge, like raisins randomly dispersed in agelatinous pudding. Thomson was later awarded the 1906 Nobel Prize in physics forhis discovery of the electron and his work on the electrical conductivity of gases.

In 1909, Robert Millikan and his graduate student Harvey Fletcher determinedthe charge on the electron using the apparatus shown in Figure 1.3. An atomizerfrom a perfume bottle was used to spray a special kind of oil droplet having a lowvapor pressure into a sealed chamber. At the bottom of the chamber were twoparallel circular plates. The upper one of these plates was the anode and it had ahole drilled into the center of it through which the oil droplets could fall under theinfluence of gravity. The apparatus was equipped with a microscope so that Millikancould observe the rate of fall of the individual droplets. Some of the droplets becamecharged as a result of friction with the tip of the nozzle, having lost one or moreof their electrons to become positively charged cations. When Millikan applied apotential difference between the two plates at the bottom of the apparatus, thepositively charged droplets were repelled by the anode and reached an equilibrium

Cathode Anode

Cathode ray

Displacement

Positive plate

Negative plate

FIGURE 1.2Schematic diagram of a cathode ray tube similar to the one used in J. J. Thomson’s discovery of the electron.[Blatt Communications.]

4 1 THE COMPOSITION OF MATTER

FIGURE 1.3Schematic diagram of theMillikan oil drop experiment todetermine the charge of theelectron. [BlattCommunications.]

Atomizer

Positively charged plate

Negatively charged plate

Telescope

Source ofionizedradiation

+

–

state where the Coulombic repulsion of like charges and the effect of gravity wereexactly balanced, so that appropriately charged particles essentially floated there inspace inside the container. By systematically varying the potential difference appliedbetween the two metal plates and counting the number of particles that fell throughthe opening in a given period of time, Millikan was able to determine that each ofthe charged particles was some integral multiple of the electronic charge, whichhe determined to be −1.592 × 10−19 C, a measurement that is fairly close to themodern value for the charge on an electron (−1.60217733 × 10−19 C). Using thisnew value of e along with Thomson’s e/m ratio, Millikan was able to determine themass of a single electron as 9.11 × 10−28 g. The remarkable thing about the mass ofthe electron was that it was 1837 times smaller than the mass of a single hydrogenatom. Another notable feature of Millikan’s work is that it very clearly demonstratedthat the electronic charge was quantized as opposed to a continuous value. Thedifferences in the charges on the oil droplets were always some integral multiple ofthe value of the electronic charge e. Millikan’s work was not without controversy,however, as it was later discovered that some of his initial data (and Fletcher’s name)were excluded from his 1913 publication. Some modern physicists have viewed thisas a potential example of pathological science. Nevertheless, Millikan won the 1923Nobel Prize in physics for this work.

Also in 1909, one of J. J. Thomson’s students, Ernest Rutherford, working withHans Geiger and a young graduate student by the name of Ernest Marsden, per-formed his famous “gold foil experiment” in order to test the validity of the plumpudding model of the atom. Rutherford was already quite famous by this time, havingwon the 1908 Nobel Prize in chemistry for his studies on radioactivity. The fact thatcertain compounds (particularly those of uranium) underwent spontaneous radioac-tive decay was discovered by Antoine Henri Becquerel in 1896. Rutherford was thefirst to show that one of the three known types of radioactive decay involved thetransmutation of an unstable radioactive element into a lighter element and a pos-itively charged isotope of helium known as an alpha particle. Alpha particles weremany thousands of times more massive than an electron. Thus, if the plum puddingmodel of the atom were correct, where the electrons were evenly dispersed in asphere of positive charge, the heavier alpha particles should be able to blow rightthrough the atom. Geiger and Marsden assembled the apparatus shown in Figure 1.4.

A beam of alpha particles was focused through a slit in a circular screen that hada phosphorescent coating of ZnS on its interior surface. When an energetic alphaparticle struck the phosphorescent screen, it would be observed as a flash of light.In the center of the apparatus was mounted a very thin piece of metal foil (althoughit is often referred to as the gold foil experiment, it was in fact a piece of platinum foil,not gold, which was used). While the majority of alpha particles struck the screen

1.1 EARLY DESCRIPTIONS OF MATTER 5

Sourceof alphaparticles

Fluorescent screenPath of undeflected

particles

Path of deflectedparticles

Thin sheetof Pt foil FIGURE 1.4

Schematic diagram of theGeiger–Marsden experiment,also known as Rutherford’s goldfoil experiment. [BlattCommunications.]

Beam ofalphaparticles

Beam ofalphaparticles

(a)

(b)

FIGURE 1.5Atomic view of the gold foilexperiment. If the plum puddingmodel of the atom wereaccurate, a beam of massivealpha particles would penetrateright through the atom withlittle or no deflections (a). Theobservation that some of thealpha particles were deflectedbackward implied that thepositive charge in the atom mustbe confined to a highly denseregion inside the atom known asthe nucleus (b). [BlattCommunications.]

immediately behind the piece of metal foil as expected, much to the amazement ofthe researchers, a number of alpha particles were also deflected and scattered atother angles. In fact, some of the particles even deflected backward from the target.In his own words, Rutherford was said to have exclaimed: “It was quite the mostincredible event that has ever happened to me in my life. It was almost as incredibleas if you fired a 15-inch shell at a piece of tissue paper and it came back and hityou. On consideration, I realized that this scattering backwards must be the resultof a single collision, and when I made calculations I saw that it was impossible to getanything of that order of magnitude unless you took a system in which the greaterpart of the mass of an atom was concentrated in a minute nucleus.” Further calcu-lations showed that the diameter of the nucleus was about five orders of magnitudesmaller than that of the atom. This led to the rather remarkable conclusion that mat-ter is mostly empty space—with the very lightweight electrons orbiting around anincredibly dense and positively charged nucleus, as shown in Figure 1.5. As a matterof fact, 99.99999999% of the atom is devoid of all matter entirely! On the atomicscale, solidity has no meaning. The reason that a macroscopic object “feels” at allhard to us is because the atom contains a huge amount of repulsive energy, so thatwhenever we try to “push” on it, there is a whole lot of energy pushing right back.

It wasn’t until 1932 that the final piece of the atomic puzzle was put into place.After 4 years as a POW in Germany during World War I, James Chadwick returnedto England to work with his former mentor Ernest Rutherford, who had taken overJ. J. Thomson’s position as Cavendish Professor at Cambridge University. It wasnot long before Rutherford appointed Chadwick as the assistant director of thenuclear physics lab. In the years immediately following Rutherford’s discovery thatthe nucleus contained protons, which existed in the nucleus and whose charges were

6 1 THE COMPOSITION OF MATTER

equal in magnitude to the electronic charge but with the opposite sign, it was widelyknown that the nuclei of most atoms weighed more than could be explained onthe basis of their atomic numbers (the atomic number is the same as the number ofprotons in the nucleus). Some scientists even hypothesized that maybe the nucleuscontained an additional number of protons and electrons, whose equal but oppositecharges cancelled each other out but which together contributed to the increasedmass of the nucleus. Others, such as Rutherford himself, postulated the existenceof an entirely new particle having roughly the same mass as a proton but no chargeat all, a particle that he called the neutron. However, there was no direct evidencesupporting this hypothesis.

Around 1930, Bothe and Becker observed that a Be atom bombarded with alphaparticles produced a ray of neutral radiation, while Curie and Joliot showed that thisnew form of radiation had enough energy to eject protons from a piece of paraffinwax. By bombarding heavier nuclei (such as N, O, and Ar) with this radiation andcalculating the resulting cross-sections, Chadwick was able to prove that the rayscould not be attributed to electromagnetic radiation. His results were, however,consistent with a neutral particle having roughly the same mass as the proton. Inhis next experiment, Chadwick bombarded a boron atom with alpha particles andallowed the resulting neutral particles to interact with nitrogen. He also measuredthe velocity of the neutrons by allowing them to interact with hydrogen atoms andmeasuring the speed of the protons after the collision. Coupling the results of eachof his experiments, Chadwick was able to prove the existence of the neutron andto determine its mass to be 1.67 × 10−27 kg. The modern-day values for the chargesand masses of the electron, proton, and neutron are listed in Table 1.1. Chadwickwon the Nobel Prize in physics in 1935 for his discovery of the neutron.

1.2 VISUALIZING ATOMS

At the beginning of this chapter, I asked the question at what point can we dividematter into such small pieces that it is no longer perceptible to the senses. In asense, this is a philosophical question and the answer depends on what we mean asbeing perceptible to the senses. Does it literally mean that we can see the individualcomponents with our naked eye, and for that matter, what are the molecular char-acteristics of vision that cause an object to be seen or not seen? How many photonsof light does it take to excite the rod and cone cells in our eyes and cause themto fire neurons down the optic nerve to the brain? The concept of perceptibilityis somewhat vague. Is it fair to say that we still see the object when it is multipliedunder an optical microscope? What if an electron microscope is used instead? Today,we have “pictures” of individual atoms, such as those shown in Figure 1.6, made bya scanning tunneling microscope (STM) and we can manipulate individual atoms on

TABLE 1.1 Summary of the properties of subatomic particles.

Particle Mass (kg) Mass (amu) Charge (C)

Electron 9.10938291 × 10−31 0.00054857990946 −1.602176565 × 10−19

Proton 1.672621777 × 10−27 1.007276466812 1.602176565 × 10−19

Neutron 1.674927351 × 10−27 1.00866491600 0

Source: The NIST Reference on Constants, Units, and Uncertainty(http://physics.nist.gov, accessed Nov 3, 2013).

1.2 VISUALIZING ATOMS 7

FIGURE 1.6Scanning tunneling microscopyof the surface of the (110) faceof a nickel crystal. [Imageoriginally created by IBMCorporation.]

a surface in order to create new chemical bonds at the molecular level using atomicforce microscopy (AFM).

But are we really capable of actually seeing an individual atom? Technically speak-ing, we cannot see anything smaller than the shortest wavelength of light with whichwe irradiate it. The shortest wavelength that a human eye can observe is about400 nm, or 4 × 10−7 m. As the diameter of an atom is on the scale of 10−11 m andthe diameter of a typical nucleus is even smaller at 10−15 m, it is therefore impossiblefor us to actually see an atom. However, we do have ways of visualizing atoms. Ascanning tunneling microscope, like the one shown in Figure 1.7, works by moving anexceptionally sharp piezoelectric tip (often only one atom thick at its point) acrossthe surface of a conductive solid, such as a piece of crystalline nickel in an evacuated

Control voltages for piezotube

Tunnelingcurrent amplifier

Tunnelingvoltage

Data processingand display

Tip

Sample

Pie

zotu

be

tub

ew

ith

ele

ctro

des

Distance controland scanning unit

FIGURE 1.7Schematic diagram of a scanningtunneling microscope (STM).[Blatt Communications.]

8 1 THE COMPOSITION OF MATTER

chamber. When a small voltage is applied to the tip of the STM, a tunneling currentdevelops whenever the tip is close to the surface of a Ni atom. This tunneling cur-rent is proportional to the distance between the tip of the probe and the atoms onthe surface of the crystal. By adjusting the STM so that the tunneling current is aconstant, the tip will move up and down as it crosses the surface of the crystal andencounters electron density around the nuclei of the nickel atoms. A computer isthen used to map out the three-dimensional contour of the nickel surface and tocolor it different shades of blue in this case, depending on the distance that the tiphas moved. The STM can also be used to pick up atoms and to move them aroundon a surface. In fact, the scientists who invented the STM (Gerd Binnig and HeinrichRohrer, both of whom shared the 1986 Nobel Prize in physics) used an STM to spellout the name of their sponsoring company IBM by moving around 35 individual Xeatoms affixed to a Ni surface.

The AFM, which has a smaller resolution than the STM, has the advantage ofbeing able to visualize nonconductive surfaces. It functions using a cantilever witha very narrow tip on the end. Instead of interacting directly with the electrons, itvibrates at a specific frequency and when it encounters an atom, the frequency ofthe vibration changes, allowing one to map out the contour of the surface.

1.3 THE PERIODIC TABLE

While chemistry is the study of matter and its interconversions, inorganic chem-istry is that subdiscipline of chemistry which deals with the physical properties andchemistry of all the elements, with the singular exclusion of carbon. An element isdefined by the number of protons in its nucleus. There are 90 naturally occurringelements (all of the elements up to and including atomic number 92, with the excep-tion of Tc (atomic number 43) and Pm (atomic number 61)). However, if all of theman-made elements are included, a total of 118 elements are currently known toexist. It has long been known that many of the elements had similar valences andchemical reactivity. In the late 1860s and early 1870s, Dmitri Mendeleev and JuliusLothar Meyer independently discovered that the elements could be arranged into atable in an orderly manner such that their properties would follow a periodic law. Inhis book Principles of Chemistry, Mendeleev wrote: “I began to look about and writedown the elements with their atomic weights and typical properties, analogous ele-ments and like atomic weights on separate cards, and this soon convinced me thatthe properties of elements are in periodic dependence upon their atomic weights.”His resulting periodic table organized the elements into eight broad categories (orGruppe) according to increasing atomic mass, as shown in Figure 1.8.

At the time of publication in 1871, only about half of the elements known todayhad yet to be discovered. One of the reasons that Mendeleev’s version of the peri-odic table became so popular was that he left gaps in his table for as yet undiscoveredelements. When the next element on his pile of cards did not fit the periodic trend,he placed the element in the next group that bore resemblance to it, figuring that anew element would someday be discovered with properties appropriate to fill in thegap. Furthermore, by interpolation from the properties of those elements on eitherside of the gaps, Mendeleev could use his table to make predictions about the reac-tivity of the unknown elements. In particular, Mendeleev predicted the properties ofgallium, scandium, and germanium, which were discovered in 1875, 1879, and 1886,respectively, and he did so with incredible accuracy. For example, Table 1.2 lists theproperties of germanium that Mendeleev predicted 15 years before its discoveryand compares them with the modern-day values. It is this predictive capacity thatmakes the periodic table one of the most powerful tools in chemistry. Mendeleev’speriodic table was organized according to increasing mass. With the discovery of

1.4 THE STANDARD MODEL 9

1

Gruppo I.

Rei

bco

2

3

4

5

6

7

8

9

10

11

12

—R1O

Gruppo II.

II=1

Li=7

K=39

Bo=9.4

Na=23

Rb=85

(Cu=63)

Sr=87

Zn=65

?Yt=88

—=68

Zr=90

—=72

Nb=94

As=75

Mo=96

So=78

—=100

Br=80

Cs=183

(Ag=108)

Ba=187

Cd=112

?Di=188

In=113

?Co=140

Sn=118

—

Sb=122

—

To=125

—

J=127

—

(Ag=199)

—

Hg=200

—

Tl=204

Th=231

Pb=207

—

Bi=208

U=240

—

—

—

— — — —

— — — —

—

(—)

—

—

?Er=178

—

?La=180

—

Ta=182

— —

W=184 —

—

Ca=40

Mg=24

—=44 Ti=48

Al=27,8 Si=28

V=51

P=31

Cr=52

S=32

Mn=55

Cl=35,5

Fo=56, Co=59,Ni=59, Cu=63.

Ru=104, Rh=104,Pd=106, Ag=108.

Os=195, Ir=197,Pt=198, Au=199.

B=11 C=12 N=14 O=16 F=19

—RO

Gruppo III.—

R1O3

Gruppo IV.

RO1RH4

Gruppo V.

R1O5RH2

Gruppo VI.

RO3RH2

Gruppo VII.

R2O7RH

Gruppo VIII.

RO4—

FIGURE 1.8Dmitri Mendeleev’s periodic table (1871).

TABLE 1.2 Properties of the element germanium (eka-silicon) aspredicted by Mendeleev in 1871 and the experimental values measuredafter its discovery in 1886.

Physical and Chemical Properties Predicted Actual

Atomic mass (amu) 72 72.3Density (g/cm3) 5.5 5.47Specific heat (J/g ∘C) 0.31 0.32Atomic volume (cm3/mol) 13 13.5Formula of oxide RO2 GeO2Oxide density (g/cm3) 4.7 4.70Formula of chloride RCl4 GeCl4Boiling point of chloride (∘C) <100 86Density of chloride (g/cm3) 1.9 1.84

the nucleus in the early 1900s, the modern form of the periodic table is insteadorganized according to increasing atomic number. Furthermore, as we shall see ina later chapter, the different blocks of groups in the periodic table quite naturallyreflect the quantum nature of atomic structure.

1.4 THE STANDARD MODEL

As an atom is the smallest particle of an element that retains the essential chemi-cal properties of that substance, one might argue that atoms are the fundamentalbuilding blocks of matter. However, as we have already seen, the atom itself is notindivisible, as Democritus believed. As early as the 1930s, it was recognized thatthere were other fundamental particles of matter besides the proton, the neutron,and the electron. The muon was discovered by Carl Anderson and Seth Nedermeyerin 1936. Anderson was studying some of the properties of cosmic radiation when henoticed a new type of negatively charged particle that was deflected by a magnetic

10 1 THE COMPOSITION OF MATTER

field to a lesser extent than was the electron. The muon has the same charge as theelectron, but it has a mass that is about 200 times larger, which explains why it wasnot deflected as much as an electron. Muons are not very stable particles, however;they have a mean lifetime of only 2.197 × 10−6 s. Muons occur when cosmic radia-tion interacts with matter and are also generated in large quantities in modern-dayparticle accelerators. As it turns out, however, the muon represents just one strangebeast in a whole zoo of subatomic particles that include hadrons, baryons, neutrinos,mesons, pions, quarks, and gluons—to name just a few, begging the question of justhow divisible is matter and what (if anything) is fundamental?

The standard model of particle physics was developed in the 1970s followingexperimental verification of quarks. The standard model incorporates the theoryof general relativity and quantum mechanics in its formulation. According to thestandard model, there are a total of 61 elementary particles, but ordinary mat-ter is composed of only six types (or flavors) of leptons and six types of quarks.Leptons and quarks are themselves examples of fermions, or particles that have aspin quantum number of 1/2 and obey the Pauli exclusion principle. It is the variouscombinations of these fundamental particles that make up all of the larger particles,such as protons and neutrons. Thus, for example, a proton is composed of twoup quarks and one down quark (pronounced in such a way that it rhymes with theword “cork”). Electrons, muons, and neutrinos are all examples of leptons. Both lep-tons and quarks can be further categorized into one of three different generations,as shown in Figure 1.9. First-generation particles, such as the electron and the upand down quarks that make up protons and neutrons, are stable, whereas second-and third-generation particles exist for only brief periods of time following theirgeneration. Furthermore, each of the 12 fundamental particles has a correspondingantiparticle. An antiparticle has the same mass as a fundamental particle, but exactlythe opposite electrical charge. The antiparticle of the electron, for instance, is thepositron, which has a mass of roughly 9.109 × 10−31 kg like the electron, but an elec-trical charge of +1.602 × 10−19 C or +1e. Whenever a particle and its antiparticlecollide, they annihilate each other and create energy. In addition to the 12 fundamen-tal particles and their antiparticles, there are also force-carrying particles, such as

FIGURE 1.9The 12 fundamental particles(leptons in green and quarks inpurple) and the force-carryingparticles (in red) that comprisethe standard model of particlephysics. The newly discoveredHiggs boson, which explains whysome particles have mass, isshown at the upper right.[Attributed to MissMJ under theCreative Commons Attribution3.0 Unported license (accessedOctober 17, 2013).]

Up

DownQua

rks

Lep

tons

Gau

ge b

oson

s

Electron

Electronneutrino

Muonneutrino

Tauneutrino

Muon

Strange Bottom

Tau

Charm Top Gluon

Photon

Z boson

W boson

Higgsboson

Mass

Spin

Charge

≈2.3 MeV/c2

1/2

2/3

≈4.8 MeV/c2

0.511 MeV/c2

<2.2 eV/c2

105.7 MeV/c2 1.777 GeV/c2 91.2 GeV/c2

≈95 MeV/c2 ≈4.18 GeV/c2

1/2

–1/3

–1

1/2

0

1/2

<0.17 MeV/c2 <15.5 MeV/c2

0

1/2

0

1/2

80.4 GeV/c2

±1

1

–1

1/2

–1

1/2

0

1

1/2

–1/3

1/2

–1/3

≈1.275 GeV/c2 ≈173.07 GeV/c2 ≈126 GeV/c2

1/2

2/3

1/2

2/3

1

0

0

0

0

1

0

0

1.4 THE STANDARD MODEL 11

Up Charm Top

Down Strange Bottom

FIGURE 1.10Cartoon representation of thesix different flavors of quarks(arranged into pairs by theirgenerations). The numbersinside each quark represent theirrespective charges. [BlattCommunications.]

the photon, which carries the electromagnetic force. Collectively, the 12 fundamen-tal particles of matter are known as fermions because they all have a spin of 1/2, whilethe force-carrying particles are called bosons and have integral spin. The differenttypes of particles in the standard model are illustrated in Figure 1.9.

There are four types of fundamental forces in the universe, arranged here inorder of increasing relative strength: (i) gravity, which affects anything with mass;(ii) the weak force, which affects all particles; (iii) electromagnetism, which affectsanything with charge; and (iv) the strong force, which only affects quarks. There aresix quarks, as shown in Figure 1.10, and they are arranged as pairs of particles intothree generations. The first quark in each pair has a spin of +2/3, while the secondone has a spin of −1/3.

Quarks also carry what is known as color charge, which is what causes themto interact with the strong force. Color charges can be represented as red, blue,or green, by analogy with the RGB additive color model, although this is really justa nonmathematical way of representing their quantum states. Like colors tend torepel one another and opposite colors attract. Because of a phenomenon knownas color confinement, an individual quark has never been directly observed becausequarks are always bound together by gluons to form hadrons, or combinations ofquarks. Baryons consist of a triplet of quarks, as shown in Figure 1.11. Protons andneutrons are examples of baryons that form the basic building blocks of the nucleus.Mesons, such as the kaon and pion, are composed of a pair of particles: a quark andan antiquark.

Unlike quarks, which always appear together in composite particles, the lep-tons are solitary creatures and prefer to exist on their own. Furthermore, theleptons do not carry color charge and they are not influenced by the strong force.The electron, muon, and tau are all negatively charged particles (with a charge of−1.602 × 10−19 C), differing only in their masses. Neutrinos, on the other hand,have no charge and are particularly difficult to detect. The electron neutrino hasan extremely small mass and can pass through ordinary matter. The heavier leptons(the muon and the tau) are not found in ordinary matter because they decay veryquickly into lighter leptons, whereas electrons and the three kinds of neutrinos arestable.

1.6 fm

Proton Neutron

FIGURE 1.11Representation of a proton,which is made from two upand one down quarks, and aneutron, which is made fromone up and two down quarks.The diameter of the protonand neutron are roughlydrawn to scale; however, thequarks are about 1000 timessmaller than a proton or aneutron. [BlattCommunications.]