principles of inorganic chemistry pdf

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PRINCIPLES OF
INORGANIC
CHEMISTRY

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PRINCIPLES OF
INORGANIC
CHEMISTRY
Brian W. Pfennig

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Copyright © 2015 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:
Pfennig, Brian William.
Principles of inorganic chemistry / Brian W. Pfennig.
pages cm
Includes 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 2015
546–dc23
2014043250
Cover image :Courtesy of the author
Typeset 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

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Contents

Preface xi
Acknowledgements xv
Chapter 1

Chapter 2

| The Composition of Matter
1.1 Early Descriptions of Matter
1.2 Visualizing Atoms 6
1.3 The Periodic Table 8
1.4 The Standard Model 9
Exercises 12
Bibliography 13

1
1

| The Structure of the Nucleus
2.1 The Nucleus 15
2.2 Nuclear Binding Energies 16
2.3 Nuclear Reactions: Fusion and Fission 17
2.4 Radioactive Decay and the Band of Stability
2.5 The Shell Model of the Nucleus 27
2.6 The Origin of the Elements 30
Exercises 38
Bibliography 39

15

22

Chapter 3

| A Brief Review of Quantum Theory
3.1 The Wavelike Properties of Light 41
3.2 Problems with the Classical Model of the Atom 48
3.3 The Bohr Model of the Atom 55
3.4 Implications of Wave-Particle Duality 58
3.5 Postulates of Quantum Mechanics 64
3.6 The Schrödinger Equation 67
3.7 The Particle in a Box Problem 70
3.8 The Harmonic Oscillator Problem 75
Exercises 78
Bibliography 79

41

Chapter 4

| Atomic Structure
4.1 The Hydrogen Atom 81
4.1.1
The Radial Wave Functions 82
4.1.2
The Angular Wave Functions 86
4.2 Polyelectronic Atoms 91
4.3 Electron Spin and the Pauli Principle 93
4.4 Electron Configurations and the Periodic Table
4.5 Atomic Term Symbols 98

81

96

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CONTENTS

4.5.1
Extracting Term Symbols Using Russell–Saunders Coupling 100

4.5.2
Extracting Term Symbols Using jj Coupling 102
4.5.3
Correlation Between RS (LS) Coupling and jj Coupling 104
4.6 Shielding and Effective Nuclear Charge 105
Exercises 107
Bibliography 108
Chapter 5

| Periodic Properties of the Elements
5.1 The Modern Periodic Table 109
5.2 Radius 111
5.3 Ionization Energy 118
5.4 Electron Affinity 121
5.5 The Uniqueness Principle 122
5.6 Diagonal Properties 124
5.7 The Metal–Nonmetal Line 125
5.8 Standard Reduction Potentials 126
5.9 The Inert-Pair Effect 129
5.10 Relativistic Effects 130
5.11 Electronegativity 133
Exercises 136
Bibliography 137

109

Chapter 6

| An Introduction to Chemical Bonding
6.1 The Bonding in Molecular Hydrogen 139

6.2 Lewis Structures 140
6.3 Covalent Bond Lengths and Bond Dissociation Energies
6.4 Resonance 146
6.5 Polar Covalent Bonding 149
Exercises 153
Bibliography 154

139

144

Chapter 7

| Molecular Geometry
7.1 The VSEPR Model 155
7.2 The Ligand Close-Packing Model 170
7.3 A Comparison of the VSEPR and LCP Models 175
Exercises 176
Bibliography 177

155

Chapter 8

| Molecular Symmetry
8.1 Symmetry Elements and Symmetry Operations
8.1.1
Identity, E 180
8.1.2
Proper Rotation, Cn 181

8.1.3
Reflection, 𝜎 182
8.1.4
Inversion, i 183
8.1.5
Improper Rotation, Sn 183
8.2 Symmetry Groups 186
8.3 Molecular Point Groups 191
8.4 Representations 195
8.5 Character Tables 202
8.6 Direct Products 209
8.7 Reducible Representations 214
Exercises 222
Bibliography 224

179
179

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vii

CONTENTS

Chapter 9

Chapter 10

Chapter 11

| Vibrational Spectroscopy
9.1 Overview of Vibrational Spectroscopy 227
9.2 Selection Rules for IR and Raman-Active Vibrational Modes 231
9.3 Determining the Symmetries of the Normal Modes of Vibration 235
9.4 Generating Symmetry Coordinates Using the Projection Operator Method
9.5 Resonance Raman Spectroscopy 252
Exercises 256
Bibliography 258
| Covalent Bonding
10.1 Valence Bond Theory 259
10.2 Molecular Orbital Theory: Diatomics 278
10.3 Molecular Orbital Theory: Polyatomics 292
10.4 Molecular Orbital Theory: pi Orbitals 305
10.5 Molecular Orbital Theory: More Complex Examples
10.6 Borane and Carborane Cluster Compounds 325
Exercises 334
Bibliography 336
| Metallic Bonding
11.1 Crystalline Lattices 339
11.2 X-Ray Diffraction 345
11.3 Closest-Packed Structures 350
11.4 The Free Electron Model of Metallic Bonding 355
11.5 Band Theory of Solids 360
11.6 Conductivity in Solids 374
11.7 Connections Between Solids and Discrete Molecules
Exercises 384
Bibliography 388

227

243

259

317

339

383

Chapter 12

| Ionic Bonding
12.1 Common Types of Ionic Solids 391
12.2 Lattice Enthalpies and the Born–Haber Cycle 398
12.3 Ionic Radii and Pauling’s Rules 404
12.4 The Silicates 417
12.5 Zeolites 422
12.6 Defects in Crystals 423
Exercises 426
Bibliography 428

391

Chapter 13

| Structure and Bonding
13.1 A Reexamination of Crystalline Solids 431

13.2 Intermediate Types of Bonding in Solids 434
13.3 Quantum Theory of Atoms in Molecules (QTAIM) 443
Exercises 449
Bibliography 452

431

Chapter 14

| Structure and Reactivity
14.1 An Overview of Chemical Reactivity 453
14.2 Acid–Base Reactions 455
14.3 Frontier Molecular Orbital Theory 467

453

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CONTENTS

14.4 Oxidation–Reduction Reactions 473
14.5 A Generalized View of Molecular Reactivity
Exercises 480
Bibliography 481

475

Chapter 15

| An Introduction to Coordination Compounds
15.1 A Historical Overview of Coordination Chemistry 483
15.2 Types of Ligands and Nomenclature 487
15.3 Stability Constants 490
15.4 Coordination Numbers and Geometries 492
15.5 Isomerism 498
15.6 The Magnetic Properties of Coordination Compounds 501
Exercises 506
Bibliography 508

Chapter 16

| Structure, Bonding, and Spectroscopy of Coordination Compounds
509
16.1 Valence Bond Model 509
16.2 Crystal Field Theory 512
16.3 Ligand Field Theory 525
16.4 The Angular Overlap Method 534
16.5 Molecular Term Symbols 541
16.5.1 Scenario 1—All the Orbitals are Completely Occupied 546
16.5.2 Scenario 2—There is a Single Unpaired Electron in One of the Orbitals 546
16.5.3 Scenario 3—There are Two Unpaired Electrons in Two Different Orbitals 546
16.5.4 Scenario 4—A Degenerate Orbital is Lacking a Single Electron 547
16.5.5 Scenario 5—There are Two Electrons in a Degenerate Orbital 547
16.5.6 Scenario 6—There are Three Electrons in a Triply Degenerate Orbital 547
16.6 Tanabe–Sugano Diagrams 549
16.7 Electronic Spectroscopy of Coordination Compounds 554

16.8 The Jahn–Teller Effect 564
Exercises 566
Bibliography 570

Chapter 17

| Reactions of Coordination Compounds
17.1 Kinetics Overview 573
17.2 Octahedral Substitution Reactions 577
17.2.1 Associative (A) Mechanism 578
17.2.2 Interchange (I) Mechanism 579
17.2.3 Dissociative (D) Mechanism 580
17.3 Square Planar Substitution Reactions 585
17.4 Electron Transfer Reactions 593
17.5 Inorganic Photochemistry 606
17.5.1 Photochemistry of Chromium(III) Ammine Compounds 607
17.5.2 Light-Induced Excited State Spin Trapping in Iron(II) Compounds 611
17.5.3 MLCT Photochemistry in Pentaammineruthenium(II) Compounds 615
17.5.4 Photochemistry and Photophysics of Ruthenium(II) Polypyridyl Compounds
Exercises 622
Bibliography 624

Chapter 18

| Structure and Bonding in Organometallic Compounds
18.1 Introduction to Organometallic Chemistry 627
18.2 Electron Counting and the 18-Electron Rule 628

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483

573

617

627


ix

CONTENTS

18.3 Carbonyl Ligands 631
18.4 Nitrosyl Ligands 635
18.5 Hydride and Dihydrogen Ligands 638
18.6 Phosphine Ligands 640
18.7 Ethylene and Related Ligands 641
18.8 Cyclopentadiene and Related Ligands 645
18.9 Carbenes, Carbynes, and Carbidos 648
Exercises 651
Bibliography 654
Chapter 19

| Reactions of Organometallic Compounds
19.1 Some General Principles 655
19.2 Organometallic Reactions Involving Changes at the Metal 656
19.2.1 Ligand Substitution Reactions 656
19.2.2 Oxidative Addition and Reductive Elimination 658

19.3 Organometallic Reactions Involving Changes at the Ligand 664
19.3.1 Insertion and Elimination Reactions 664
19.3.2 Nucleophilic Attack on the Ligands 667
19.3.3 Electrophilic Attack on the Ligands 669
19.4 Metathesis Reactions 670
19.4.1 𝜋-Bond Metathesis 670
19.4.2 Ziegler–Natta Polymerization of Alkenes 671
19.4.3 𝜎-Bond Metathesis 671
19.5 Commercial Catalytic Processes 674
19.5.1 Catalytic Hydrogenation 674
19.5.2 Hydroformylation 674
19.5.3 Wacker–Smidt Process 676
19.5.4 Monsanto Acetic Acid Process 677
19.6 Organometallic Photochemistry 678
19.6.1 Photosubstitution of CO 678
19.6.2 Photoinduced Cleavage of Metal–Metal Bonds 680
19.6.3 Photochemistry of Metallocenes 682
19.7 The Isolobal Analogy and Metal–Metal Bonding in Organometallic Clusters
Exercises 689
Bibliography 691

655

683

Appendix: A Derivation of the Classical Wave Equation
Bibliography 694

693

Appendix: B Character Tables
Bibliography 708

695

Appendix: C Direct Product Tables
Bibliography 713

709

Appendix: D Correlation Tables
Bibliography 721

715

Appendix: E

723

The 230 Space Groups
Bibliography 728

Index

729

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Preface

This book was written as a result of the perceived need of mine and several other
colleagues for a more advanced physical inorganic text with a strong emphasis on
group theory and its applications. Many of the inorganic textbooks on the market are
either disjointed—with one chapter completely unrelated to the next—or encyclopedic, so that the student of inorganic chemistry is left to wonder if the only way to
master the field is to memorize a large body of facts. While there is certainly some
merit to a descriptive approach, this text will focus on a more principles-based pedagogy, teaching students how to rationalize the structure and reactivity of inorganic
compounds—rather than relying on rote memorization.
After many years of teaching the inorganic course without a suitable text, I
decided to write my own. Beginning in the summer of 2006, I drew on a variety of
different sources and tried to pull together bits and pieces from different texts and
reference books, finishing a first draft (containing 10 chapters) in August, 2007. I used
this version of the text as supplementary reading for a few years before taking up the
task of writing again in earnest in 2012, subdividing and expanding the upon original
10 chapters to the current 19, adding references and more colorful illustrations, and
including problems at the ends of each chapter.
The book was written with my students in mind. I am a teacher first and a scientist second. I make no claims about my limited knowledge of this incredibly expansive
field. My main contribution has been to collect material from various sources and to
organize and present it in a pedagogically coherent manner so that my students can
understand and appreciate the principles underlying such a diverse and interesting
subject as inorganic chemistry.
The book is organized in a logical progression. Chapter 1 provides a basic
introduction to the composition of matter and the experiments that led to the
development of the periodic table. Chapter 2 then examines the structure and
reactivity of the nucleus. Chapter 3 follows with a basic primer on wave-particle

duality and some of the fundamentals of quantum mechanics. Chapter 4 discusses
the solutions to the Schrödinger equation for the hydrogen atom, the Pauli principle,
the shapes of the orbitals, polyelectronic wave functions, shielding, and the quantum mechanical basis for the underlying structure of the periodic table. Chapter 5
concludes this section of the text by examining the various periodic trends that
influence the physical and chemical properties of the elements. Chapter 6 then
begins a series of chapters relating to chemical bonding by reviewing the basics
of Lewis structures, resonance, and formal charge. Chapter 7 is devoted to the
molecular geometries of molecules and includes not only a more extensive treatment of the VSEPR model than most other textbooks but it also presents the ligand
close-packing model as a complementary model for the prediction of molecular
geometries. Symmetry and group theory are introduced in detail in Chapter 8 and
will reappear as a recurring theme throughout the remainder of the text. Unlike
most inorganic textbooks on the market, ample coverage is given to representations of groups, reducing representations, direct products, the projection operator,
and applications of group theory. Chapter 9 focuses on one of the applications of
group theory to the vibrational spectroscopy of molecules, showing how symmetry
coordinates can be used to approximate the normal modes of vibration of small
molecules. The selection rules for IR and Raman spectroscopy are discussed and

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xii

PREFACE

the chapter closes with a brief introduction to resonance Raman spectroscopy. The
next three chapters focus on the three different types of chemical bonding: covalent,
metallic, and ionic bonding. Chapter 10 examines the valence bond and molecular
orbital models, which expands upon the application of group theory to chemical
problems. Chapter 11 then delves into metallic bonding, beginning with a primer on

crystallography 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 coverage of the silicates and zeolites. The structure of solids is reviewed in greater detail
in Chapter 13, which explores the interface between the different types of chemical bonding in both solids and discrete molecules. Switching gears for a while from
structure and bonding to chemical reactivity, Chapter 14 introduces the two major
types of chemical reactions: acid–base reactions and oxidation–reduction reactions.
In addition to the usual coverage of hard–soft acid–base theory, this chapter also
examines a more general overview of chemical reactivity that is based on the different topologies of the MOs involved in chemical transformations. This chapter
also serves as a bridge to the transition metals. Chapter 15 presents an introduction to coordination compounds and their thermodynamic and magnetic properties.
Chapter 16 examines the structure, bonding, and electronic spectroscopy of coordination compounds, making extensive use of group theory. Chapter 17 investigates
the reactions of coordination compounds in detail, including a section on inorganic
photochemistry. Finally, the text closes with two chapters on organometallic chemistry: Chapter 18 looks at the different types of bonding in organometallics from an
MO point of view, while Chapter 19 presents of a survey of organometallic reaction
mechanisms, catalysis, and organometallic photochemistry and then concludes with
connections to main group chemistry using the isolobal analogy. Throughout the
textbook, there is a continual building on earlier material, especially as it relates to
group theory and MOT, which serve as the underlying themes for the majority of
the book.
This text was originally written for undergraduate students taking an advanced
inorganic chemistry course at the undergraduate level, although it is equally suitable as a graduate-level text. I have written the book with the more capable and
intellectually curious students in my undergraduate courses in mind. The prose is
rather informal and directly challenges the student to examine each new experimental observation in the context of previously introduced principles of inorganic
chemistry. Students should appreciate the ample number of solved sample problems
interwoven throughout the body of the text and the clear, annotated figures and
illustrations. The end-of-chapter problems are designed to invoke an active wrangling
with the material and to force students to examine the data from several different
points of view. While the text is very physical in emphasis, it is not overly mathematical and thorough derivations are provided for the more important physical
relationships. It is my hope that students will not only enjoy using this textbook in
their classes but will read and reread it again as a valuable reference book throughout
the remainder of their chemical careers.

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

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xiii

PREFACE

dedicated e-mail account for just such a purpose at I look
forward to hearing your suggestions.
BRIAN W. PFENNIG
Lancaster, PA
June, 2014

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Acknowledgments

This book would not have been possible without the generous contributions of
others. I am especially indebted to my teachers and mentors over the years who
always 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 of
the 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 and
advice 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 your
encouragement.
There is little original content in this inorganic text that cannot be found elsewhere. My only real contribution has been to crystallize the content of many other
authors and to organize it in a way that hopefully makes sense to the student. I
have therefore drawn heavily on the following inorganic texts: Inorganic Chemistry
(Miessler and Tarr), Inorganic Chemistry (Huheey, Keiter, and Keiter), Chemical Applications of Group Theory (Cotton), Molecular Symmetry and Group Theory (Carter),
Symmetry and Spectroscopy (Harris and Bertulucci), Problems in Molecular Orbital Theory (Albright and Burdett), Chemical Bonding and Molecular Geometry (Gillespie and
Hargittai), Ligand Field Theory (Figgis and Hitchman), Physical Chemistry (McQuarrie
and 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 the
preparation of my manuscript, especially to the many people who have reviewed
sample chapters of the textbook or who have generously provided permission to
use their figures. I am especially indebted to Lori Blatt at Blatt Communications for
producing many of the amazing illustrations in the text and to Aubrey Paris for her
invaluable 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 to
write a volume of this magnitude. I am especially indebted to the intellectual interactions 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 acknowledge

the most important people in my life, without whose undying support and tolerance
I would never have been able to complete this work—my family. I am especially
grateful 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 to
my incredibly talented daughter Rachel, who more than anyone has suffered from
lack of my attention as I struggled to complete this work.

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The Composition
of 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 a
sense, chemistry is a study of the physical world in which we live. But how much do
we really know about the fundamental structure of matter and its relationship to the
larger macroscopic world? I have in my rock collection, which I have had since I was a
boy, a sample of the mineral cinnabar, which is several centimeters across and weighs
about 10 g. Cinnabar is a reddish granular solid with a density about eight times that
of water and the chemical composition mercuric sulfide. Now suppose that some
primal instinct suddenly overcame me and I were inclined to demolish this precious
talisman from my childhood. I could take a hammer to it and smash it into a billion
little pieces. Choosing the smallest of these chunks, I could further disintegrate the
material in a mortar and pestle, grinding it into ever finer and finer grains until I was
left with nothing but a red powder (in fact, this powder is known as vermilion and
has 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 the
same material that I started with—that is, it would have precisely the same chemical
and physical properties as the original. I might therefore wonder to myself if there is
some inherent limitation as to how finely I can divide the substance or if this is simply
limited by the tools at my disposal. With the proper equipment, would I be able to
continue dividing the compound into smaller and smaller pieces until ultimately I
obtained the unit cell, or smallest basic building block of the crystalline structure of
HgS, as shown in Figure 1.1? For that matter (no pun intended), is there a way for
me 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, at
what point does it become impossible (or at the very least impractical) for me to
continue to measure the mass of the individual grains or for them to no longer be
perceptible to my senses (even if placed under an optical microscope)? The ancient
philosopher Democritus (ca 460–370 BC) was one of the first to propose that matter
is constructed of tiny indivisible particles known as atomos (or atoms), the different
varieties (sizes, shapes, masses, etc.) of which form the fundamental building blocks

of 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.

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2

1 THE COMPOSITION OF MATTER

(a)

(b)

FIGURE 1.1
Three examples of the same
chemical material ranging from
the macroscopic to the atomic
scale: (a) the mineral cinnabar,
(b) vermilion powder, and (c) the
unit cell of mercuric sulfide.
[Vermilion pigment photo
courtesy of Kremer
Pigments, Inc.]

(c)

finely I can continue to carve up my little chunk of cinnabar. As far back as the Middle

Ages, the alchemists learned that one could decompose a sample of HgS by heating
it up in a crucible. At temperatures above 580 ∘ C, the heat drives off the sulfur and
leaves behind a pool of silvery liquid mercury. Eventually, I could break the molecule
itself apart into its individual atoms, but then I could go no further.

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3

1.1 EARLY DESCRIPTIONS OF MATTER

Or could I? In the late 1800s, scientists discovered that if they constructed a hollow glass tube with an anode in one end and a cathode in the other and pumped out
as much of the air as they could, an electrical discharge between the two electrodes
could produce a faint glow within the tube. Later, cathode ray tubes, as they became
to be known, were more sophisticated and contained a phosphorescent coating in
one end of the tube. William Crookes demonstrated that the rays were emitted
from the cathode and that they traveled in straight lines and could not bend around
objects in their path. A while later, Julius Plücker was able to show that a magnet
applied to the exterior of the cathode ray tube could change the position of the
phosphorescence. Physicists knew that the cathode ray carried a negative charge (in
physics, the cathode is the negatively charged electrode and because the beam originated from the cathode, it must therefore be negatively charged). However, they did
not know whether the charge and the ray could be separated from one another. In
1897, Joseph J. Thomson finally resolved the issue by demonstrating that both the
beam and the charged particles could be bent by an electrical field that was applied
perpendicular to the path of the beam, as shown in Figure 1.2. By systematically varying the electric field strength and measuring the angle of deflection, Thomson was
able to determine the charge-to-mass (e/m) ratio of the particles, which he called
corpuscles and which are now known as electrons. Thomson measured the e/m ratio
as −1.76 × 108 C/g, a value that was at least a thousand times larger than the one

expected 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 a
typical atom. In other words, the atom was not indivisible, and could itself be broken down into smaller components, with the electron being one of these subatomic
particles. As a result of his discovery, Thomson proposed the so-called plum pudding model of the atom, where the atom consisted of one or more of these tiny
electrons distributed in a sea of positive charge, like raisins randomly dispersed in a
gelatinous pudding. Thomson was later awarded the 1906 Nobel Prize in physics for
his discovery of the electron and his work on the electrical conductivity of gases.
In 1909, Robert Millikan and his graduate student Harvey Fletcher determined
the charge on the electron using the apparatus shown in Figure 1.3. An atomizer
from a perfume bottle was used to spray a special kind of oil droplet having a low
vapor pressure into a sealed chamber. At the bottom of the chamber were two
parallel circular plates. The upper one of these plates was the anode and it had a
hole drilled into the center of it through which the oil droplets could fall under the
influence of gravity. The apparatus was equipped with a microscope so that Millikan
could observe the rate of fall of the individual droplets. Some of the droplets became
charged as a result of friction with the tip of the nozzle, having lost one or more
of their electrons to become positively charged cations. When Millikan applied a
potential difference between the two plates at the bottom of the apparatus, the
positively charged droplets were repelled by the anode and reached an equilibrium

Displacement
Negative plate

Positive plate
Cathode

Cathode ray

Anode

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

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4

1 THE COMPOSITION OF MATTER

Atomizer

+
Positively charged plate

FIGURE 1.3
Schematic diagram of the
Millikan oil drop experiment to
determine the charge of the
electron. [Blatt
Communications.]

Source of
ionized
radiation

Telescope

–

Negatively charged plate

state where the Coulombic repulsion of like charges and the effect of gravity were
exactly balanced, so that appropriately charged particles essentially floated there in
space inside the container. By systematically varying the potential difference applied
between the two metal plates and counting the number of particles that fell through
the opening in a given period of time, Millikan was able to determine that each of
the charged particles was some integral multiple of the electronic charge, which
he determined to be −1.592 × 10−19 C, a measurement that is fairly close to the
modern value for the charge on an electron (−1.60217733 × 10−19 C). Using this
new value of e along with Thomson’s e/m ratio, Millikan was able to determine the
mass of a single electron as 9.11 × 10−28 g. The remarkable thing about the mass of
the electron was that it was 1837 times smaller than the mass of a single hydrogen
atom. Another notable feature of Millikan’s work is that it very clearly demonstrated
that the electronic charge was quantized as opposed to a continuous value. The
differences in the charges on the oil droplets were always some integral multiple of
the 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 this
as a potential example of pathological science. Nevertheless, Millikan won the 1923
Nobel Prize in physics for this work.
Also in 1909, one of J. J. Thomson’s students, Ernest Rutherford, working with
Hans Geiger and a young graduate student by the name of Ernest Marsden, performed his famous “gold foil experiment” in order to test the validity of the plum
pudding model of the atom. Rutherford was already quite famous by this time, having
won the 1908 Nobel Prize in chemistry for his studies on radioactivity. The fact that
certain compounds (particularly those of uranium) underwent spontaneous radioactive decay was discovered by Antoine Henri Becquerel in 1896. Rutherford was the
first to show that one of the three known types of radioactive decay involved the
transmutation of an unstable radioactive element into a lighter element and a positively charged isotope of helium known as an alpha particle. Alpha particles were

many thousands of times more massive than an electron. Thus, if the plum pudding
model of the atom were correct, where the electrons were evenly dispersed in a
sphere of positive charge, the heavier alpha particles should be able to blow right
through 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 had
a phosphorescent coating of ZnS on its interior surface. When an energetic alpha
particle 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 (although
it 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

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5

1.1 EARLY DESCRIPTIONS OF MATTER

Path of deflected
particles

Source
of alpha
particles
Thin sheet
of Pt foil

Fluorescent screen

Path of undeflected
particles

Beam of
alpha
particles

(a)

Beam of
alpha
particles

(b)

immediately behind the piece of metal foil as expected, much to the amazement of
the researchers, a number of alpha particles were also deflected and scattered at
other 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 most
incredible event that has ever happened to me in my life. It was almost as incredible
as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit
you. On consideration, I realized that this scattering backwards must be the result
of a single collision, and when I made calculations I saw that it was impossible to get
anything of that order of magnitude unless you took a system in which the greater
part of the mass of an atom was concentrated in a minute nucleus.” Further calculations showed that the diameter of the nucleus was about five orders of magnitude
smaller than that of the atom. This led to the rather remarkable conclusion that matter is mostly empty space—with the very lightweight electrons orbiting around an
incredibly dense and positively charged nucleus, as shown in Figure 1.5. As a matter
of fact, 99.99999999% of the atom is devoid of all matter entirely! On the atomic
scale, solidity has no meaning. The reason that a macroscopic object “feels” at all
hard to us is because the atom contains a huge amount of repulsive energy, so that

whenever 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 returned
to England to work with his former mentor Ernest Rutherford, who had taken over
J. J. Thomson’s position as Cavendish Professor at Cambridge University. It was
not long before Rutherford appointed Chadwick as the assistant director of the
nuclear physics lab. In the years immediately following Rutherford’s discovery that
the nucleus contained protons, which existed in the nucleus and whose charges were

FIGURE 1.4
Schematic diagram of the
Geiger–Marsden experiment,
also known as Rutherford’s gold
foil experiment. [Blatt
Communications.]
FIGURE 1.5
Atomic view of the gold foil
experiment. If the plum pudding
model of the atom were
accurate, a beam of massive
alpha particles would penetrate
right through the atom with
little or no deflections (a). The
observation that some of the
alpha particles were deflected
backward implied that the
positive charge in the atom must
be confined to a highly dense
region inside the atom known as
the nucleus (b). [Blatt

Communications.]

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6

1 THE COMPOSITION OF MATTER

equal in magnitude to the electronic charge but with the opposite sign, it was widely
known that the nuclei of most atoms weighed more than could be explained on
the basis of their atomic numbers (the atomic number is the same as the number of
protons in the nucleus). Some scientists even hypothesized that maybe the nucleus
contained an additional number of protons and electrons, whose equal but opposite
charges cancelled each other out but which together contributed to the increased
mass of the nucleus. Others, such as Rutherford himself, postulated the existence
of an entirely new particle having roughly the same mass as a proton but no charge
at all, a particle that he called the neutron. However, there was no direct evidence
supporting this hypothesis.
Around 1930, Bothe and Becker observed that a Be atom bombarded with alpha
particles produced a ray of neutral radiation, while Curie and Joliot showed that this
new form of radiation had enough energy to eject protons from a piece of paraffin
wax. By bombarding heavier nuclei (such as N, O, and Ar) with this radiation and
calculating the resulting cross-sections, Chadwick was able to prove that the rays
could not be attributed to electromagnetic radiation. His results were, however,
consistent with a neutral particle having roughly the same mass as the proton. In
his next experiment, Chadwick bombarded a boron atom with alpha particles and
allowed the resulting neutral particles to interact with nitrogen. He also measured
the velocity of the neutrons by allowing them to interact with hydrogen atoms and

measuring the speed of the protons after the collision. Coupling the results of each
of his experiments, Chadwick was able to prove the existence of the neutron and
to determine its mass to be 1.67 × 10−27 kg. The modern-day values for the charges
and masses of the electron, proton, and neutron are listed in Table 1.1. Chadwick
won 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 divide
matter into such small pieces that it is no longer perceptible to the senses. In a
sense, this is a philosophical question and the answer depends on what we mean as
being perceptible to the senses. Does it literally mean that we can see the individual
components with our naked eye, and for that matter, what are the molecular characteristics of vision that cause an object to be seen or not seen? How many photons
of light does it take to excite the rod and cone cells in our eyes and cause them
to fire neurons down the optic nerve to the brain? The concept of perceptibility
is somewhat vague. Is it fair to say that we still see the object when it is multiplied
under 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 by
a 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
−27
Neutron 1.674927351 × 10
1.00866491600
0
Source: The NIST Reference on Constants,
(, accessed Nov 3, 2013).

Units,

and

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Uncertainty