UNDERSTANDING PHYSICS

Series EditorsJohn P. ErtelRobert C. HilbornDavid PeakThomas RossingCindy Schwarz

SpringerNew YorkBerlinHeidelbergHong KongLondonMilanParisTokyo

UNDERGRADUATE TEXTS IN CONTEMPORARY PHYSICS

Cassidy, Holton, and Rutherford, Understanding Physics

Enns and McGuire, Computer Algebra Recipes: A Gourmet’s Guide to the Mathematical Models of Science

Hassani, Mathematical Methods: For Students of Physics and Related Fields

Holbrow, Lloyd, and Amato, Modern Introductory Physics

Roe, Probability and Statistics in Experimental Physics, Second Edition

Rossing and Chiaverina, Light Science: Physics and the Visual Arts

UNDERSTANDING PHYSICSDavid CassidyGerald HoltonJames Rutherford

With 571 Illustrations, with 6 in Full Color

123

David Cassidy Gerald HoltonProfessor of Natural Science Mallinckrodt Professor of Physics and History Natural Science Program of Science, EmeritusHofstra University 358 Jefferson Physical LaboratoryHempstead, NY 11549 Harvard UniversityUSA Cambridge, MA 02138chmdcc@Hofstra.edu USA

James RutherfordEducation AdvisorAmerican Association for Advancement

of ScienceWashington, DC 20005USA

Series Editors

John P. Ertel Robert C. Hilborn Cindy SchwarzDepartment of Physics Department of Physics Department of Physics and United States Naval Academy Amherst College Astronomy572 Holloway Road Amherst, MA 01002 Vassar CollegeAnnapolis, MD 21402-5026 USA Poughkeepsie, NY 12601USA rchilborn@amherst.edu USAjpe@nadn.navy.mil schwarz@vaxsar.vassar.edu

David Peak Thomas RossingDepartment of Physics Department of PhysicsUtah State University Northern Illinois UniversityLogan, UT 84322 De Kalb, IL 60115USA USApeakd@cc.usu.edu rossing@physics.niu.edu

Library of Congress Cataloging-in-Publication Data

Cassidy, David C., 1945–Understanding physics / David Cassidy, Gerald Holton, F. James Rutherford.

p. cm. — (Undergraduate texts in contemporary physics)Rev. ed. of: The project physics course. 1971.Includes bibliographical references and index.ISBN 0-387-98756-8 (pbk. : acid-free paper)

1. Physics. I. Holton, Gerald James. II. Rutherford, F. James (Floyd James), 1924–III. Harvard Project Physics. Project physics course. IV. Title. V. Series.

QC23.2 .C37 2002530—dc21 2002020937

ISBN 0-387-98756-8 Printed on acid-free paper.

© 2002 Springer-Verlag New York, Inc.All rights reserved. This work may not be translated or copied in whole or in part without the writtenpermission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010,USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection withany form of information storage and retrieval, electronic adaptation, computer software, or by similaror dissimilar methodology now known or hereafter developed is forbidden.The use in this publication of trade names, trademarks, service marks, and similar terms, even if theyare not identified as such, is not to be taken as an expression of opinion as to whether or not they aresubject to proprietary rights.

Printed in the United States of America.

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Springer-Verlag New York Berlin HeidelbergA member of BertelsmannSpringer Science�Business Media GmbH

To the students and instructors whose advice, while using the draft versions of the text and guides, helped to improve our work greatly;

and to Joan Laws, whose quiet expertise all these years helped to bring the project to success.

Science is an adventure of the whole human race to learn to live in and perhapsto love the universe in which they are. To be a part of it is to understand, to un-derstand oneself, to begin to feel that there is a capacity within man far beyondwhat he felt he had, of an infinite extension of human possibilities. . . .

I propose that science be taught at whatever level, from the lowest to the high-est, in the humanistic way. It should be taught with a certain historical under-standing, with a certain philosophical understanding, with a social understandingand a human understanding in the sense of the biography, the nature of the peo-ple who made this construction, the triumphs, the trials, the tribulations.

—I.I. Rabi, Nobel Laureate in Physics

Preface

Understanding Physics is a completely revised, updated, and expanded edi-tion of the Project Physics Course. It is an integrated introductory physicscourse, developed with funding from the Carnegie Corporation and theSloan Foundation and with the close cooperation of Springer-Verlag New York.

In approach and content, Understanding Physics follows the trail blazedby the earlier versions, but it includes more recent developments in physicsand a stronger emphasis on the relationships among physics, technology,and society. We have sought especially to incorporate the salient lessons ofrecent physics education research and practical experience gained in theclassroom.

The Audience

Understanding Physics is written primarily for undergraduate college stu-dents not intending (at least initially) to enter careers in science or engi-neering. These may include liberal-arts students, business majors, prelegal,and prospective architecture students. We have found that when the courseis taken with laboratory work, it has been deemed suitable by medicalschools for premedical students.

An important group that this course is intended to serve are persons whoplan to teach, or are already teaching, in K–12 classrooms. As has beenwidely discussed, there is a special need for improvement in the science education of current and future teachers as an important step toward achiev-ing greater scientific literacy in general. Many states have recently incor-porated the contextual approach used in Understanding Physics into state sci-ence education criteria. It is in part to meet the challenges of teachereducation that this course was developed as a resource, along with the usualpedagogical training.

Since college students in introductory science courses usually representa wide spectrum of expertise in science and mathematics, this book assumes

ix

no prerequisites in science or mathematics beyond high-school algebra,geometry, and general science. In this text we have taken great care to de-rive all necessary equations very patiently, but whenever possible we haveused narrative text instead of equations to convey the meanings of laws andconcepts. Even if students have taken physics in high school, they oftenstill lack proficiency in even the most basic concepts and techniques. Oneof the aims of this course is to enable all students to gain experience andconfidence with physical-science concepts and quantitative methods, andwith an understanding of the nature of science itself. Of course, for classesin which the students are sufficiently prepared, instructors may decide toplace more emphasis on quantitative or other aspects of physics as appro-priate. The course is designed with such flexibility in mind.

The Approach

A unique feature of this text, like its predecessor, is that it places the fun-damental concepts of physics within the broader humanistic and historicalcontexts in which they arose, but without handicapping students in teststhat compare their performance with students who have taken a less broadlyconceived, conventional physics course. Research has shown that studentsexposed to our approach gain a much deeper understanding of both thecontent and the processes of scientific research, as well as an appreciationnot only of what we know, but also of how and why we think we know it.This approach has been endorsed by several national organizations, in-cluding the National Science Foundation, the Research Council of the National Academy of Sciences, and Project 2061 of the American Associ-ation for the Advancement of Science. The National Research Councilstated in its National Science Education Standards:*

In learning science, students need to understand that science re-flects its history and is an ongoing, changing enterprise. The stan-dards for the history and nature of science recommend the use ofhistory in school science programs to clarify different aspects of sci-entific inquiry, the human aspects of science, and the role that sci-ence has played in the development of various cultures.

Thus, Understanding Physics operates on two levels, providing both thefundamental concepts of physics and the humanistic and intellectual con-texts in which the concepts developed. In addition to the necessary con-cepts and equations, intentionally developed patiently, and using easy-to-visualize examples, it aims to convey a real sense of the nature of scientific

x PREFACE

* Washington, DC: National Academy Press, 1996; p. 107.

thinking, the way intuitions about science had to be, often painfully, ac-quired by scientists, and what our current concepts really mean. However,this text is not intended to be used by itself, but rather as part of a pro-gram as integrated as possible with hands-on activities, small-group dis-cussions either in or out of class, and other encouragements to active learn-ing that enable the subject matter to come alive. Some of these and otherpossible activities are suggested in the accompanying Student Guide.

Understanding Physics is divided into two parts. Each part is self-contained, with enough material for a course lasting at least one semester.Each part encompasses topics in classical physics along with one of the twocontemporary nonclassical physics: relativity theory and quantum mechan-ics. Both parts taken together may serve for a full one-year course. We havesought from the beginning to provide instructors with maximum flexibil-ity in adapting the course to students of different backgrounds, to differ-ent educational settings, to different semester time frames, and to differ-ent preferences for course topics. Some suggestions for different scenariosare provided in the accompanying Instructor Guide. All of the course’sprinted materials, as well as links to many related Web sites for both in-structors and students, may also be accessed on the World Wide Web viathe publisher’s site at http://www.springer-ny.com/up.

Acknowledgments

We are grateful to the Carnegie Corporation of New York and to the SloanFoundation for their generous and timely support. Thomas von Foersterand the staff of Springer-Verlag New York provided much-appreciated en-couragement, support, and helpful advice during the years of preparationand testing of these materials in draft form. We also thank David Couzens,our developmental editor, whose outstanding work on the illustrations andhis suggestions regarding the content contributed greatly to this work, andEdwin F. Taylor for his very helpful comments regarding the chapter onrelativity theory. We are indebted to our colleagues at Hofstra Universityand to the other instructors who thoroughly tested the draft of the text andguides in their classes, and offered many helpful comments and sugges-tions. We also thank our colleagues and the individuals who carefully re-viewed the materials and provided insightful suggestions. Last but not least,we thank the students at all testing sites for their valuable suggestions andencouragement. Without the contributions of all of these individuals andinstitutions, this work would not have been possible.

David CassidyGerald HoltonJames Rutherford

PREFACE xi

Brief Contents

Preface ix

PART ONE: MATTER AND MOTIONPrologue to Part One 31 Motion Matters 152 Moving the Earth 573 Understanding Motion 1174 Newton’s Unified Theory 1715 Conserving Matter and Motion 2116 The Dynamics of Heat 2537 Heat: A Matter of Motion 2938 Wave Motion 3319 Einstein and Relativity Theory 405

PART TWO: FIELDS AND ATOMSPrologue to Part Two 45110 Electricity and Magnetism 45911 The Electric Age 50512 Electromagnetic Waves 54913 Probing the Atom 58514 The Quantum Model of the Atom 62115 Quantum Mechanics 66116 Solids Matter 69317 Probing the Nucleus 72318 The Nucleus and Its Applications 763

Illustration Credits 819Index 829 xiii

Contents

Preface ix

PART ONE: MATTER AND MOTION

PROLOGUE TO PART ONE 3

1 Living Ideas 3

2 Our Place in Time and Space 4

3 First Things First 6

4 Aristotle’s Universe 9

CHAPTER 1. MOTION MATTERS 15

1.1 Motion 15

1.2 Galileo 16

1.3 A Moving Object 18

1.4 Picturing Motion 25

1.5 Speed and Velocity 30

1.6 Changing the Speed 31

1.7 Falling Freely 36

1.8 Two New Sciences 38

1.9 Falling Objects 41

1.10 The Consequences 47

xv

CHAPTER 2. MOVING THE EARTH 57

2.1 Astronomy, Motion, and Mechanics 57

2.2 The Scientific Revolution 58

2.3 Copernicus 59

2.4 The Geocentric View 61

2.5 Copernicus versus Ptolemy 75

2.6 Arguments for the Heliocentric System 79

2.7 Arguments against the Heliocentric System 82

2.8 Carrying Forth the Revolution 86

2.9 New Data 88

2.10 New Orbits 92

2.11 New Observations 102

2.12 Galileo Condemned 109

CHAPTER 3. UNDERSTANDING MOTION 117

A. THE THREE LAWS OF MOTION 117

3.1 Natural Motion and Newton’s First Law 117

3.2 Forces in Equilibrium 123

3.3 More about Vectors 125

3.4 Newton’s Second Law of Motion 128

3.5 Measuring Mass and Force 132

3.6 More about Weight, and Weightlessness 136

3.7 Newton’s Third Law of Motion 140

B. THE THREE LAWS IN ACTION 143

3.8 Projectile Motion 143

3.9 The Earth Can Move! 146

3.10 Galilean Relativity 149

3.11 Orbiting Satellites 150

3.12 Circular Motion 156

xvi CONTENTS

CHAPTER 4. NEWTON’S UNIFIED THEORY 171

4.1 Newton and Seventeenth-Century Science 171

4.2 Isaac Newton 173

4.3 Newton’s Principia 176

4.4 The Inverse-Square Law 179

4.5 The Law of Universal Gravitation 182

4.6 Newton’s Syntheses 185

4.7 Newton and Hypotheses 186

4.8 The Magnitude of the Gravitational Force 188

4.9 The Value of G, and Some Consequences 192

4.10 Further Successes 198

4.11 The Nature of Newton’s Work 204

CHAPTER 5. CONSERVING MATTER AND MOTION 211

5.1 Conservation of Mass 211

5.2 Collisions 217

5.3 Conservation of Momentum 219

5.4 Momentum and Newton’s Laws of Motion 223

5.5 Isolated Systems 226

5.6 Elastic Collisions 228

5.7 Leibniz and the Conservation Law 231

5.8 Work 233

5.9 Work and Kinetic Energy 235

5.10 Potential Energy 236

5.11 Conservation of Mechanical Energy 239

5.12 Forces that Do No Work 243

CHAPTER 6. THE DYNAMICS OF HEAT 253

6.1 Heat as a Form of Energy 253

6.2 The Steam Engine and the Industrial Revolution 258

6.3 Power and Efficiency of Engines 267

CONTENTS xvii

6.4 Carnot and the Beginnings of Thermodynamics 269

6.5 Arriving at a General Conservation Law 273

6.6 The Two Laws of Thermodynamics 278

6.7 Faith in the Laws of Thermodynamics 282

CHAPTER 7. HEAT: A MATTER OF MOTION 293

A. THE KINETIC THEORY 293

7.1 An Ideal Gas 293

7.2 A Model for the Gaseous State 300

7.3 The Speeds of Molecules 302

7.4 The Sizes of Molecules 305

B. APPLYING THE KINETIC THEORY 308

7.5 Kinetic-Theory Explanation of the Ideal Gas Law 308

7.6 Kinetic-Theory Explanation of the Second Law 313

7.7 Maxwell’s Demon and the Statistical View of the Second Law 315

7.8 Two Challenges 319

CHAPTER 8. WAVE MOTION 331

A. WAVES 331

8.1 What Is a Wave? 331

8.2 The Properties of Waves 332

8.3 Wave Propagation 336

8.4 Periodic Waves 338

8.5 When Waves Meet 342

8.6 A Two-Source Interference Pattern 345

8.7 Standing Waves 350

8.8 Wave Fronts and Diffraction 354

8.9 Reflection 360

8.10 Refraction 366

8.11 Sound Waves 370

xviii CONTENTS

B. LIGHT 373

8.12 What Is Light? 373

8.13 Propagation of Light 375

8.14 Reflection and Refraction 378

8.15 Interference and Diffraction 382

8.16 What Is Color? 386

8.17 Why Is the Sky Blue? 390

8.18 Polarization 392

8.19 The Ether 395

CHAPTER 9. EINSTEIN AND RELATIVITY THEORY 405

9.1 The New Physics 405

9.2 Albert Einstein 408

9.3 The Relativity Principle 410

9.4 Constancy of the Speed of Light 415

9.5 Simultaneous Events 418

9.6 Relativity of Time 420

9.7 Time Dilation 424

9.8 Relativity of Length 428

9.9 Relativity of Mass 431

9.10 Mass and Energy 433

9.11 Confirming Relativity 434

9.12 Breaking with the Past 441

PART TWO: FIELDS AND ATOMS

PROLOGUE TO PART TWO 451

1 A Revolution in Science 451

2 The Mechanical World View 455

3 Energy and Atoms 455

CONTENTS xix

CHAPTER 10. ELECTRICITY AND MAGNETISM 459

10.1 Gilbert’s Magnets 459

10.2 Electric Charges and Electric Forces 462

10.3 Forces and Fields 472

10.4 Electric Currents 479

10.5 Electric Potential Difference 482

10.6 Electric Potential Difference and Current 486

10.7 Electric Potential Difference and Power 487

10.8 Currents Act on Magnets 488

10.9 Currents Act on Currents 492

10.10 Magnetic Fields and Moving Charges 495

CHAPTER 11. THE ELECTRIC AGE 505

11.1 Transporting Energy from One Place to Another 505

11.2 Faraday’s First Electric Motor 506

11.3 The Discovery of Electromagnetic Induction 507

11.4 Generating Electricity: The Generator 512

11.5 Putting Electricity to Work: The Motor 516

11.6 The Electric Light Bulb 520

11.7 AC versus DC: The Niagara Falls Power Plant 525

11.8 The Energy Picture Today 528

11.9 Conservation 531

11.10 Renewable and Alternative Energy Sources 537

CHAPTER 12. ELECTROMAGNETIC WAVES 549

12.1 Faraday’s Suggestion 549

12.2 Maxwell’s Principles of Electromagnetism 551

12.3 The Propagation of Electromagnetic Waves 556

12.4 Hertz’s Experimental Confirmation 560

12.5 The Electromagnetic Spectrum 563

12.6 What About the Ether Now? 578

xx CONTENTS

CHAPTER 13. PROBING THE ATOM 585

13.1 The Periodic Table 585

13.2 The Idea of Atomic Structure 589

13.3 Cathode Rays 590

13.4 The Smallest Charge 594

13.5 Thomson’s Model of the Atom 596

13.6 The Photoelectric Effect 598

13.7 Einstein’s Theory of the Photoelectric Effect 602

13.8 X Rays 608

CHAPTER 14. THE QUANTUM MODEL OF THE ATOM 621

14.1 Spectra of Gases 621

14.2 Regularities in the Hydrogen Spectrum 626

14.3 Rutherford’s Nuclear Model of the Atom 630

14.4 Nuclear Charge and Size 635

14.5 Bohr’s Theory: The Postulates 637

14.6 The Size of the Hydrogen Atom 640

14.7 Other Consequences of the Bohr Model 641

14.8 Bohr Accounts for the Series Spectra of Hydrogen 642

14.9 Do Stationary States Really Exist? 647

14.10 Constructing the Periodic Table 648

14.11 Evaluating the Bohr Model 654

CHAPTER 15. QUANTUM MECHANICS 661

15.1 The Quantum 661

15.2 The Particle-Like Behavior of Light 662

15.3 The Wave-Like Behavior of Particles 665

15.4 Constructing Quantum Mechanics 669

15.5 The Uncertainty Principle 673

15.6 Origins and a Consequence of the Uncertainty Principle 676

15.7 The Probability Interpretation 679

CONTENTS xxi

15.8 The Complementarity Principle 682

15.9 Some Reactions 685

CHAPTER 16. SOLIDS MATTER 693

16.1 The Success of Quantum Mechanics 693

16.2 Forming a Solid 694

16.3 Quantum Solids 697

16.4 Conducting Electrons 699

16.5 Banding Together 702

16.6 Superconductors 705

16.7 Semiconductors 707

16.8 Introducing Impurities 709

16.9 Semiconductor Devices 710

16.10 Transistors 714

16.11 Some Applications of Transistors 717

CHAPTER 17. PROBING THE NUCLEUS 723

17.1 Questions about the Nucleus 723

17.2 Becquerel’s Discovery 724

17.3 The Curies Discover Other Radioactive Elements 728

17.4 Identifying the Rays 733

17.5 The Charge and Mass of the Rays 734

17.6 Rutherford’s “Mousetrap” 737

17.7 Radioactive Transformations 739

17.8 Radioactive Decay Series 740

17.9 Decay Rate and Half-Life 743

17.10 The Concept of Isotopes 746

17.11 Transformation Rules 749

17.12 Summary of Notation for Nuclides and Nuclear Reactions 751

17.13 Some Useful Applications of Radioactivity 753

xxii CONTENTS

CHAPTER 18. THE NUCLEUS AND ITS APPLICATIONS 763

18.1 The Problem of Nuclear Structure 763

18.2 The Proton–Electron Hypothesis 764

18.3 The Discovery of Artificial Transmutation 766

18.4 The Discovery of the Neutron 769

18.5 The Proton–Neutron Model 773

18.6 The Neutrino 775

18.7 The Need for Particle Accelerators 777

18.8 The Energy of Nuclear Binding 780

18.9 Nuclear Binding Energy and Stability 783

18.10 Nuclear Fission: Discovery 786

18.11 Controlling Chain Reactions 791

18.12 Nuclear Power Plants 797

18.13 Nuclear Weapons 799

18.14 Nuclear Fusion 805

Illustration Credits 819

Index 829

CONTENTS xxiii