DERN PHYSICS FOR SCIENTISTS AND ENGINEERS

Stephen T. Thornton University of Virginia

Andrew Rex University of Puget Sound

-ML

Saunders Golden Sunburst Series SAUNDERS COLLEGE PUBLISHING A Harcourt Brace Jovanovich College Publisher

Fort Worth Philadelphia San Diego New York Orlando Austin San Antonio Toronto Montreal London Sydney Tokyo

CONTENTS

C H A P T E R 1

One Hundred Years Ago

1.1 Classical Physics of the 1890s 2 Mechanics 3 Electromagnetism 4 Thermodynamics 5

1.2 The Kinetic Theory of Gases 5

1.3 Waves and Particles 9

1.4 Conservation Laws and Fundamental Forces 10

Fundamental Forces 11

1.5 The Atomic Theory of Matter 13

1.6 Outstanding Problems of 1895 and New Horizons 16

On the Horizon 18

Summary 18

CHAPTER 2

Special Theory of Relativity 20 2.1 Historical Perspective 21

2.2 The Michelson-Morley Experiment 22

2.3 Einstein's Postulates 27

2.4 The Lorentz Transformation (optional) 30

2.5 Time Dilation and Length Contraction 33 Time Dilation 33 Length Contraction 36

2.6 Addition of Velocities 39

2.7 Experimental Verification 43 Muon Decay 43 Atomic Clock Measurement 44

Velocity Addition 45

2.8 Twin Paradox 46

2.9 Spacetime 47

2.10 Doppler Effect 51

Special Topic: Applications of the Doppler Effect 54

Summary 57

CHAPTER 3

Relativistic Dynamics; General Relativity 62

3.1 Relativistic Momentum 63

3.2 Relativistic Energy 67 Total Energy and Rest Energy 70 Equivalence of Mass and Energy 71 Relationship of Energy and Momentum 72 Massless Particles 73

3.3 Computations in Modern Physics 73

Binding Energy 76

3.4 Electromagnetism and Relativity 79

3.5 General Relativity 81

3.6 Tests of General Relativity 85 Bending of Light 85

xii Contents

Gravitational Redshift Perihelion Shift of Mercury Light Retardation

3.7 Predictions of General Relativity Gravitational Waves Black Holes

Special Topic: Gravitational Waves

Summary

C H A P T E R 4

The Experimental Basis of Quantum Theory

86 88 88

89 89 91

90

93

97

4.1 Discovery of the X-Ray and the Electron 98

4.2 Determination of Electron Charge 101

4.3 Line Spectra 104

Special Topic: The Discovery of Helium 106

4.4 Quantization 109

4.5 Blackbody Radiation (optional) 109

4.6 Photoelectric Effect 115 Experimental Results of Photoelectric Effect 116 Classical Interpretation 118 Einstein's Theory 119

Quantum Interpretation 120

4.7 X-Ray Production 123

4.8 Compton Effect 125

4.9 Pair Production and Annihilation 129

Summary 133

Essay: X-Ray Lithography 137 by Franco Cerrina University of Wisconsin, Center for X-Ray Lithography

CHAPTER 5

Structure of the Atom 1 4 0

5.1 The Atomic Models of Thomson and Rutherford 141

5.2 Rutherford Scattering (optional) 144

Special Topic: Lord Rutherford of Nelson 146

5.3 The Classical Atomic Model 153

5.4 Bohr Model of the Hydrogen Atom 155

5.5 Successes and Failures of the Bohr Model 161

5.6 Characteristic X-Ray Spectra and Atomic Number 164

5.7 Atomic Excitation by Electrons

Summary

CHAPTER 6

Wave Properties of Matter

167

169

173 6.1 X-Ray Scattering

6.2 De Broglie Waves Bohr's Quantization Condition

6.3 Electron Scattering

6.4 Wave Motion

6.5 Waves or Particles?

Special Topic: Single Particle Interference

6.6 Relationship Between Probability and Wave Function

6.7 Uncertainty Principle

Summary

173

178 180

180

184

190

194

197

200

204

C H A P T E R 7

The Quantum Theory

C H A P T E R 8

The Hydrogen Atom

208

7.1

7.2

7.3

7.4

7.5

7.6

7.7

The Schrödinger Wave Equation Normalization and Probability Boundary Conditions Time-Independent Schrödinger Wave Equation

Expectation Values

Infinite Square Well Potential

Finite Square Well Potential (optional)

Three-Dimensional Infinite Potential Well

Particle in a Closed Box

Simple Harmonic Oscillator (optional)

Barriers and Tunneling Potential Barrier with E > V0

Potential Barrier with E <V0

Potential Well Alpha Decay

Special Topic: Scanning Probe Microscopes

Summary

208 211 213

213

215

218

223

225 226

228

234 234 236 239 239

240

243

247

8.1 Application of the Schrödinger Equation to the Hydrogen Atom 247

8.2 Solution of the Schrödinger Equation for Hydrogen (optional) 249

Contents хш

Separation of Variables 249 Relation Between the Quantum Numbers € and rri( 250 Solution of the Radial Equation 251 Solution of the Angular and Azimuthal Equations 252

8.3 Quantum Numbers 253 Principal Quantum Number n 254 Orbital Angular Momentum Quantum Number € 254 Magnetic Quantum Number mg 255

Special Topic: Rydberg Atoms 256

8.4 Magnetic Effects on Atomic Spectra—The Normal Zeeman Effect 258

8.5 Intrinsic Spin 262

8.6 Energy Levels and Electron Probabilities (optional) 264

Selection Rules 265 Probability Distribution Functions 267

Summary 271

Essay: Indeterminacy and Nonlocality in Quantum Mechanics 274 by David Griffiths Reed College

C H A P T E R 9

Many-Electron Atoms 278 9.1

9.2

9.3

Atomic Structure and the Periodic Table Inert Gases Alkalis Alkaline Earths Halogens Transition Metals Lanthanides Actinides

Total Angular Momentum (optional) Single-Electron Atoms Many-Electron Atoms LS, or Russell-Saunders, Coupling jj Coupling

Anomalous Zeeman Effect (optional)

Summary

278 284 284 284 284 284 285 285

285 286 289 289 292

295

298

CHAPTER 10

Statistical Physics 301 10.1 Historical Overview

10.2 Maxwell Velocity Distribution

301

304

10.3 Equipartition Theorem 306

10.4 Maxwell Speed Distribution 309

10.5 Classical and Quantum Statistics 313 Classical Distributions 313 Quantum Distributions 315

10.6 Fermi-Dirac Statistics 317 Introduction to Fermi-Dirac Theory 317 Classical Theory of Electrical Conduction 318 Quantum Theory of Electrical Conduction 320

10.7 Bose-Einstein Statistics 325 Blackbody Radiation 325 Liquid Helium 327

Special Topic: Superfluid 3 H e 332

Summary 334

C H A P T E R 1 1

Molecules and Solids 337 11.1 Molecular Bonding and Spectra 337

Rotational States 339 Vibrational States 340 Vibration and Rotation Combined 342

11.2 Stimulated Emission and Lasers 345 Scientific Applications 350 Holography 351 Other Applications 352

11.3 Structural Properties of Solids 353

11.4 Thermal and Magnetic Properties of Solids 356

Thermal Expansion 356 Thermal Conductivity 358 Magnetic Properties 359 Diamagnetism 360 Paramagnetism 360 Ferromagnetism 362 Antiferromagnetism and Ferrimagnetism 363

11.5 Superconductivity 363 The Search for a Higher Tc 370

Special Topic: Low-Temperature Methods 372

Superconducting Fullerenes 375 11.6 Applications of Superconductivity 377

Josephson Junctions 377 Maglev 378 Generation and Transmission of Electricity 379 Other Scientific and Medical Applications 379

Summary 381

xiv Contents

Essay: Holography—Modern Applications by Tung H. Jeong Lake Forest College

C H A P T E R 12

Semiconductor Theory and Devices

386

388

12.1 Band Theory of Solids 388 Kronig-Penney Model 390 Conductors, Insulators, and Semiconductors 392

12.2 Semiconductor Theory 393

Special Topic: The Quantum Hall Effect 396

Thermoelectric Effect 400

12.3 Semiconductor Devices 402 Diodes 403 Bridge Rectifiers 405 Zener Diodes 405 Light Emitting Diodes 405 Photovoltaic Cells 406 Transistors 409 Field Effect Transistors 412 MOSFETs 412 Schotfky Barriers 412 Integrated Circuits 413

Summary 415

Essay: Photovoltaic Devices by Lawrence L. Kazmerski National Renewable Energy Laboratory

C H A P T E R 13

The Atomic Nucleus

418

425

13.1 Discovery of the Neutron

13.2 Nuclear Properties Sizes and Shapes of Nuclei Intrinsic Spin Intrinsic Magnetic Moment

13.3 The Deuteron

13.4 Nuclear Forces

13.5 Nuclear Stability Nuclear Models

13.6 Radioactive Decay

13.7 Alpha, Beta, and Gamma Decay Alpha Decay Beta Decay

425

428 429 432 432

433

435

436 442

444

447 448 452

Special Topic: Neutrino Detection

Gamma Decay

13.8 Radioactive Nuclides Time Dating Using Lead Isotopes Radioactive Carbon Dating Uranium-Thorium Dating

Summary

C H A P T E R 14

Nuclear Interactions and Applications

454

458

460 462 463 465

465

469 14.1

14.2

14.3

14.4

14.5

Nuclear Reactions Cross Sections

Reaction Kinematics

Reaction Mechanisms The Compound Nucleus Direct Reactions

Fission

Fission Reactors

Special Topic: Early Fission Reactors

14.6

14.7

Breeder Reactors

Fusion Formation of Elements Nuclear Fusion on Earth Controlled Thermonuclear Reactions

Special Applications Medicine Archeology Art

Special Topic: How to Prove an Art Forgery

14.8

14.9

Crime Detection Agriculture Mining and Oil Materials Industry Small Power Systems New Elements

Particle Interactions in Matter (optional)

Heavy Charged Particles Electrons Photons Neutrons

Radiation Dose and Hazards (optional)

Summary

469 472

474

476 477 480

481

485

488

490

491 491 493 494

498 499 500 500

502

502 503 504 504 506 507 508

509 509 511 511 513

514

516

Contents xv

CHAPTER 1 5

Elementary Particles 521

15.1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

The Early Beginnings The Positron Yukawa's Meson

The Fundamental Interactions

Classification of Elementary Particles Leptons Hadrons Particles and Lifetimes

Conservation Laws and Symmetries Symmetries

Quarks Quark Description of Particles Color Confinement Hadron Masses

The Families of Matter

The Standard Model and GUTs Grand Unifying Theories

Accelerators (optional)

Special Topic: Experimental Ingenuity

15.9

Synchrotrons Linear Accelerators Fixed-Target Accelerators Colliders

Particle Detectors (optional) Gas-Filled Ionization Detectors Scintillation Counters Semiconductors Cherenkov Counters Shower Counters Track Recording Detectors

Summary

522 522 524

525

527 528 529 530

532 535

536 537 539 540 540

542

543 545

547

548

550 553 553 554

556 556 557 558 559 559 559

564

CHAPTER 16

Cosmology—The Beginning and the End 567

16.1 Evidence of the Big Bang 567 Hubble's Measurements 569 Cosmic Microwave Background Radiation 572 Nucleosynthesis 573

16.2 The Big Bang 575

Special Topic: Planck's Time, Length, and Mass 578

16.3 Stellar Evolution 578 Eventual Fate of Stars 581

16.4 Astronomical Objects

Novae and Supernovae

16.5 Problems with the Big Bang

Special Topic: Adaptive Optics

16.6 The Future The Demise of the Sun The Future of the Universe?

Summary

Essay: The Hubble Constant and the Age of the Universe by Robert D. McClure Dominion Astrophysical Observatory, National Research Council, Canada

APPENDIX 1

Fundamental Constants

APPENDIX 2

Conversion Factors

APPENDIX 3

Mathematical Relations

APPENDIX 4

Periodic Table of the Elements

APPENDIX 5

Mean Values and Distributions

APPENDIX 6

Probability Integrals

/„ = x" expl-ax^dx

-4)

APPENDIX 7

Integrals of the Type x""1dx

e - 1

APPENDIX 8

Atomic Mass Table

APPENDIX 9

Nobel Laureates in Physics

Answers to Selected Problems

Index

583

587

591

592 596 596 596

600

603

A.1

A.2

A.4

A.5

A.6

A.8

A.10

A.12

A.35

A.41

1.1