MODERN PHYSICS www.com MODERN PHYSICS Third edition K e n n e t h S. K r a n e DEPARTMENT OF PHYSICS OREGON STATE UNIVERSITY JOHN WILEY & SONS, INC www.com VP AND EXECUTIVE PUBLISHER Kaye Pace EXECUTIVE EDITOR Stuart Johnson MARKETING MANAGER Christine Kushner DESIGN DIRECTOR Jeof Vita DESIGNER Kristine Carney PRODUCTION MANAGER Janis Soo ASSISTANT PRODUCTION EDITOR Elaine S. Chew PHOTO DEPARTMENT MANAGER Hilary Newman PHOTO EDITOR Sheena Goldstein COVER DESIGNER Seng Ping Ngieng COVER IMAGE CERN/SCIENCE PHOTO LIBRARY/Photo Researchers, Inc. This book was set in Times by Laserwords Private Limited and printed and bound by R.
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Outside of the United States, please contact your local sales representative. Library of Congress Cataloging-in-Publication Data Krane, Kenneth S. Modern physics/Kenneth S. Includes bibliographical references and index.K7 2012 539--dc23 2011039948 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 PREFACE This textbook is meant to serve a first course in modern physics, including relativity, quantum mechanics, and their applications.
Such a course often follows the standard introductory course in calculus-based classical physics. The course addresses two different audiences: (1) Physics majors, who will later take a more rigorous course in quantum mechanics, find an introductory modern course helpful in providing background for the rigors of their imminent coursework in classical mechanics, thermodynamics, and electromagnetism. (2) Nonmajors, who may take no additional physics class, find an increasing need for concepts from modern physics in their disciplines—a classical introductory course is not sufficient background for chemists, computer scientists, nuclear and electrical engineers, or molecular biologists. Necessary prerequisites for undertaking the text include any standard calculus- based course covering mechanics, electromagnetism, thermal physics, and optics.
Calculus is used extensively, but no previous knowledge of differential equations, complex variables, or partial derivatives is assumed (although some familiarity with these topics would be helpful). Chapters 1–8 constitute the core of the text. They cover special relativity and quantum theory through atomic structure. At that point the reader may continue with Chapters 9–11 (molecules, quantum statistics, and solids) or branch to Chapters 12–14 (nuclei and particles).
The final chapter covers cosmology and can be considered the capstone of modern physics as it brings together topics from relativity (special and general) as well as from nearly all of the previous material covered in the text. The unifying theme of the text is the empirical basis of modern physics. Experimental tests of derived properties are discussed throughout. These include the latest tests of special and general relativity as well as studies of wave-particle duality for photons and material particles.
Applications of basic phenomena are extensively presented, and data from the literature are used not only to illustrate those phenomena but to offer insight into how “real” physics is done. Students using the text have the opportunity to study how laboratory results and the analysis based on quantum theory go hand-in-hand to illuminate such diverse topics as Bose-Einstein condensation, heat capacities of solids, paramagnetism, the cosmic microwave background radiation, X-ray spectra, dilute mixtures of 3 He in 4 He, and molecular spectroscopy of the interstellar medium. This third edition offers many changes from the previous edition. Most of the chapters have undergone considerable or complete rewriting.
New topics have been introduced and others have been rearranged. More experimental results are presented and recent discoveries are highlighted, such as the WMAP microwave background data and Bose-Einstein condensation. End-of-chapter problem sets now include problems organized according to chapter section, which offer the student an opportunity to gain familiarity with a particular topic, as well as general problems, which often require the student to apply a broader array of concepts or techniques. The number of worked examples in the chapters and the number of end-of-chapter questions and problems have each increased by about 15% from the previous edition.
The range of abilities required to solve the problems has been www.com vi Preface broadened, so that this edition includes both more straightforward problems that build confidence as well as more difficult problems that will challenge students. Each chapter now includes a brief summary of the important points. Some of the end-of-chapter problems are available for assignment using the WebAssign program (www. A new development in physics teaching since the appearance of the 2nd edition of this text has been the availability of a large and robust body of literature from physics education research (PER).
My own teaching style has been profoundly influenced by PER findings, and in preparing this new edition I have tried to incorporate PER results wherever possible. One of the major themes that has emerged from PER in the past decade or two is that students can often learn successful algorithms for solving problems while lacking a fundamental understanding of the underlying concepts. Many approaches to addressing this problem are based on pre-class conceptual exercises and in-class individual or group activities that help students to reason through diverse problems that can’t be resolved by plugging numbers into an equation. It is absolutely essential to devote class time to these exercises and to follow through with exam questions that require similar analysis and articulation of the conceptual reasoning.
More details regarding the application of PER to the teaching of modern physics, including references to articles from the PER literature, are included in the Instructor’s Manual for this text, which can be found at www.com/college/krane. The Instructor’s Manual also includes examples of conceptual questions for in-class discussion or exams that have been developed and class tested through the support of a Course, Curriculum and Laboratory Improvement grant from the National Science Foundation. Specific changes to the chapters include the following: Chapter 1: The sections on Units and Dimensions and on Significant Figures have been removed. In their place, a more detailed review of applications of classical energy and momentum conservation is offered.
The need for special relativity is briefly established with a discussion of the failures of the classical concepts of space and time, and the need for quantum theory is previewed in the failure of Maxwell-Boltzmann particle statistics to account for the heat capacities of diatomic gases. Chapter 2: Spacetime diagrams have been introduced to help illustrate relation- ships in the twin paradox. The application of the relativistic conservation laws to decay and collisions processes is now given a separate section to help students learn to apply those laws. The section on tests of special relativity has been updated to include recent results.
Chapter 3: The section on thermal radiation has been rewritten, and more detailed derivations of the Rayleigh-Jeans and Planck formulas are now given. Chapter 4: New experimental results for particle diffraction and interference are discussed. The sections on the classical uncertainty relationships and on wave packet construction and motion have been rewritten. Chapter 5: To help students understand the processes involved in applying boundary conditions to solutions of the Schrödinger equation, a new section on wave boundary conditions has been added.
A new introductory section on particle confinement introduces energy quantization and helps to build the connection between the wave function and the uncertainty relationships. Time dependence of the wave function is introduced more explicitly at an Preface vii earlier stage in the formulism. Graphic illustrations for step and barrier problems now show the real and imaginary parts of the wave function as well as its squared magnitude. Chapter 6: The derivation of the Thomson model scattering angle has been modified, and the section on deficiencies of the Bohr model has been rewritten.
Chapter 7: To ease the entry into the 3-dimensional Schrödinger analysis of the hydrogen atom in spherical coordinates, a new section on the one- dimensional hydrogen atom has been added. Angular momentum concepts relating to the hydrogen atom are now introduced before the full solutions to the wave equation. Chapter 8: Much of the material has been reorganized for clarity and ease of presentation. The screening discussion has been made more explicit.
Chapter 9: More emphasis has been given to the use of bonding and antibonding orbitals to predict the relative stability of molecules. Sections on molecular vibrations and rotations have been rewritten. Chapter 10: This chapter has been extensively rewritten. A new section on the density of states function allows statistical distributions for photons or particles to be discussed more rigorously.
New applications of quantum statistics include Bose-Einstein condensation, white dwarf stars, and dilute mixtures of 3 He in 4 He. Chapter 11: The chapter has been rewritten to broaden the applications of the quantum theory of solids to include not only electrical conductivity but also the heat capacity of solids and paramagnetism. Chapter 12: To emphasize the unity of various topics within modern physics, this chapter now includes proton and neutron separation energies, a new section on quantum states in nuclei, and nuclear vibrational and rotational states, all of which have analogues in atomic or molecular structure. Chapter 13: The discussion of the physics of fission has been expanded while that of the properties of nuclear reactors has been reduced somewhat.
Because much current research in nuclear physics is related to astrophysics, this chapter now features a section on nucleosynthesis. Chapter 14: New material on quarkonium and neutrino oscillations has been added. Chapter 15: Chapters 15 and 16 of the 2nd edition have been collapsed into a single chapter on cosmology. New results from COBE and WMAP are included, along with discussions of the horizon and flatness problems (and their inflationary solution).
Many reviewers and class-testers of the manuscript of this edition have offered suggestions to improve both the physics and its presentation. I am particularly grateful to: David Bannon, Oregon State University Gerald Crawford, Fort Lewis College Luther Frommhold, University of Texas-Austin Gary Goldstein, Tufts University Leon Gunther, Tufts University Gary Ihas, University of Florida www.