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Alternate Second Edition Elementary Modern Physics RICHARD T. WEIDNER Professor of Physics Rutgers University New Brunswick, New Jersey ROBERT L. SELLS Professor of Physics State University College of Arts and Sciences Geneseo, New York Allyn and Bacon, Inc. Boston ((; Copyright 1973 by Allyn and Bacon, Inc. 0 Copyright 1968 by Allyn and Bacon, Inc. Q Copyright 1960 by Allyn and Bacon, Inc. 470 Atlantic Avenue, Boston. All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any informational storage and retrieval system, without written permission from the copyright owner. Library of Congress Catalog Card Number: 72 90874. Printed in the United States of America. NUCLEAR STRUCTURE 31 6 9-1 The Nuclear Constituents 9-2 The Forces between Nucleons 9-3 The Deuteron 9-4 Stable Nuclei 9-5 Nuclear Radii 9-6 The Binding Energy of Stable Nuclei 9-7 Nuclear Models 9-8 The Decay of Unstable Nuclei 9-9 11 Decay 9-10 a Decay 9-11 p Decay 9-12 Natural Radioactivity Summary NUCLEAR REACTIONS 370 10-1 Low-energy Nuclear Reactions 10-2 The Energetics of Nuclear Reactions 10-3 The Conservation of Momentum in Nuclear Reactions 10-4 Cross Section 10-5 The Compound Nucleus and Nuclear Energy Levels 10-6 Neutron Production, Detection, Measurement, and Moderation 10-7 Nuclear Fission 10-8 Nuclear Reactors 10-9 Nuclear Fusion THE ELEMENTARY PARTICLES 407 11-1 The Electromagnetic Interaction 11-2 The Strong Interaction 11-3 A 13-Particle Universe 11-4 The Fundamental Particles 11-5 A 34-Particle Universe MOLECULAR AND SOLID-STATE PHYSICS 443 12-1 Molecular Binding 12-2 Molecular Rotation and Vibration 12-3 The Statistical Distribution Laws 12-4 Maxwell-Boltzmann Statistics Applied to an Ideal Gas 12-5 Maxwell-Boltzmann Statistics Applied to the Specific Heat of a Diatomic Gas 12-6 The Laser 12-7 Blackbody Radiation 12-8 The Quantum Theory of the Specific Heats of Solids 12-9 The Free-electron Theory of Metals 12-10 The Band Theory of Solids: Conductors, Insulators, and Semiconductors Summary APPENDIX I 502 The Atomic Masses ANSWERS TO ODD-NUMBERED PROBLEMS INDEX Preface The aim of ELEMENTARY MODERN PHYSICS remains that of treating the funda- mentals of the physics of the twentieth century fairly rigorously, but at an elementary level. The text is intended primarily for the concluding portion of the general physics course for students of science and engineering, or as a basis for a separate course in modern physics. It is a companion to the second edition of the authors' ELEMENTARY CLASSICAL PHYSICS (Boston: Allyn and Bacon, Inc., 1973), to which detailed references are made. The prerequisites, however, are merely an elementary knowledge of classical physics and introductory calculus. Our strategy is to give a logically coherent and sequential account of the basic principles of the relativity and quantum theories, of atomic and nuclear structure, and of a few topics in elementary-particle, molecular, and solid-state physics. We begin, after some preliminaries, with a simple treatment of special relativity, not only as the foundation of all later chapters, but particularly in anticipating the properties of the photon as a completely relativistic particle. Quantum effects are then introduced through the basis photon-electron interactions, and the wave properties of material particles are treated. With the basic principles of relativity and quantum physics developed, these are then applied to atomic, nuclear, elementary-particle, and solid-state physics. We make no pretense for comprehensive treatment of all, or even most, of the topics of interest in contemporary physics. Rather, the text is intended as a meaningful introduction to those central ideas which dominate modern physics, together with illustrations of how these general principles apply to some spe- cialized areas. Some minor topics, such as the focusing of charged particles by electric and magnetic fields, are dealt with only in problems. In this alternate second edition a significant fraction of the problems at the chapter ends are different, either by replacement or by modification from those appearin; in the second edition. Answers to odd-numbered problems are given in the bacl of the book. Succinct summaries are also given at the chapter ends, as are references to other sources. In its entirety this text provides enough material for a one- or two-semester course at the levels of the sophomore or junior year. The arrangement of topics is such, however, that it can be used for a shorter treatment without serious discontinuities; one might, for example, omit the latter portions of the chapters on special relativity (Chaps. 2 and 3), large portions of the chapter on many- electron atoms (Chap. 6), instruments and accelerating machines used in nuclear physics (Chap. 8), and elementary particles (Chap. ll), and possibly all of that on molecular and solid-state physics (Chap. 12). We continue to benefit from the many users of the text who have been good enough to send us their comments and suggestions for improvement. Although the text for the alternate second edition is essentially identical to that in the second edition, we hope to have corrected all residual errors. We are also indebted to Dr. Arthur E. Walters for assistance in constructing new problems. The publisher and authors solicit the opinions of this alternate second edition from users, both professors and students; a simple questionnaire form has been provided in the back of the book for your convenience. Some Preliminaries What is modern physics? How does it differ from, and in what ways is it similar to, classical physics?" What central ideas of classical physics are carried over into twentieth-century physics, in which one encounters the very small and the very fast? Which of the classical ideas remain unchanged, and which must be modified or replaced? These questions and other important ones are dealt with in this introductory chapter. 1-1 THE PROGRAM OF PHYSICS The program of physics is to devise concepts and laws that can help us to understand the universe. Physical laws are constructions of the human mind, subject to all the limitations of human understanding. They are not necessarily fixed, immutable, or good for all time, and nature is not compelled to obey them. A law in physics is a statement, usually in the succinct and precise language of mathematics, of a relationship that has been found by repeated experiment to obtain among physical quantities and that reflects persistent regularities in the behavior of the physical world. A "good" physical law has the greatest possible generality, simplicity, and preci- sion. The final criterion of a successful law of physics is how accurately CHAP. 1 Somr Pntlmh.rism Speerl of -Relativistic- l1~)lt quantum physics it can predict the results that experiments will yield. For example, our confidence in the essential co~ectnesosf the law of universal gravitation leads us to expect with almost complete certainty that, when the gravita- tional acceleration is peasured at the surface of Mara. it will be very close to 3.6 rnlsz. We ,say that our certainty is a h t c omplete, inasmuch as extrapolating from any law outside the range of its tested validity may predict results that come to be inconsistent with later experiment. As physics developed, some early theories end laws were found to be inadequate with respect to phenomena for which they had not been tested. These have been supplanted by more general, comprehensive theories and laws, which more adequately describe phenomena in the new as well as in the old regions of investigation. Figure 1-1 shows the various regions of applicability of classical physics, sektiuity physics, quantum physics, and relativistic quantum physics. Classical physics is the physics of ordinary-sized objects moving at ordinary speeds ; it embraces newtonian mechanics and electromagnetism (including the theory of light). Far object s p d s a pproaching that of light classical physics must be supplanted by relativity physics; for object sizes of about 10-'O m, approximately the aize of an atom, classical physics must be supplanted by quantum physics. Far subatomic dimensions and speeds approaching that of light only relativistic. quantum physics ig adequate. The limits of the several physical theories are not sharply defined; in fact, they overlap. Relativistic quantum physics is the most comprehensive and complete theoretical structure in contemporary physics4 At dimensions of about lo-'&m , the approximate size of the atomic nucleus, different and perplexing phenomena appear; at present they are only partly understood. The foundations of our understanding of atomic and nuclear structure lie in the two great ideas of modern physics, relativity theory and quantum theory. Both had their origins early in thig century, a The Conservation Laws of Physics ' SEC. 1-2 period in which improved experimental techniques first made possible the study of phenomena of small dimensions and high speeds and energies. After reviewing some crucial aspects of classical physics, we shall study the theory of relativity and the quantum theory and apply them to an analysis of atomic and nuclear structure. We shall be concerned with situations in which some familiar notions in physics may be in- applicable, situations in which classical physics is downright wrong. Does this mean, then, that all the time and effort spent in studying elementary classical physics is wasted, that one might better begin with relativity and quantum theory? Not at all! All results of experiment, however remote from our ordinary experience, must ultimately be expressed in classical terms, that is, in the classicbl concepts of momentum, energy, position, and time. Furthermore, we shall see that many of the concepts and laws of classical physics are carried over into the new physics. 1-2 THE CONSERVATION LAWS OF PHYSICS Both in classical and in modern physics nothing is more basic or simple than the conservation laws. In each conservation law the total amount of a certain physical quantity within a given system is constant, or conserved, provided only that the system as a whole is isolated from a specified external influence. For example, the total vector momentum of a system isolated from external forces is constant. Internal changes may take place within the boundaries of an isolated system,through the mutual interaction of the particles within, but they have 'no effect on the total amount of the conserved quantity. Therein lies the power of a conservation law. We need not be concerned with the details of what goes on within the system-indeed, we may actually be ignorant of the internal interactions-but if the system is truly isolated, the conserved quantities remain unchanged. Thus, in classical physics we know that the total mass, energy, linear momentum, angular momentum, and electric charge going into a collision between two or more particles isolated from external influence is precisely the same as the total mass, energy, linear momentum, angular momentum, and electric charging coming out of the collision. The conservation laws of classical physics are these: the laws of the conservation of mass, of energy, of linear momentum>of angular momentum, and of electric charge. The Law of Mass Conservation: The total mass of an isolated, or leakproof, system is constant. Despite changes that may occur in other quantities (e.g., energy, volume, and temperature) in a system, the total mass is unchanged. This law may also be stated in the following form: Mass cannot be created or destroyed; or, mass cannot be produced or annihilated. CHAP. 1 Some Preliminaries The Law of Energy Conservation: If no,work is done on or by a system, and if no thermal energy enters or leaves the system as heat, the total energy of the system is constant. Since all energy is ultimately either kinetic energy or potential energy, the law of energy conservation states that the sum of the kinetic energies of the particles and the potential energies of their mutual interaction in a system is constant. Thermal energy is merely the disordered mechanical energy of molecules or atoms in random mytion on a scale so microscopic that the kinetic and potential energies of individual particles are not distinguished. (The first law of thermo- dynamics is merely the law of the conservation of energy expressed in its most comprehensive form, which includes heat, the transfer of thermal energy by virtue of a temperature difference.) The Law of Linear-momentum Conservation: When a system is subject to no net external force, the total linear momentum of the system remains constant both in magnitude and direction. Newton's laws of motion are, of course, the foundation of classical mechanics, and it is useful to state these laws in the language of linear momentum. 1. The momentum p = mv of a particle subject to no net external force is constant.? 2. When a body is subject to a net external for9 e , the force equals the time rate of change of the linear moment m. When the mass is unchanged, the force is simply the product of mass and acceleration: In classical physics a particle's mass is constant, independent of its speed or any other circumstance. The total mass of a system of particles changes only to the degree that particles enter or leave the system. This law has a profound consequence: If one knows the forces acting on a body and its initial position and velocity, it is possible, at least in principle, to predict in complete detail its future history, that is, to project precisely its position and velocity for all future times. In the International System of Units (SI) (the rationalized meter- kilogram-second system of units), which will be used throughout this book, one newton is that force which acts on a mass of one kilogram to give it an acceleration of one meter per second squared. 3. When two bodies interact, the momentum imparted to one body during an infinitesimal time interval is equal but opposite to the momentum imparted to the second body during the same interval; , therefore, the action and reaction forces, here both interval forces, are equal and opposite. t A vector quantity is indicated by boldface type; its magnitude, by ordinary type.