Modern Physics PDF
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MODERN PHYSICS Physics Modern JOHN C. SLATER Professor of Physics Massachusetts Institute of Technology McGRAW-HILL BOOK COMPANY, INC. New York Toronto London 1955 MODERN PHYSICS Copyright © 1955 by the McGraw-Hill Book Company, Inc. Printed in the United States of America. All rights reserved. This book, or parts thereof, may not be reproduced in any form without permission of the publishers. Library of Congress Catalog Card Number 55-7284 III THE MAPLE PRESS COMPANY, YORK,. PA. PREFACE Modern physics-the atomic physics of the twentieth century f orms one of the most fascinating subjects in the whole of science. It has developed with great speed, helped along by some of the keenest thinkers of the age. It has taken the structure of the atom, which was largely a field for speculation in 1900, and has brought it to the point where it forms a precise, quantitative, mathematical branch of physics. The way in which these developments have come about is a revealing chapter in the history of human thought, showing us how great ideas arise. It is my effort in this volume to trace the development of these ideas. These developments of the physics of the twentieth century should interest a broad variety of students. The physicist himself, of course, and the chemist, whose interest in atomic and molecular structure is identical with that of the physicist, will see in these topics the whole foundation of modern work in their fields. Other sciences, too, for instance biology, are depending more and more on our new knowledge of the structure of atoms, and the students of all sciences should be aware of twentieth-century physics. But in addition to(Scientists, engineers must take a very lively inter est in modern physi~sJ,_ Physics forms the foundation of engineering, and the older and more conventional branches of engineering are based on the classical physics of the nineteenth century, or earlier. It is a characteristic of the present century, however, that new dis coveries are being put to use very much faster than ever before. One of has only to contrast the development the atomic bomb, in the years leading up to 1945, based on the discovery of nuclear fission in 1939, with the many decades which elapsed between Faraday's discovery of electromagnetic induction in 1832, and the practical use of electrical machinery late in the nineteenth century, to realize this. Some of the most exciting engineering developments of the present century are based directly on modern physics: electronics, with which everyone is now familiar; the application of solid-state physics to electronic prob lems, in such devices as the transistor; and of course the application of nuclear or atomic energy to military problems and power development. These rapid advances are only indications of what will undoubtedly come in the future. v vi PREFACE In all these fields, physicists were the pioneers, because they had followed the developments and were trained to deal with them. If engineers of the future are to be able to keep up with their profession, they too must follow the advances of modern physics. The engineer ing graduate of today is almost certain, before he finishes his profes sional career, to be making practical use of discoveries in physics which have not even been made yet. The forward-looking engineer must accustom himself to following the day-to-day progress of physics, keeping his eye constantly open for practical applications. The best way to train himself for this is to follow the exciting developments of physics during the last fifty years, so that he can learn how physicists think, what sort of problems they work on, and can be alert when new discoveries are made. It is no longer true that the physicist is an impractical scientist, working only on useless and theoretical prob lems. The most unlikely branches of advanced and theoretical physics are proving to have remarkable applications, and a mutual understand ing between the engineer and the research physicist is an absolute necessity if practical advances are to continue at their present remark able rate. Quite aside from the scientists and engineers, however, modern physics should be of absorbing interest to the student of history, of human thought, and of general culture. In many ways, the most dis tinguishing feature of the last three or four centuries has been the development of modern science. The human race had gone through millennia of developing culture before a particular combination of cir cumstances led to the inquiring mind, the experimental method, and the confidence in a rational explanation of the physical world, which started in the time of Galileo and Newton and have continued to the scientific developments of the present day. Here we find a continuing, progressing, intellectual effort, which is finding its culmination before our eyes in the physics of the twentieth century, and which has every indication of advancing in the future from one discovery to another. A study of the confident and vital nature of modern thinking in physics cannot fail to be a refreshing contrast to the pessimistic and uncertain state of thought in many other fields. Modern physics really is a branch of liberal culture, which should be of absorbing interest to the student of the history of thought and civilization. A mark of the narrowness of much current thinking on the part of non scientists is that they so often treat modern science as a contrast to true culture, rather than realizing that in fact science forms one of its brightest pages. PREFACE vii ·· In writing this book, I have had in mind this whole group of students to whom I wished to appeal. For this reason, I have kept the mathe matical level rather low. The only place where I have allowed much mathematics more advanced than elementary calculus to intrude is in the discussion of Schrodinger's equation and its applications to mole cules and solids, in Chaps. 9 and 10. I have done it there, because these ideas are hardly comprehensible without some mathematics; but the reader will still be able to get a good deal even if he skips most of the mathematics in those chapters. Even so, there is not enough mathematics to form a proper introduction to the subject; what I have put in is only enough, I hope, to whet the appetite of the student with mathematical inclinations, and to induce him to read further, in more advanced texts. This volume, in other words, is not a text on mathematical physics 1 as my other books have been; I have no illusions that the student will have more understanding of mathematical techniques when he finishes reading it than when he started. It is rather a history of the develop ment of ideas, tied together with only enough theory to make it com prehensible. Of course, one cannot escape the fact that the ideas of modern physics are largely mathematical, and that a book on this level cannot completely do justice to them. But if I had written on a mathematical level really adequate for the ideas, I should have defeated my own purpose: for the book would then have grown so big, and so hard to read, that the continuity of the story, which is what I have mainly tried to make clear, would have been lost. There is, I think, no level of mathematical sophistication on which a completely satisfac tory brief account of modern physics can be written, and I have tried to make the best compromise I could. I hope that the book will be useful as a textbook for advanced under graduate students, both in physics and in other sciences and engineer ing subjects; more and more such students are realizing their need for studying modern physics. As I have said, for students with less mathematical training, there are some of the mathematical sections which can well be skipped. A student who is not going further with modern physics should be able, I believe, to get more of the spirit of the subject from this sort of development, historical and descriptive, than from a text which puts more emphasis on experiments and their experimental details than on the ideas to which they contributed. I should suppose that a course of this sort would have lectures, prefera bly with demonstrations, laboratory work, and a good deal of material not contained in this text; but the text would, I hope, tie the general line of development of modern physics together. For the benefit of viii PREFACE students in such courses, I have included some problems of a very elementary sort, intended to give facility in the simple sort of calcu lations possible in some aspects of modern physics rather than leading into the more advanced parts of the subject. Aside from the student who is not going much further with modern physics, however, I should hope that this book would be useful for more advanced students. The ideas and historical developments which are described here are not elementary, even though they are stated in simple language. A graduate student who has had his training in a number of disconnected courses, without getting a general view of the development of modern physics, could well find this book to be profitable, even though easy, reading. I have even been told by a number of p~ofessors that they were fascinated to read of modern physics in the consecutive and historical way in which it is presented here. It could well be that a student who had read the book early in his career would wish to come back to it again, after he had acquired more background. The student meeting these topics for the first time will, I hope, be inspired to look further into many of the questions which have had to be covered very hurriedly or superficially in these chapters. I have indicated in the Appendix a number of references which may supply good suggestions for additional reading. For the student who is interested in following the mathematical ideas further, I give refer ences to the texts on theoretical physics, written by myself, partly in collaboration with Prof. N. H. Frank, presented in much the same spirit as the present book but going much further into the various branches of theoretical physics. It might well be that some teachers would prefer to present the material of this volume, not in the descrip tive way in which it is written, but as part of a more advanced and theoretical course. In that case, a combination of this volume and those on theoretical physics could profitably be used. Finally I should like to express sincere thanks to a number of prof es sors in various universities, and in particular to my colleague Prof. W.W. Buechner, who have been good enough to read the manuscript and present valuable suggestions. c. JOHN SLATER CONTENTS v PREFACE CHAPTER 1. THE ATOM IN NINETEENTH-CENTURY PHYSICS. 1 1-1. Introduction 1 1-2. Nineteenth-century Ideas of Atoms . 2 1-3. The Kinetic Theory of Gases. 3 1-4. The Maxwell-Boltzmann Distribution Law. 6 1-5. Equipartition of Energy and Specific Heats 9 1-6. Black-body Radiation. 13 1-7. Indications of the Future . 17 CHAPTER 2. THE ELECTRON THEORY AND RELATIVITY . 21 2-1. Introduction 21 2-2. The Determination of Electronic Charge and Mass . 24 2-3. Electron Dynamics and Relativity . 29 2-4. Lorentz and Drude's Electron Theory of Solids 37 CHAPTER 3. BEGINNING OF THE QUANTUM THEORY . 45 3-1. Introduction 45 3-2. Planck's Radiation Law . 49 3-3. The Specific Heat of Solids . 56 3-4. The Photoelectric Effect and X Rays . 60 CHAPTER 4. THE NUCLEAR ATOM • 64 4-1. Introduction 64 4-2. Scintillations, Counters, and Cloud Chambers . 69 4-3. Rutherford's Scattering Experiment. 72 CHAPTER 5. THE BOHR ATOM . 77 5-1. Introduction 77 5-2. Atomic Spectra. 78 5-3. Bohr's Stationary States . 81 5-4. The Stationary States of Hydrogen . 84 5-5. Elliptical Orbits in Hydrogen. 88 Ix
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