ATOMIC AND NUCLEAR PHYSICS THE MODERN UNIVERSITY PliYSICS SERIES This series is intended for readers whose main interest is in physics, or who need the methods of physics in the study of science and technology. Some of the books will provide a sound treatment of topics essential in any physics training, while other, more advanced, volumes will be suitable as preliminary reading for research in the field covered. New titles will be added from time to time. Clark: A First Course in Quantum Mechanics Littlefield and Thorley: Atomic and Nuclear Physics Lothian: Optics and Its Uses Lovell, Avery and Vernon: Physical Properties of Materials Perina: Coherence of Light Tritton: Physical Fluid Dynamics Wolbarst: Symmetry and Quantum Systems ATOMIC AND NUCLEAR PHYSICS An Introduction 3rd edition T. A. LITTLEFIELD and N. THORLEY Senior Lecturer School of Physics University of Newcastle upon Tyne ~ SPRINGER SCIENCE+BUSINESS MEDIA, LLC © 1979, Springer Science+Business Media New York Originally published by Van Nostrand Reinhold Co. Ltd. in 1979 First edition 1963 Second edition 1968 All rights reserved. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means - graphic, electronic, or mechanical, including photocopying, recording, taping, or information storage or retrieval systems - without the written permission of the publishers Library of Congress Cataloging in Publication Data Littlefield, Thomas Albert, 1912- Atomic and nuclear physics. (The Modern university physics series) Bibliography: p. Includes index. 1. Atoms. 2. Nuclear physics. 3. QUafitum theory. I. Thorley, Norman, 1913 - joint author. II. Title. QCI73.L76 1979 539.7 78-31250 ISBN 0-442-30189-8 ISBN 0-442-30190-1 pbk. ISBN 0-442-30178-2 ELBS ISBN 978-0-442-30190-3 ISBN 978-1-4684-1470-7 (eBook) DOI 10.1007/978-1-4684-1470-7 \ \ \ K+ Computer display of the decay of the two charmed particles DO(cu)-+K-n+ and DO(cu)-+K+~- produced from an energetic electron-positron collision. The display shows the cross­ section of the beam pipe (centre) and the surrounding spark chambers and scintillation counters of the particle detector arrangement. The tracks of the particles are plotted by the triggered spark chambers. (Photograph taken from Fundamental Particles with Charm, Roy F. Schwitters, Scientilic American, October 1977, p. 57.) T ABLE OF PHYSICAL CONSTANTS Speed of light (vacuum) c=2·997 926 x 108 m s-1 Elementary charge (proton) e= 1·602189 x 10-19 C Unified atomic mass constant U = 1'660 565 x 10 - 27 kg Electron rest mass m.=9·109 534 x 10- 31 kg = 5·485803 x 10-4 u Proton rest mass mp= 1·672 648 x 10-27 kg = 1·007 276 u Neutron rest mass mn = 1·674954 x 10-27 kg = 1·008 665 u Mass of hydrogen atom mH = 1·673559 x 10-27 kg = 1·007 825 u Electron charge-to-mass ratio e/m.= 1·7588045 x 1011 C kg- 1 Proton-to-electron mass ratio mp/m.= 1836'151 Neutron-to-electron mass ratio mn/me= 1838·682 Avogadro constant N A =6'022 045 x 1023 mol- 1 Planck constant h=6'626176 x 10-34 J s 11 = 1·054 589 x 10 - 34 J s Faraday constant F=9'648456 x 104 C mol- 1 First Bohr radius ao = 5'291 771 x 10- 11 m Gas constant R=8·31441 J K- 1 mol- 1 Boltzmann constant k = 1· 380 662 x 10 - 23 J K - 1 Bohr magnet on IlB=9'274 078 X 10-24 J T- 1 Nuclear magneton IlN=5'050 824 x 10-27 J T- 1 Energy conversion factors 1 eV = 1·602189 x 10- 19 J 1 u=931·502 MeV Rydberg constant Roo = 1·097 373 x 107 m- 1 Magnetic constant (permeability of a vacuum) 1l0=41t X 10- 7 H m- 1 Electric constant (permittivity of a vacuum) Bo=8'854188 x 10-12 F m- 1 Standard atmosphere 1 atm = 103 125 Pa These figures are adapted from Quantities, Units and Symbols, published by the Symbols Committee of the Royal Society, London, 1975. PREFACE TO THE THIRD EDITION After the death of Dr. Littlefield it was decided that I should undertake the revision ofthe whole of Atomic and Nuclear Physics: an Introduction for the third edition, and it was soon apparent that major changes were necessary. I am confident that these changes would have had Dr. Littlefield's approval. The prime consideration for the present edition has been to modernize at a minimum cost. As much as possible of the second edition has therefore been retained, but where changes have been made they have been fairly drastic. Thus the chapters on fine structure, wave mechanics, the vector model of the atom, Pauli's principle and the Zeeman effect have been completely restructured. The chapters on nuclear models, cosmic rays, fusion systems and fundamental particles have been brought up to date while a new chapter on charm and the latest ideas on quarks has been included. It is hoped that the presentation of the last named will give readers a feeling that physics research can be full of adventure and surprises. The student targets for the book are the first and second years of an undergraduate course in atomic and nuclear physics at our universities and polytechnics. It will also be useful to those first and second year engineers requiring an atomic and nuclear physics background. The book must not be judged as a final honours text since too many topics are omitted and the mathematical depth is insufficient for this purpose. It is more suitable for all general or ordinary degree students and for first year single honours students. It could also be profitably used by H.N.C. students taking applied physics. The changes made and the new material used are well within the compass of such students. No references to original papers have been given because it is the writer's experience that only those students who are deeply concerned with the subject in their third years take the trouble to use the library for reference purposes. Furthermore, the addition of references within or at the end of each chapter would have added to the cost of this edition. However, many new problems have been included, some of which (marked N) have been taken from the physics papers of the University of Newcastle upon Tyne, and the writer would like to record his thanks to the Senate of this university for permission to use these questions. I must also thank my colleagues Dr. I. D. C. Gurney, Dr. E. L. Lewis, Dr. B. Peart and Professor K. T. Dolder for helpful discussions and I am indebted to Professor A. W. Wolfendale for help with the section on cosmic ray research. Needless to say the writer takes full responsibility for any lack of clarity which vii persists and would be glad to receive comments, corrections and criticisms of the text which might be included in a future printing. Grateful acknowledgement is made to the Culham Laboratory of the U.K.A.E.A. at Abingdon for the use of Fig. 24.11. Grateful acknowledgement and thanks are due to Mrs. Dot"othy Cooper for the excellent art work she produced from the writer's sketches; to the publishers Van Nostrand Reinhold Co. Ltd.; and most especially to Miss L. J. Ward, the College Editor, for her patience during the preparation of this edition. Finally, to my wife, Mrs. Joan Thorley, for much encouragement over the last few months and for transforming my scrawl into a typescript. N.T. Dec 1978 Vlll CONTENTS Table of Physical Constants XVI Chapter 1 KINETIC THEORY 1 1.1 The Atom in History 1 1.2 Brownian Motion 2 1.3 Basic Assumptions of Kinetic Theory 3 1.4 Pressure of a Gas 4 1.5 Molecular Velocities 6 1.6 Temperature of a Gas: Avogadro's Hypothesis 6 1. 7 Mean Free Path 7 1.8 Thermal Conductivity and Viscosity 8 1.9 Specific Heat Capacities 9 1.10 Atomicity 10 1.11 Molar Heat Capacities 12 1.12 Van der Waals' Equation 12 1.13 Molecular Sizes 15 1.14 Summary 16 Chapter 2 THE ELECTRON 19 2.1 Electrical Conduction in Solutions 19 2.2 Conduction in Gases 20 2.3 Properties of Cathode Rays 22 2.4 Thomson's Method for Measuring Charge per Unit Mass (elm) 22 2.5 Dunnington's Method for elm 23 2.6 Charge on the Electron 25 Chapter 3 NATURAL RADIOACTIVITY 30 3.1 Introduction 30 3.2 elm for p-Rays 30 3.3 Bucherer's Method for elm of p-Rays 32 3.4 The Charge-Mass Ratio (ElM) for IX-Rays 33 3.5 Charge on IX-Particles 35 3.6 Identification of IX-Particles 36 3.7 Early Models of the Atom 37 3.8 The Scattering of IX-Particles 38 3.9 Estimates of Nuclear Diameter and Charge 41 3.10 The Neutron 42 IX Chapter 4 RADIOACTIVE SERIES AND ISOTOPES 46 4.1 Introduction 46 4.2 Equation of Radioactive Decay 46 4.3 Mean Lifetime of Radioactive Substance 47 4.4 Half-Lives of Radioactive Substances 49 4.5 Radioactive Series 49 4.6 Radioactive Equilibrium 50 4.7 Isotopes 52 4.8 The Bainbridge Mass Spectrograph 55 Chapter 5 THE ELECTROMAGNETIC SPECTRUM 59 5.1 Theories of Light 59 5.2 Interference 59 5.3 Diffraction 61 5.4 Spectra 62 5.5 The Electromagnetic Theory 63 5.6 Hertz's Experiment 65 5.7 The Electromagnetic Spectrum 66 Chapter 6 QUANTUM THEORY 69 6.1 The Continuous Spectrum 69 6.2 Planck's Quantum Theory 70 6.3 The Photoelectric Effect 71 6.4 Einstein's Equation 72 6.5 The Discovery of X-Rays 74 6.6 Diffraction of X-Rays 75 6.7 X-Ray Wavelengths 77 ~.8 Continuous Spectrum of X-Rays 79 6.9 Compton Effect 80 6.10 Summary 82 CHAPTER 7 SPECTRA 85 7.1 The Hydrogen Spectrum 85 7.2 The Bohr Theory of the Hydrogen Atom 86 7.3 Isotope Effect 90 7.4 The Spectrum of Sodium 93 7.5 Quantum Defects - Interpretation 95 7.6 Selection Rules and the Correspondence Principle 97 7.7 Excitation Potentials 99 7.8 Controlled Excitation of Spectra 101 7.9 X-Ray Spectra 101 7.10 Moseley's Work 102 7.11 The Interpretation of X-Ray Spectra 104 Chapter 8 FINE STRUCTURE AND ELECTRON SPIN 109 8.1 Fine Structure of Alkali-Metal Spectra 109 8.2 Electron