Introduction to Atomic and Nuclear Physics

Introduction to Atomic and Nuclear Physics

Aerial view of the National Accelerator Laboratory, Batavia, Illinois. (Photograph courtesy of NAL.)

Introduction to Atomic and Nuclear Physics HENRY SEMAT Professor Emeritus The City College of the City University of New York JOHN R. ALBRIGHT The Florida State University FIFTH EDITION LONDON NEW YORK CHAPMAN AN D HALL

First edition 1939 Fifth edition, first published in the U.S.A. by Holt, Rinehart and Winston, Inc. Fifth edition first published in Great Britain 1973 by Chapman and Hall Ltd 11 New Fetter Lane, London EC4P 4EE Reprinted as a paperback 1978 Reprinted 1979, 1983, 1985 1939, 1946, 1954, 1962 by Henry Semat 1972 by Holt, Rinehart and Winston, Inc. Fletcher & Son Ltd, Norwich ISBN-13: 978-0-412-15670-0 e-isbn-13: 978-1-4615-9701-8 DOl: 10.1007/978-1-4615-9701-8 All rights reserved. No part of this book may be reprinted, or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage and retrieval system, without permission in writing from the Publisher. This paperback edition is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, resold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition being imposed on the subsequent purchaser.

To our respective wives Ray K. Sernat and Christina B. Albright

Preface The fifth edition of this book is the product of many years of teaching this subject by the senior author (H.S.) and incorporates the advice, comments, and suggestions of the many teachers, reviewers, and students who have used it. This new edition also incorporates the modem views, teaching experience, and research activities of the junior author (J.R.A.) The emphasis in this edition is still on the experimental foundations of atomic and nuclear physics with a fair amount of historical material. The major changes consist of (a) the omission of some material, (b) the rearrangement of some of the topics for pedagogical reasons and for a more logical presentation, (c) the updating of all the data, and (d) the addition of many new problems and references. Some details of these changes follow. The chapter on electricity and magnetism has been omitted and the equations pertaining to these subjects have been written with a constant k so that they can be used with either mks or cgs units as the reader may prefer. 1. In the chapter on special relativity, the material on momentum, energy, and mass has been rewritten so as to emphasize the invariance of mass under Lorentz transformation. This change in approach has been found to enhance the student's problem-solving ability, and it brings his thinking in line with that of physicists who use relativity in their daily work. 2. A chapter on simple Schroedinger quantum mechanics has been added. The calculations are mostly (but not entirely) in one dimension, with no time dependence. The emphasis is on providing a quantitative picture of the origin of (a) the uncertainty principle, (b) quantum numbers for bound states, (c) barrier penetration, and (d) selection rules. The presentation starts from a postulational approach, designed to minimize the amount of effort required to get the student to the point where he can solve problems. 3. A new chapter (11) deals with molecules, statistical mechanics, and solid state physics. 4. The chapter on fundamental particles has been expanded and brought upto-date by the addition of material on muon-neutrinos, resonances, and the unitary symmetry scheme of Gell-Mann for classifying particles. 5. A new chapter on detecting devices and beam-transport devices has been added. 6. New mathematical appendixes have been added; tables with numerical values of atomic and nuclear properties have been reorganized and brought up-to-date. Answers to most problems are given at the end of the book. Practically all the other problems contain the answers in the statements of the problems. A sepa-

viii Preface rate Solutions Manual containing the solutions to all the problems is available to instructors only. The book is intended for a one-year course in atomic physics at the sophomorejunior level. With proper selection (Chapters 1-11) it can be used for a onesemester course in atomic physics at this level. It can also be used for a onesemester course in nuclear physics at the junior-senior level (Chapters 3, 11-18). Appropriate acknowledgments have been made in the earlier editions for the generous help given by many teachers and physicists in preparing those editions. Many of their ideas and suggestions are contained in this new edition. We wish to thank them once again for their help. We wish to thank Professor Carl H. Poppe of the University of Minnesota, Professor Margaret C. Foster of the State University of New York at Stony Brook, and Professor A. E. Walters of Rutgers, the State University of New Jersey, who were kind enough to read the entire manuscript of this edition. Their suggestions and criticisms have been very valuable and most of them have been incorporated in the book. Our greatest thanks and appreciation must go to our respective wives, Ray K. Semat and Christina B. Albright, for typing and retyping the manuscript and for their continued encouragement to complete this book. New York Tallahassee, Florida September 1971 H.S. J. R.A.

Contents PART ONE Foundations of Atomic and Nuclear Physics 1 1 Atoms, Ions, and Electrons 3 1-1 Introduction 3 1-2 The Avogadro Number 4 1-3 The Avogadro Number and the Electronic Charge 6 1-4 Atomic Masses 8 1-5 Brownian Motion 9 1-6 Vertical Distribution of Particles 10 1-7 Displacement of Particles in Brownian Motion 13 1-8 Determination of the Charge of an Electron 14 1-9 Electric Discharge through Gases 18 1-10 Determination of elm for Cathode Rays 20 1-11 Mass of an Electron 22 2 The Special Theory of Relativity 25 2-1 Introduction 25 2-2 The Michelson-Morley Experiment 26 2-3 Newtonian Relativity; Inertial Systems 28 2-4 Fundamental Postulates of Einstein's Special Theory of Relativity 30 2-5 The Einstein-Lorentz Transformations 31 2-6 Relativity of Length 33 2-7 Relativity of Time 35 2-8 Relative Velocity 36 2-9 Momentum and Energy in Special Relativity 38 2-10 Conservation of Momentum and Energy 40 2-11 Rest Energy, Kinetic Energy, and Total Energy 41 2-12 Relativistic Mass 44 2-13 Relativity and Gravitation 45 3 The Nuclear Atom 49 3-1 Discovery of Natural Radioactivity 49 3-2 Radiation Emitted by Radioactive Substances 50 3-3 Determination of QIM for Alpha Particles 51 3-4 Nature of the Alpha Particles 53 3-5 Velocities of the Alpha Particles 56 3-6 Rutherford's Nuclear Theory of the Atom 57 3-7 Single Scattering of Alpha Particles by Thin Foils 58 3-8 Experimental Verification of Rutherford's Nuclear Theory of the Atom 60 3-9 Nuclear Sizes: Radii 64

x Contents 3-10 Nuclear Cross Section 65 3-11 Isotopic Masses 66 3-12 Isotopic Masses and the Constitution of Nuclei 67 3-13 Mass of a Nucleus 69 3-14 Energy and Mass Units 70 4 Some Properties of Electromagnetic Radiation 75 4-1 The Nature of Light 75 4-2 Radiation from an Accelerated Charge 76 4-3 Polarization of Light 80 4-4 Circular and Elliptic Polarization 82 4-5 Blackbody Radiation 85 4-6 The Planck Radiation Law 87 4-7 Einstein's Derivation of Planck's Radiation Law 90 4-8 Photoelectric Effect 93 4-9 Velocity of the Photoelectrons 94 4-10 Einstein's Photoelectric Equation 96 4-11 Photoelectrons and Conduction Electrons 97 4-12 Phototubes 99 4-13 Pressure and Momentum of Radiation 101 4-14 Angular Momentum of Radiation 103 5 X-Rays 109 5-1 Discovery of X-Rays 106 5-2 Production of X-Rays 106 5-3 Measurement of the Intensity of X-Rays 111 5-4 Diffraction of X-Rays 112 5-5 Single Crystal X-Ray Spectrometer 117 5-6 The Grati ng Space of Rocksalt Crystals 118 5-7 Typical X-Ray Spectra 120 5-8 Continuous X-Ray Spectra 122 5-9 Wavelengths of Gamma Rays 124 5-10 X-Ray Powder Crystal Diffraction 126 5-11 Refraction of X-Rays 127 5-12 Measurement of X-Ray Wavelengths by Ruled Gratings 132 5-13 Absorption of X-Rays 134 5-14 Atomic Absorption Coefficient 136 5-15 Scattering of X-Rays 137 5-16 Determination of the Number of Electrons per Atom 139 5-17 Polarization of X-Rays 141 5-18 Intensity of Scattered X-Rays 142 5-19 The Compton Effect 143 5-20 Compton Recoil Electrons 147 6 Waves and Particles 153 6-1 De Broglie's Hypothesis 153

Contents xi 6-2 Electron Diffraction Experiments of Davisson and Germer 155 6-3 Electron Diffraction Experiments of G. P. Thomson 159 6-4 Waves Associated with Atoms and Molecules 161 6-5 Diffraction of Neutrons 163 6-6 Velocity of De Broglie Waves 167 6-7 Wave and Group Velocities 169 6-8 Group Velocity and Particle Velocity 171 6-9 Heisenberg's Uncertainty Principle 171 6-10 Probabi lity Concept 175 6-11 Schroedinger's Equation for a Single Particle 177 6-12 Electron Optics 179 7 Elements of Quantum Mechanics 186 7-1 Postulates of Quantum Mechanics 186 7-2 The Infinite Square Well 188 7-3 Expectation Values for the Infinite Square Well 192 7-4 The Free Particle 194 7-5 The Step Potential 196 7-6 The Harmonic Oscillator 199 7-7 The Square Well in Three Dimensions 203 7-8 Selection Rules 205 7-9 Penetration of a Potential Barrier 208 PART TWO 8 9 The Extranuclear Structure of the Atom 217 The Hydrogen Atom 219 8-1 Historical Survey 219 8-2 Bohr's Theory of the Hydrogen Atom 222 8-3 Motion of the Hydrogen Nucleus 229 8-4 The Schroedinger Solution of the Hydrogen Atom 233 8-5 Interpretation of the Schroedinger Solution 239 8-6 Selection Rules for Hydrogen 242 8-7 Electronic Orbits of Hydrogen 243 8-8 The Correspondence Principle 246 8-9 Elliptic Orbits for Hydrogen 247 Optical Spectra and Electronic Structure 256 9-1 Introduction 256 9-2 Optical Spectral Series 257 9-3 Vector Model of the Atom: Orbital Angular Momentum 259 9-4 Electron Spin 261 9-5 Total Angular Momentum Vector 262 9-6 Magnetic Moment of an Orbital Electron 264 9-7 Magnetic Moment due to Spin 265 9-8 Magnetic Quantum Numbers 266

xii Contents 9-9 9-10 9-11 9-12 9-13 9-14 9-15 9-16 9-17 9-18 9-19 9-20 9-21 Pauli's Exclusion Principle 270 Distribution of Electrons in an Atom 270 Spectral Notation 275 Spectrum of Sodium 276 Absorption of Energy 279 The Zeeman Effect 282 Explanations of the Normal Zeeman Effect 284 The Lande 9 Factor 290 The Anomalous Zeeman Effect 292 The Stern-Gerlach Experiment and Electron Spin 295 Fine Structure of the Hydrogen Energy Levels 296 Spectra of Two-Electron Atoms 297 The Laser 300 10 X-Ray Spectra 309 10-1 Characteristic X-Ray Spectra 309 10-2 X-Ray Energy-Level Diagram 311 10-3 X-Ray Absorption Spectra 315 10-4 X-Ray Critical Voltages 317 10-5 Magnetic Spectrograph 318 10-6 X-Ray Terms and Selection Rules 319 10-7 Radiationless Transitions-Auger Effect 321 10-8 Production of Characteristic X-Ray Spectra 322 11 PART THREE 11-1 11-2 11-3 11-4 11-5 11-6 11-7 11-8 Selected Applications of Quantum Physics Introduction 325 Molecular Physics 325 Statistical Mechanics Blackbody Radiation 332 339 Specific Heat of Solids Free Electrons in Metals 342 346 The Band Theory of Conduction-Electrons Josephson Effect 354 Nuclear Physics 361 348 325 12 13 12-1 12-2 12-3 12-4 12-5 12-6 12-7 12-8 Particle Accelerators 363 Introduction 363 Electrostatic Accelerators 364 The Cyclotron 367 The Betatron 369 Linear Accelerators 373 Frequency-Modulated Cyclotron Electron Synchrotron 380 Proton Synchrotron 384 377 Beam Transport and Detecting Devices 13-1 Introduction 394 394

Contents xiii 13-2 13-3 13-4 13-5 13-6 13-7 13-8 13-9 13-10 13-11 Bending Magnets 395 Quadrupole Magnets 397 Velocity Spectrometers 400 Photographic Emulsions 402 Gas-Filled Detectors 404 Scintillation Counters and Solid-State Detectors Cerenkov Counters 411 Cloud Chambers 413 Bubble Chambers 414 Principles of Particle Indentification 419 409 14 15 14-1 14-2 14-3 14-4 14-5 14-6 14-7 14-8 14-9 14-10 14-11 14-12 14-13 14-14 14-15 14-16 14-17 14-18 14-19 15-1 15-2 15-3 15-4 15-5 15-6 15-7 15-8 15-9 15-10 15-11 15-12 15-13 15-14 15-15 Radioactivity 425 Resume of Some Known Properties of Nuclei Natural Radioactive Transformations 427 The Curie 428 Radioactive Series The Neptunium Series 425 428 432 Branching 433 Nuclear Isomers 433 Radioactive Isotopes of the Lighter Elements 434 Alpha-Particle Disintegration Energy 435 Range of Alpha Particles 437 Alpha Decay 440 Beta-Ray Spectra 442 Beta Decay 445 Gamma-Decay 447 Selection Rules for Gamma Decay 449 Isomeric States 450 Resonance Absorption of Gamma Rays 452 The Moessbauer Effect 454 Application of Moessbauer Effect to General Relativity 458 Nuclear Reactions 467 Introduction 467 Discovery of Artificial Disintegration 468 The (a,p) Reaction 471 Discovery of the Neutron 474 The (a,n) Reaction 476 Discovery of the Positron 478 Discovery of Artificial or Induced Radioactivity 479 Induced Beta Decay 481 Simple Alpha-Particle Capture; Radiative Capture 482 Disintegrations by Proton Bombardment 484 Disintegration by Deuteron Bombardment 486 Disintegration of Nuclei by Photons 490 Disintegration by Neutron Bombardment 492 Radioactive Decay of the Neutron 498 Electron Capture by Nuclei 500

xiv Contents 16 Fission and Fusion of Nuclei 508 16-1 Discovery of Nuclear Fission 508 16-2 Fission of Uranium 509 16-3 Energies of the Fission Fragments 513 16-4 Some Products of Nuclear Fission 515 16-5 Neutrons from Thermal Fission of 235U 517 16-6 Energy of Neutrons from Thermal Fission of 235U 518 16-7 Delayed Neutron Emission by Fission Fragments 520 16-8 Transuranic Elements-Neptunium and Plutonium 521 16-9 Photofission of Nuclei 523 16-10 Ternary Fission 524 16-11 Spontaneous Fission 525 16-12 Fission of Heavy Nuclei 526 16-13 Fission of Lighter Nuclei 527 16-14 Fission Chain Reaction 529 16-15 Processes within a Reactor 530 16-16 Types of Nuclear Reactors 532 16-17 Transuranic Elements 535 16-18 Stellar Energy of Nuclear Origin 538 16-19 Stellar Evolution 539 16-20 Fusion of Light Nuclei 541 17 Nuclear Processes 546 17-1 Stability of Nuclei 546 17-2 Nuclear Spins 548 17-3 Nuclear Magnetic Moments-Molecular Beam Method 549 17-4 Nuclear Induction and Resonance Absorption 553 17-5 Orbital Angular Momentum of the Deuteron 556 17-6 Nuclear Models 557 17-7 Properties of the Compound Nucleus 560 17-8 Formation of a Compound Nucleus 560 17-9 Nuclear Shell Structure 563 17-10 Beta Decay 567 17-11 Comparative Half-Lives for Beta Decay 569 17-12 Evidence for the Neutrino 571 17-13 Rest Mass of the Neutrino 575 17-14 Intermediate-Energy Nuclear Reactions 576 17-15 Charge Distribution in Nuclei 578 18 Fundamental Particles 583 18-1 The Four Forces 583 18-2 The Discovery of the Mesol) 584 18-3 Properties of Muons and Pions 589 18-4 Cosmic Rays 592 18-5 Primary Cosmic-Ray Particles 593 18-6 Antiparticles 594

Contents xv 18-7 18-8 18-9 18-10 18-1 i 18-12 18-13 18-14 18-15 18-16 18-17 18-18 18-19 The Concepts of Parity and Time-Reversal Nonconservation of Parity in Beta Decay Nonconservation of Parity in Meson Decays Longitudinal Polarization of Beta Particles Neutrinos and Their Interactions 609 K Mesons 614 Hyperons 616 Antibaryons 620 The Classification of Particles 625 Selection Rules 628 Resonances 629 Unitary Symmetry 635 Frontiers 640 599 601 605 607 APPENDIXES Physical Constants and Conversion Factors 649 The Greek Alphabet II Atomic Weights of the Elements 652 III Periodic Table of the Elements 654 IV Table of Nuclear Properties 655 V-1 Review of Vector Notation 667 V-2 Displacement Equation for Brownian Motion 669 V-3 Path of an Alpha Particle in a Coulomb Field of Force 672 V-4 Derivation of the Equations for the Compton Effect 677 V-5 Evaluation of Integrals of the Form 1000 V" exp (_AV2) dv 681 V-6 Quantum Mechanrcal Solution of the Harmonic Osci liator 683 V-7 Evaluation of f Pr dr = nrh 687 V-8 Derivation of the Fermi-Dirac and Bose-Einstein Distributions 691 V-9 Probability Density Functions 693 Answers to Selected Problems 695 Index 701