Introduction to Atomic and Nuclear Physics

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1 Introduction to Atomic and Nuclear Physics

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

3 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

4 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, , 1946, 1954, 1962 by Henry Semat 1972 by Holt, Rinehart and Winston, Inc. Fletcher & Son Ltd, Norwich ISBN-13: e-isbn-13: DOl: / 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.

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

6 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-

7 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.

8 Contents PART ONE Foundations of Atomic and Nuclear Physics 1 1 Atoms, Ions, and Electrons Introduction The Avogadro Number The Avogadro Number and the Electronic Charge Atomic Masses Brownian Motion Vertical Distribution of Particles Displacement of Particles in Brownian Motion Determination of the Charge of an Electron Electric Discharge through Gases Determination of elm for Cathode Rays Mass of an Electron 22 2 The Special Theory of Relativity Introduction The Michelson-Morley Experiment Newtonian Relativity; Inertial Systems Fundamental Postulates of Einstein's Special Theory of Relativity The Einstein-Lorentz Transformations Relativity of Length Relativity of Time Relative Velocity Momentum and Energy in Special Relativity Conservation of Momentum and Energy Rest Energy, Kinetic Energy, and Total Energy Relativistic Mass Relativity and Gravitation 45 3 The Nuclear Atom Discovery of Natural Radioactivity Radiation Emitted by Radioactive Substances Determination of QIM for Alpha Particles Nature of the Alpha Particles Velocities of the Alpha Particles Rutherford's Nuclear Theory of the Atom Single Scattering of Alpha Particles by Thin Foils Experimental Verification of Rutherford's Nuclear Theory of the Atom Nuclear Sizes: Radii 64

9 x Contents 3-10 Nuclear Cross Section Isotopic Masses Isotopic Masses and the Constitution of Nuclei Mass of a Nucleus Energy and Mass Units 70 4 Some Properties of Electromagnetic Radiation The Nature of Light Radiation from an Accelerated Charge Polarization of Light Circular and Elliptic Polarization Blackbody Radiation The Planck Radiation Law Einstein's Derivation of Planck's Radiation Law Photoelectric Effect Velocity of the Photoelectrons Einstein's Photoelectric Equation Photoelectrons and Conduction Electrons Phototubes Pressure and Momentum of Radiation Angular Momentum of Radiation X-Rays Discovery of X-Rays Production of X-Rays Measurement of the Intensity of X-Rays Diffraction of X-Rays Single Crystal X-Ray Spectrometer The Grati ng Space of Rocksalt Crystals Typical X-Ray Spectra Continuous X-Ray Spectra Wavelengths of Gamma Rays X-Ray Powder Crystal Diffraction Refraction of X-Rays Measurement of X-Ray Wavelengths by Ruled Gratings Absorption of X-Rays Atomic Absorption Coefficient Scattering of X-Rays Determination of the Number of Electrons per Atom Polarization of X-Rays Intensity of Scattered X-Rays The Compton Effect Compton Recoil Electrons Waves and Particles De Broglie's Hypothesis 153

10 Contents xi 6-2 Electron Diffraction Experiments of Davisson and Germer Electron Diffraction Experiments of G. P. Thomson Waves Associated with Atoms and Molecules Diffraction of Neutrons Velocity of De Broglie Waves Wave and Group Velocities Group Velocity and Particle Velocity Heisenberg's Uncertainty Principle Probabi lity Concept Schroedinger's Equation for a Single Particle Electron Optics Elements of Quantum Mechanics Postulates of Quantum Mechanics The Infinite Square Well Expectation Values for the Infinite Square Well The Free Particle The Step Potential The Harmonic Oscillator The Square Well in Three Dimensions Selection Rules Penetration of a Potential Barrier 208 PART TWO 8 9 The Extranuclear Structure of the Atom 217 The Hydrogen Atom Historical Survey Bohr's Theory of the Hydrogen Atom Motion of the Hydrogen Nucleus The Schroedinger Solution of the Hydrogen Atom Interpretation of the Schroedinger Solution Selection Rules for Hydrogen Electronic Orbits of Hydrogen The Correspondence Principle Elliptic Orbits for Hydrogen 247 Optical Spectra and Electronic Structure Introduction Optical Spectral Series Vector Model of the Atom: Orbital Angular Momentum Electron Spin Total Angular Momentum Vector Magnetic Moment of an Orbital Electron Magnetic Moment due to Spin Magnetic Quantum Numbers 266

11 xii Contents 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 X-Ray Spectra Characteristic X-Ray Spectra X-Ray Energy-Level Diagram X-Ray Absorption Spectra X-Ray Critical Voltages Magnetic Spectrograph X-Ray Terms and Selection Rules Radiationless Transitions-Auger Effect Production of Characteristic X-Ray Spectra PART THREE Selected Applications of Quantum Physics Introduction 325 Molecular Physics 325 Statistical Mechanics Blackbody Radiation Specific Heat of Solids Free Electrons in Metals The Band Theory of Conduction-Electrons Josephson Effect 354 Nuclear Physics 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 Beam Transport and Detecting Devices 13-1 Introduction

12 Contents xiii 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 Radioactivity 425 Resume of Some Known Properties of Nuclei Natural Radioactive Transformations 427 The Curie 428 Radioactive Series The Neptunium Series 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

13 xiv Contents 16 Fission and Fusion of Nuclei Discovery of Nuclear Fission Fission of Uranium Energies of the Fission Fragments Some Products of Nuclear Fission Neutrons from Thermal Fission of 235U Energy of Neutrons from Thermal Fission of 235U Delayed Neutron Emission by Fission Fragments Transuranic Elements-Neptunium and Plutonium Photofission of Nuclei Ternary Fission Spontaneous Fission Fission of Heavy Nuclei Fission of Lighter Nuclei Fission Chain Reaction Processes within a Reactor Types of Nuclear Reactors Transuranic Elements Stellar Energy of Nuclear Origin Stellar Evolution Fusion of Light Nuclei Nuclear Processes Stability of Nuclei Nuclear Spins Nuclear Magnetic Moments-Molecular Beam Method Nuclear Induction and Resonance Absorption Orbital Angular Momentum of the Deuteron Nuclear Models Properties of the Compound Nucleus Formation of a Compound Nucleus Nuclear Shell Structure Beta Decay Comparative Half-Lives for Beta Decay Evidence for the Neutrino Rest Mass of the Neutrino Intermediate-Energy Nuclear Reactions Charge Distribution in Nuclei Fundamental Particles The Four Forces The Discovery of the Mesol) Properties of Muons and Pions Cosmic Rays Primary Cosmic-Ray Particles Antiparticles 594

14 Contents xv i 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 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

MODERN PHYSICS Frank J. Blatt Professor of Physics, University of Vermont

MODERN PHYSICS Frank J. Blatt Professor of Physics, University of Vermont McGRAW-HILL, INC. New York St. Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico Milan Montreal New Delhi