Introduction to Atomic and Nuclear Physics

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.

One Foundations of Atomic and Nuclear Physics.- 1 Atoms, Ions, and Electrons.- 1-1 Introduction.- 1-2 The Avogadro Number.- 1-3 The Avogadro Number and the Electronic Charge.- 1-4 Atomic Masses.- 1-5 Brownian Motion.- 1-6 Vertical Distribution of Particles.- 1-7 Displacement of Particles in Brownian Motion.- 1-8 Determination of the Charge of an Electron.- 1-9 Electric Discharge through Gases.- 1-10 Determination of e/m for Cathode Rays.- 1-11 Mass of an Electron.- 2 The Special Theory of Relativity.- 2-1 Introduction.- 2-2 The Michelson-Morley Experiment.- 2-3 Newtonian Relativity; Inertial Systems.- 2-4 Fundamental Postulates of Einstein’s Special Theory of Relativity.- 2-5 The Einstein-Lorentz Transformations.- 2-6 Relativity of Length.- 2-7 Relativity of Time.- 2-8 Relative Velocity.- 2-9 Momentum and Energy in Special Relativity.- 2-10 Conservation of Momentum and Energy.- 2-11 Rest Energy, Kinetic Energy, and Total Energy.- 2-12 Relativistic Mass.- 2-13 Relativity and Gravitation.- 3 The Nuclear Atom.- 3-1 Discovery of Natural Radioactivity.- 3-2 Radiation Emitted by Radioactive Substances.- 3-3 Determination of Q/M for Alpha Particles.- 3-4 Nature of the Alpha Particles.- 3-5 Velocities of the Alpha Particles.- 3-6 Rutherford’s Nuclear Theory of the Atom.- 3-7 Single Scattering of Alpha Particles by Thin Foils.- 3-8 Experimental Verification of Rutherford’s Nuclear Theory of the Atom.- 3-9 Nuclear Sizes: Radii.- 3-10 Nuclear Cross Section.- 3-11 Isotopic Masses.- 3-12 Isotopic Masses and the Constitution of Nuclei.- 3-13 Mass of a Nucleus.- 3-14 Energy and Mass Units.- 4 Some Properties of Electromagnetic Radiation.- 4-1 The Nature of Light.- 4-2 Radiation from an Accelerated Charge.- 4-3 Polarization of Light.- 4-4 Circular and Elliptic Polarization.- 4-5 Blackbody Radiation.- 4-6 The Planck Radiation Law.- 4-7 Einstein’s Derivation of Planck’s Radiation Law.- 4-8 Photoelectric Effect.- 4-9 Velocity of the Photoelectrons.- 4-10 Einstein’s Photoelectric Equation.- 4-11 Photoelectrons and Conduction Electrons.- 4-12 Phototubes.- 4-13 Pressure and Momentum of Radiation.- 4-14 Angular Momentum of Radiation.- 5 X-Rays.- 5-1 Discovery of X-Rays.- 5-2 Production of X-Rays.- 5-3 Measurement of the Intensity of X-Rays.- 5-4 Diffraction of X-Rays.- 5-5 Single Crystal X-Ray Spectrometer.- 5-6 The Grating Space of Rocksalt Crystals.- 5-7 Typical X-Ray Spectra.- 5-8 Continuous X-Ray Spectra.- 5-9 Wavelengths of Gamma Rays.- 5-10 X-Ray Powder Crystal Diffraction.- 5-11 Refraction of X-Rays.- 5-12 Measurement of X-Ray Wavelengths by Ruled Gratings.- 5-13 Absorption of X-Rays.- 5-14 Atomic Absorption Coefficient.- 5-15 Scattering of X-Rays.- 5-16 Determination of the Number of Electrons per Atom.- 5-17 Polarization of X-Rays.- 5-18 Intensity of Scattered X-Rays.- 5-19 The Compton Effect.- 5-20 Compton Recoil Electrons.- 6 Waves and Particles 153 6-1 De Brogue’s Hypothesis.- 6-2 Electron Diffraction Experiments of Davisson and Germer.- 6-3 Electron Diffraction Experiments of G. P. Thomson.- 6-4 Waves Associated with Atoms and Molecules.- 6-5 Diffraction of Neutrons.- 6-6 Velocity of De Broglie Waves.- 6-7 Wave and Group Velocities.- 6-8 Group Velocity and Particle Velocity.- 6-9 Heisenberg’s Uncertainty Principle.- 6-10 Probability Concept.- 6-11 Schroedinger’s Equation for a Single Particle.- 6-12 Electron Optics.- 7 Elements of Quantum Mechanics.- 7-1 Postulates of Quantum Mechanics.- 7-2 The Infinite Square Well.- 7-3 Expectation Values for the Infinite Square Well.- 7-4 The Free Particle.- 7-5 The Step Potential.- 7-6 The Harmonic Oscillator.- 7-7 The Square Well in Three Dimensions.- 7-8 Selection Rules.- 7-9 Penetration of a Potential Barrier.- Two The Extranuclear Structure of the Atom.- 8 The Hydrogen Atom.- 8-1 Historical Survey.- 8-2 Bohr’s Theory of the Hydrogen Atom.- 8-3 Motion of the Hydrogen Nucleus.- 8-4 The Schroedinger Solution of the Hydrogen Atom.- 8-5 Interpretation of the Schroedinger Solution.- 8-6 Selection Rules for Hydrogen.- 8-7 Electronic Orbits of Hydrogen.- 8-8 The Correspondence Principle.- 8-9 Elliptic Orbits for Hydrogen.- 9 Optical Spectra and Electronic Structure.- 9-1 Introduction.- 9-2 Optical Spectral Series.- 9-3 Vector Model of the Atom: Orbital Angular Momentum.- 9-4 Electron Spin.- 9-5 Total Angular Momentum Vector.- 9-6 Magnetic Moment of an Orbital Electron.- 9-7 Magnetic Moment due to Spin.- 9-8 Magnetic Quantum Numbers.- 9-9 Pauli’s Exclusion Principle.- 9-10 Distribution of Electrons in an Atom.- 9-11 Spectral Notation.- 9-12 Spectrum of Sodium.- 9-13 Absorption of Energy.- 9-14 The Zeeman Effect.- 9-15 Explanations of the Normal Zeeman Effect.- 9-16 The Landé g Factor.- 9-17 The Anomalous Zeeman Effect.- 9-18 The Stern-Gerlach Experiment and Electron Spin.- 9-19 Fine Structure of the Hydrogen Energy Levels.- 9-20 Spectra of Two-Electron Atoms.- 9-21 The Laser.- 10 X-Ray Spectra.- 10-1 Characteristic X-Ray Spectra.- 10-2 X-Ray Energy-Level Diagram.- 10-3 X-Ray Absorption Spectra.- 10-4 X-Ray Critical Voltages.- 10-5 Magnetic Spectrograph.- 10-6 X-Ray Terms and Selection Rules.- 10-7 Radiationless Transitions—Auger Effect.- 10-8 Production of Characteristic X-Ray Spectra.- 11 Selected Applications of Quantum Physics.- 11-1 Introduction.- 11-2 Molecular Physics.- 11-3 Statistical Mechanics.- 11-4 Blackbody Radiation.- 11-5 Specific Heat of Solids.- 11-6 Free Electrons in Metals.- 11-7 The Band Theory of Conduction-Electrons.- 11-8 Josephson Effect.- Three Nuclear Physics.- 12 Particle Accelerators.- 12-1 Introduction.- 12-2 Electrostatic Accelerators.- 12-3 The Cyclotron.- 12-4 The Betatron.- 12-5 Linear Accelerators.- 12-6 Frequency-Modulated Cyclotron.- 12-7 Electron Synchrotron.- 12-8 Proton Synchrotron.- 13 Beam Transport and Detecting Devices.- 13-1 Introduction.- 13-2 Bending Magnets.- 13-3 Quadrupole Magnets.- 13-4 Velocity Spectrometers.- 13-5 Photographic Emulsions.- 13-6 Gas-Filled Detectors.- 13-7 Scintillation Counters and Solid-State Detectors.- 13-8 Cerenkov Counters.- 13-9 Cloud Chambers.- 13-10 Bubble Chambers.- 13-11 Principles of Particle Indentification.- 14 Radioactivity.- 14-1 Résumé of Some Known Properties of Nuclei.- 14-2 Natural Radioactive Transformations.- 14-3 The Curie.- 14-4 Radioactive Series.- 14-5 The Neptunium Series.- 14-6 Branching.- 14-7 Nuclear Isomers.- 14-8 Radioactive Isotopes of the Lighter Elements.- 14-9 Alpha-Particle Disintegration Energy.- 14-10 Range of Alpha Particles.- 14-11 Alpha Decay.- 14-12 Beta-Ray Spectra.- 14-13 Beta Decay.- 14-14 Gamma-Decay.- 14-15 Selection Rules for Gamma Decay.- 14-16 Isomeric States.- 14-17 Resonance Absorption of Gamma Rays.- 14-18 The Moessbauer Effect.- 14-19 Application of Moessbauer Effect to General Relativity.- 15 Nuclear Reactions.- 15-1 Introduction.- 15-2 Discovery of Artificial Disintegration.- 15-3 The (?p) Reaction.- 15-4 Discovery of the Neutron.- 15-5 The (?n) Reaction.- 15-6 Discovery of the Positron.- 15-7 Discovery of Artificial or Induced Radioactivity.- 15-8 Induced Beta Decay.- 15-9 Simple Alpha-Particle Capture; Radiative Capture.- 15-10 Disintegrations by Proton Bombardment.- 15-11 Disintegration by Deuteron Bombardment.- 15-12 Disintegration of Nuclei by Photons.- 15-13 Disintegration by Neutron Bombardment.- 15-14 Radioactive Decay of the Neutron.- 15-15 Electron Capture by Nuclei.- 16 Fission and Fusion of Nuclei.- 16-1 Discovery of Nuclear Fission.- 16-2 Fission of Uranium.- 16-3 Energies of the Fission Fragments.- 16-4 Some Products of Nuclear Fission.- 16-5 Neutrons from Thermal Fission of 235U.- 16-6 Energy of Neutrons from Thermal Fission of 235U.- 16-7 Delayed Neutron Emission by Fission Fragments.- 16-8 Transuranic Elements—Neptunium and Plutonium.- 16-9 Photofission of Nuclei.- 16-10 Ternary Fission.- 16-11 Spontaneous Fission.- 16-12 Fission of Heavy Nuclei.- 16-13 Fission of Lighter Nuclei.- 16-14 Fission Chain Reaction.- 16-15 Processes within a Reactor.- 16-16 Types of Nuclear Reactors.- 16-17 Transuranic Elements.- 16-18 Stellar Energy of Nuclear Origin.- 16-19 Stellar Evolution.- 16-20 Fusion of Light Nuclei.- 17 Nuclear Processes.- 17-1 Stability of Nuclei.- 17-2 Nuclear Spins.- 17-3 Nuclear Magnetic Moments—Molecular Beam Method.- 17-4 Nuclear Induction and Resonance Absorption.- 17-5 Orbital Angular Momentum of the Deuteron.- 17-6 Nuclear Models.- 17-7 Properties of the Compound Nucleus.- 17-8 Formation of a Compound Nucleus.- 17-9 Nuclear Shell Structure.- 17-10 Beta Decay.- 17-11 Comparative Half-Lives for Beta Decay.- 17-12 Evidence for the Neutrino.- 17-13 Rest Mass of the Neutrino.- 17-14 Intermediate-Energy Nuclear Reactions.- 17-15 Charge Distribution in Nuclei.- 18 Fundamental Particles.- 18-1 The Four Forces.- 18-2 The Discovery of the Meson.- 18-3 Properties of Muons and Pions.- 18-4 Cosmic Rays.- 18-5 Primary Cosmic-Ray Particles.- 18-6 Antiparticles.- 18-7 The Concepts of Parity and Time-Reversal.- 18-8 Nonconservation of Parity in Beta Decay.- 18-9 Nonconservation of Parity in Meson Decays.- 18-10 Longitudinal Polarization of Beta Particles.- 18-11 Neutrinos and Their Interactions.- 18-12 K Mesons.- 18-13 Hyperons.- 18-14 Antibaryons.- 18-15 The Classification of Particles.- 18-16 Selection Rules.- 18-17 Resonances.- 18-18 Unitary Symmetry.- 18-19 Frontiers.- Appendixes.- I Physical Constants and Conversion Factors The Greek Alphabet.- II Atomic Weights of the Elements.- III Periodic Table of the Elements.- IV Table of Nuclear Properties 655 V-1 Review of Vector Notation.- V-2 Displacement Equation for Brownian Motion.- V-3 Path of an Alpha Particle in a Coulomb Field of Force.- V-4 Derivation of the Equations for the Compton Effect.- V-6 Quantum Mechanrcal Solution of the Harmonic Oscillator.- V-8 Derivation of the Fermi-Dirac and Bose-Einstein Distributions.- V-9 Probability Density Functions.- Answers to Selected Problems.