An Rso Manual revision July16 2015

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    Nevada

    Technical

    AssociatesRadiation Safety Training

    P.O. Box 93355 • Las Vegas, Nevada 89193-3355

    1-702-564-2798 • www.ntanet.net

    Radiation

    Safety Officer

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    Radiation Safety Officer

    Robert Holloway, Ted Allen, and Eva Mart

    16 July, 2015

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    RSO   CONTENTS 

    Contents

    1 Introduction   111.1 Radiation Safety Officer Training Course Roadmap   . . . . . . . . . . . . . . . . . . 131.2 What is Radioactivity?   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.3 Atomic Structure   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    1.4 Chemical Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.4.1 Modification to the Bohr Atomic Model   . . . . . . . . . . . . . . . . . . . . 201.4.2 Periodic Table of Elements  . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

    1.5 Mass & Energy Equivalency   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221.6 Binding Energy   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.7 Naturally Occurring Radionuclides   . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

    1.7.1 Cosmic Rays   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261.7.2 Cosmogenic Radionuclides   . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271.7.3 Primordial Radionuclides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.7.4 Areas of Unusually High Levels of NORM   . . . . . . . . . . . . . . . . . . . 301.7.5 Natural Reactor at Oklo   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

    1.7.6 Consumer Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311.8 Historical Highlights Related to Nuclear Science   . . . . . . . . . . . . . . . . . . . . 32

    2 Radioactive Decay   392.1 Radioactive Decay Kinetics   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

    2.1.1 Serial Decay   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.1.2 Parent-Daughter Equilibrium   . . . . . . . . . . . . . . . . . . . . . . . . . . 45

    2.2 Radioactive Decay Modes   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492.2.1 Alpha Particle Decay  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502.2.2 Beta Particle Decay & Internal Conversion   . . . . . . . . . . . . . . . . . . . 522.2.3 Positron Decay & K-Capture   . . . . . . . . . . . . . . . . . . . . . . . . . . 542.2.4 Photons Emitted During Decay   . . . . . . . . . . . . . . . . . . . . . . . . . 562.2.5 Spontaneous Fission:   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

    2.3 Chart of the Nuclides  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.4 Decay Statistics   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

    2.4.1 Reducing Uncertainty   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632.4.2 Computing Uncertainty in Background Corrected Values   . . . . . . . . . . . 64

    3 Interactions of Radiation with Matter   673.1 Energy Transfer   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

    3.1.1 Range   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

    3.2 Alpha Particle Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.2.1 Alpha Particle Paths   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.2.2 Alpha Particle Kinetic Energies & Velocities   . . . . . . . . . . . . . . . . . . 723.2.3 Alpha Particle Specific Ionizations . . . . . . . . . . . . . . . . . . . . . . . . 723.2.4 Alpha Particle Range  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

    3.3 Beta Particle Interactions   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.3.1 Beta Particle Paths  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.3.2 Beta Particle Kinetic Energies & Velocities  . . . . . . . . . . . . . . . . . . . 753.3.3 Beta Particle Specific Ionization  . . . . . . . . . . . . . . . . . . . . . . . . . 76

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    3.3.4 Beta Particle Energy Dissipation   . . . . . . . . . . . . . . . . . . . . . . . . 763.3.5 Beta Particle Range:   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

    3.4 Positron Interactions   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793.5 High-Energy Photon (Gamma and X-ray) Interactions   . . . . . . . . . . . . . . . . 79

    3.5.1 Electromagnetic Spectrum   . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.5.2 Photon Energy   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

    3.5.3 Gamma and X-ray Specific Ionization Rates   . . . . . . . . . . . . . . . . . . 813.5.4 Gamma and X-ray Interactions with Matter   . . . . . . . . . . . . . . . . . . 813.5.5 Photoelectric Effect  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823.5.6 Compton Scattering   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.5.7 Pair Production  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.5.8 Combined Gamma-ray Cross Sections . . . . . . . . . . . . . . . . . . . . . . 853.5.9 Gamma and X-ray Ranges   . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

    3.6 Neutron Interactions   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.6.1 Neutron Energies   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.6.2 Types of Neutron Interactions   . . . . . . . . . . . . . . . . . . . . . . . . . . 883.6.3 Neutron Specific Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883.6.4 Neutron Attenuation   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883.6.5 Neutron Specific Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

    4 Radiation Detection and Measurement   934.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

    4.1.1 Basic Survey Instruments Parts   . . . . . . . . . . . . . . . . . . . . . . . . . 954.1.2 Types of Radiation   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

    4.2 Operating Principles   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.2.1 Gas Filled Cylinders   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.2.2 Operating Voltages - Gas Filled   . . . . . . . . . . . . . . . . . . . . . . . . . 100

    4.2.3 Nuclear Spectroscopy  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.2.4 Scintillation Detectors   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024.2.5 Semiconductor (solid-state) Detectors  . . . . . . . . . . . . . . . . . . . . . . 103

    4.3 Instruments Classified by Function   . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034.3.1 Beta Detectors   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044.3.2 Alpha Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054.3.3 Photon Detectors   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.3.4 Neutron Detectors   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

    4.4 Survey Instrument Concerns   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.4.1 Survey Instrument Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.4.2 Background Radiation   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

    4.4.3 Minimum Detectable Levels   . . . . . . . . . . . . . . . . . . . . . . . . . . . 1094.4.4 Survey Instrument Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . 110

    5 Biological Effects of Radiation   1115.1 History of Radiobiology   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135.2 Dose Terms   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1145.3 Dose Pathways   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

    5.3.1 External Pathways   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.3.2 Internal Pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

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    5.3.3 Bio kinetic Models   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.3.4 Effective half-life   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.3.5 Protective Measures after Intake . . . . . . . . . . . . . . . . . . . . . . . . . 1175.3.6 Internal Dose Units  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

    5.4 The Cell   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1175.5 Effects of Radiation on Cells  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

    5.6 Cell Survival Curves   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1205.6.1 Factors Affecting Amount of Cellular Damage   . . . . . . . . . . . . . . . . . 1215.6.2 Relative Biological Effectiveness (RBE)  . . . . . . . . . . . . . . . . . . . . . 125

    5.7 Human Health Effects from Radiation Exposure   . . . . . . . . . . . . . . . . . . . . 1265.7.1 Non-stochastic (Deterministic) Effects   . . . . . . . . . . . . . . . . . . . . . 1265.7.2 Stochastic Effects  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1275.7.3 Prenatal Exposure   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1285.7.4 Life Shortening   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1295.7.5 Genetic Effects   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

    5.8 Risk   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1315.8.1 Risk Evaluation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1315.8.2 Risk Estimates   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1335.8.3 Risk Comparison   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1335.8.4 Risk Communication   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

    5.9 Dose Terms & Concepts   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

    6 Shielding   1556.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1576.2 Ionizing Radiation Shielding   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

    6.2.1 Shielding of Charged Particles   . . . . . . . . . . . . . . . . . . . . . . . . . . 1576.2.2 Shielding of Photons   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

    6.2.3 Shielding of Neutrons  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1636.3 Facility Shielding   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

    7 Personnel Dosimetry Devices and Methods   1737.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1757.2 External Personnel Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

    7.2.1 Charged Particle Equilibrium and Bragg-Gray   . . . . . . . . . . . . . . . . . 1757.2.2 Photodosimetry   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1767.2.3 Thermoluminescence Dosimetry   . . . . . . . . . . . . . . . . . . . . . . . . . 1797.2.4 Neutron Dosimetry   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1817.2.5 Pocket Dosimeters   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

    7.2.6 Other External Dosimetric Devices and Instruments  . . . . . . . . . . . . . . 1847.2.7 Performance Testing   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

    7.3 External Dose Evaluation   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1867.3.1 Point Source Calculations   . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1867.3.2 Other Geometries   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1887.3.3 Neutron Dose   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1907.3.4 Dose from Beta Particles   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

    7.4 Internal Personnel Monitoring   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1917.4.1 Monitoring Methods   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

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    7.4.2 Internal Dose Evaluation   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

    8 Regulations and Guidance   2058.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2078.2 Chronology of Protection Standards in the U.S.   . . . . . . . . . . . . . . . . . . . . 2088.3 Sources of Standards, Recommendations, and Requirements   . . . . . . . . . . . . . 209

    8.3.1 ICRP, ICRU, NCRP, and ANSI   . . . . . . . . . . . . . . . . . . . . . . . . . 2098.3.2 HPS, ACR, and CRCPD  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2108.3.3 Regulatory Guides, Notices, and Bulletins   . . . . . . . . . . . . . . . . . . . 210

    8.4 Basis for Current Protection Standards   . . . . . . . . . . . . . . . . . . . . . . . . . 2108.5 Current Regulations   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

    8.5.1 10 CFR 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2118.5.2 Additional Radiation Safety Regulations   . . . . . . . . . . . . . . . . . . . . 215

    8.6 Licensing Procedures   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2198.6.1 Applicable Regulations   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2208.6.2 Licensing Applications   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

    8.7 10 CFR 20 Summaries   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

    8.8   Typical RSO Duties And Responsibilities   . . . . . . . . . . . . . . . . . . . . 2318.9   BROAD SCOPE LICENSE APPLICATION SUMMARY   . . . . . . . . . . 2338.10 AMERICAN NATIONAL STANDARDS   . . . . . . . . . . . . . . . . . . . . . . . . 2398.11 US NRC Regulatory Guides Series Division 8 - Occupational Health  . . . . . . . . . 241

    9 Radiological Safety Surveys, Control, and Documents   2439.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2459.2 Surveys and Inspections   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

    9.2.1 Types of Surveys with Instruments   . . . . . . . . . . . . . . . . . . . . . . . 2479.2.2 Radiation Level Surveys   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2479.2.3 Radioactivity Contamination Surveys  . . . . . . . . . . . . . . . . . . . . . . 2489.2.4 Airborne Radioactivity Surveys   . . . . . . . . . . . . . . . . . . . . . . . . . 249

    9.3 Radiological Controls   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2519.3.1 Work Area Controls   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2519.3.2 Work Practices   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2519.3.3 Containment and Ventilation Systems . . . . . . . . . . . . . . . . . . . . . . 2529.3.4 Decontamination Practices  . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2539.3.5 Security and Other Physical Controls   . . . . . . . . . . . . . . . . . . . . . . 2539.3.6 Administrative Controls   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2549.3.7 ALARA and “Best Practices”   . . . . . . . . . . . . . . . . . . . . . . . . . . 255

    9.4 Records and Documents   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

    9.4.1 Radioactive Material License/Registration   . . . . . . . . . . . . . . . . . . . 2569.4.2 Radioactive Material Receipt, Transfer, and Disposal Records   . . . . . . . . 2569.4.3 Radioactive Material Inventories . . . . . . . . . . . . . . . . . . . . . . . . . 2569.4.4 Sealed Source Leak Test Records   . . . . . . . . . . . . . . . . . . . . . . . . 2569.4.5 Radiation and Contamination Survey Records   . . . . . . . . . . . . . . . . . 2569.4.6 Personnel Dosimetry Records   . . . . . . . . . . . . . . . . . . . . . . . . . . 2579.4.7 Instrument Calibration and Safety Test Records   . . . . . . . . . . . . . . . . 2579.4.8 Personnel Selection, Training, and Supervision Records   . . . . . . . . . . . . 2589.4.9 Audits   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

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    9.4.10 Notifications, Documentation, and Reporting of Radiation Accidents   . . . . 2599.4.11 Operating and Emergency Procedures   . . . . . . . . . . . . . . . . . . . . . 2599.4.12 Document Control   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

    10 Transportation and Disposal Regulations   26110.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

    10.2 Packaging of Radioactive Material for Shipment   . . . . . . . . . . . . . . . . . . . . 26310.2.1 Transportation Package Categories   . . . . . . . . . . . . . . . . . . . . . . . 26410.2.2 Radiation and Contamination Limits   . . . . . . . . . . . . . . . . . . . . . . 26510.2.3 Transport Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26610.2.4 Receiving and Opening Packages   . . . . . . . . . . . . . . . . . . . . . . . . 26610.2.5 Manifest and Hazardous Material Documents   . . . . . . . . . . . . . . . . . 26710.2.6 Package Marking, Labels, and Vehicle Placards   . . . . . . . . . . . . . . . . 267

    10.3 Radioactive Waste Disposal   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26910.3.1 Solid Radioactive Waste Disposal   . . . . . . . . . . . . . . . . . . . . . . . . 26910.3.2 Liquid Radioactive Waste Disposal   . . . . . . . . . . . . . . . . . . . . . . . 27110.3.3 Airborne Radioactive Waste   . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

    10.3.4 Radioactive Waste Disposal Sites   . . . . . . . . . . . . . . . . . . . . . . . . 271

    11 Radiological Emergencies   27711.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27911.2 Responsibilities   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27911.3 Assistance   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27911.4 Preparedness   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28011.5 Classification of Incidents   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

    11.5.1 Classification by Location   . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28111.5.2 Classification by Radiological Condition   . . . . . . . . . . . . . . . . . . . . 28111.5.3 Classification by Degree of Severity   . . . . . . . . . . . . . . . . . . . . . . . 281

    11.6 Incident Phases   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28111.7 Incident Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

    11.7.1 Scene Isolation   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28311.7.2 Radiation and Medical Evaluations   . . . . . . . . . . . . . . . . . . . . . . . 28311.7.3 Personnel Decontamination   . . . . . . . . . . . . . . . . . . . . . . . . . . . 28311.7.4 Notifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

    11.8 Review of Radiological Incidents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

    12 References   293

    13 NCRP Publications   315

    14 License Examples   325

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    1 Introduction

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    1.1 Radiation Safety Officer Training Course Roadmap

    Radiation safety (aka Health Physics) draws from many different scientific disciplines in developingprinciples, procedures and techniques for the protection of personnel, the public, and the environ-ment from the effects of radiation. This course presents theoretical concepts, practical information,and real-life examples to equip you to fulfill essential Radiation Safety Officer (RSO) duties.

    Some subjects may be repeated in separate lessons under different contexts. Such repetition isintended, and should help you master certain key concepts. The following table summarizes thecontents of each lesson.

    Table 1:  Radiation Safety Officer Training Roadmap

    Section 1 Introduction

    Chemical Interactions

    Mass-Energy Equivalence

    Binding EnergyNaturally Occurring Radionuclides

    Historical Highlights

    Section 2  Radioactive Decay

    Processes

    Radioactive Decay Equilibrium

    Decay Processes

    Chart of the Nuclides

    Decay Statistics

    Section 3  Interaction of 

    Radiation with Matter

    Modes of Interaction and Ranges for

    alpha particles

    beta particles

    gamma & x-rays

    neutrons

    Section 4  Radiation Detection &

    Measurement

    Operating Principles of Instrumentation

    Detection Issues Related to Type of Radiation

    Section 5  Biological Effects of 

    Radiation

    Dose Units

    Mechanisms of Biological Damage

    Deterministic Effects

    Stochastic EffectsWhat is Risk?

    Section 6 Shielding

    Shielding Related to Types of Radiation:

    charged particles

    gamma rays

    neutrons

    General Issues in Facility Shielding

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    Table 1:  Radiation Safety Officer Training Roadmap Cont.

    Section 7 Personnel Dosimetry

    External Dosimeters

    External Dose Evaluations

    Internal Dose Evaluations

    Section 8 Regulations & Guides

    Chronology

    Sources

    Current Regulations

    NRC Licensing Procedures

    Section 9  Surveys, Records &

    Documentation

    Surveys & Inspections

    Radiological Controls & Work Practices

    ALARA

    Record-keeping & Documentation

    Operating & Emergency Procedures

    Section 10  Transportation &

    Disposal Regulations

    Applicable Regulations

    Packaging for Transport

    Package Marking and Labels & Vehicle Placards

    Radioactive Waste Disposal

    Section 11

      Radiological

    Emergencies

    Emergency Classification

    Accident Phases

    Notifications

    Assistance Teams

    Emergency Response

    Accident Causes & Examples

    Section 12 Reference Info

    Mailing Lists & Websites

    Glossary

    Abbreviations

    List of Elements

    Conversion Factors

    References

    Section 13 Reference Info NRC Publications

    Section 14 Reference Info NRC Materials License Application Example

    Section 15 Reference Info Safety Videos & Training CDs Available fromNevada Technical Associates

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    1.2 What is Radioactivity?

    Although radioactivity has existed since the Earth’s formation, the discovery of this phenomenonis a recent event. Radioactive processes involve atomic nuclei, in contrast to chemical reactionswhich involve changes in the arrangement of outer electrons.

    Chemical reactions can result in the formation of new compounds due to the rearrangement of elements, such as HCl + NaOH

     → NaCl + H

    2

    O. Nuclear processes, on the other hand, typically,result in the formation of new elements (for example,   14C →   14N + electron).

    Table 2:   Radiation & Radioactivity Definitions

    Radioactivity The spontaneous process by which unstable atoms emit or radi-ate excess energy from their nuclei, and thus, change or decayto atoms of a different element or to a lower energy state of thesame element.

    Radionuclide Unstable atomic species which spontaneously “decay” and emit

    radiation.

    Radiation High energy particles and electromagnetic rays emitted fromatomic nuclei during radioactive disintegration.

    However, the term “radiation”, is also often used instead of thelonger term, “electro-magnetic radiation” (aka electromagneticrays or photons), whether or not they originate in the nucleus.And, there are two broad categories or electromagnetic radia-tion (ionizing and non-ionizing). For example, x-rays originateoutside of nuclei and typically have sufficient energy to ionize

    atoms.

    Electromagnetic Radiation Another term for  “photon”   which is an electromagnetic “par-ticle” or “corpuscle” that always travel in waves at a velocityof 3 × 108 m/ s in a vacuum. Each particle has zero mass, noelectric charge, and an indefinitely long lifetime. The energy of a photon is   inversely proportional to its wavelength .

    Ionizing ElectromagneticRadiation

    Ionizing electromagnetic radiation  consists of photons possessingenough energy to completely free electrons from atoms, therebyproducing ions. An ion is an atom which has lost or gained oneor more electrons, making it negatively or positively charged.

    Non-IonizingElectromagnetic Radiation

    Non-ionizing electromagnetic radiation  consists of photons thatdo not possess sufficient energy to ionize atoms. However, non-ionizing electromagnetic radiation may have enough energy toexcite electrons, that is cause them to move to a higher energystate. Examples include near ultraviolet rays, visible light, in-frared light, microwaves, and radio waves.

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    Figure 1:  Bohr Atomic Model   1

    1.3 Atomic Structure

    An atom is considered the most basic and fundamental particle of matter, although it’s made upof subatomic particles (e.g. electrons, protons & neutrons, which in turn consist of even smallerparticles). When radioactivity was first discovered, little was known about the structure of anatom.

    Models are theoretical constructs developed to explain the manner in which things happen.Since no one can ‘see’ an atom, let alone a nucleus, our ability to understand an atom is basedon observing what they do when placed under certain conditions. Models are then developed by“figuring backwards”. For example, Rutherford surmised that an atom consists mostly of a verydense nucleus surrounded by empty space and an electron cloud, because of the way alpha particleswere deflected when they impinged upon a thin gold sheet. Models are useful in that they describe

    observed phenomena and permit prediction of the consequences of certain acts.Philosophically, most scientists subscribe to a school of thought called “logical positivism”. Ac-cording to this philosophy, “reality” (model or theory) cannot be verified with certainty. Therefore,science is instead concerned with the simplest possible unified description of as many experimentalfindings as possible. According to this philosophy of science, ascribing to even different models toexplain one phenomenon is acceptable provided each theory is capable of describing experimentalfacts the others cannot explain. Thus, models stand, are enhanced, or even entirely debunked asknowledge increases and new instrumentation enhances our powers of observation. For example,based on newly published quantum mechanics (first by Plank and then added to by Einstein),Bohr expanded upon Rutherford’s initial solar system type atomic model.

    Bohr’s model illustrates that electrons orbit the nucleus in differing energy regions called orbits

    or shells (analogous to planets orbiting the sun, but not in a single plane). Bohr’s Model isconsidered a “planetary-type” model because the attractive gravitational force in a solar systemand the attractive Coulomb force (between the positively charged nucleus and the negativelycharged electrons) in an atom are mathematically of the same form. However, these forces differ.The intrinsic strength of the Coulomb interaction is much larger than that of the gravitationalinteraction. In addition, Coulomb forces can be attractive or repulsive, whereas the gravitational

    1A schematic illustration of the Bohr model of the atom by Adrignola available at   https://commons.wikimedia.org/wiki/File:Bohr%27s_model.svg   under a Creative Commons Attribution 3.0. Full terms athttp://creativecommons.org/licenses/by-sa/3.0/

    16

    https://commons.wikimedia.org/wiki/File:Bohr%27s_model.svghttps://commons.wikimedia.org/wiki/File:Bohr%27s_model.svghttp://creativecommons.org/licenses/by-sa/3.0/http://creativecommons.org/licenses/by-sa/3.0/https://commons.wikimedia.org/wiki/File:Bohr%27s_model.svghttps://commons.wikimedia.org/wiki/File:Bohr%27s_model.svg

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    force is always attractive. The key feature of quantum mechanics that is incorporated in the BohrModel is that electrons are restricted to certain discrete energy values (called shells or orbits).The energy associated with a given shell is said to be quantized. This means that only certainelectron orbits with certain radii are allowed; orbits in-between do not exist. Electrons can maketransitions between the shells allowed by quantum mechanics by absorbing or emitting exactly theenergy difference between the orbitals. By absorbing an energy equal to, or more than, what is

    called the ionization potential, an electron can become freed from an atom and no longer bound toit leaving the atom ionized. Amazingly, Bohr’s 1913 atomic theory still approximates the currentmost accepted atomic model, where:

    •  There are two sets of forces acting upon the nucleus. 1) ordinary coulomb forces of repulsionbetween the positively charged protons in close proximity; and 2) a “strong nuclear force”holding the protons and neutrons together.

    –  The combined effects of these two forces enable only certain neutron to proton ratiosto be stable.

    •  The majority of an atom’s mass is contained within a small, dense nucleus (on the order of 10 mega-tons/cm3).

    •   The diameter of a nucleus is on the order of 1 × 10−12 cm. It’s surrounded by a largely emptyregion 1 × 10−8 cm in diameter in which electrons orbit the nucleus. Thus, the diameter of anucleus is around 10,000 times less than the overall atom diameter.

    •   The nucleus contains positively charged protons (each 1.6 × 10−19 C) and neutrally chargedneutrons. The masses of protons and neutrons are: 1.6726 × 10−24 g and 1.6749 × 10−24 g,respectively.)

    •  The number of extranuclear electrons equals the number of protons within the nucleus. Eachelectron carries the same charge as a proton, but negative instead of positive. Thus, the net

    charge of an atom is zero.

    –  Electrons have a mass around 9.11 × 10−28 g.–  Electrons orbit nuclei in fixed energy shells (quantized orbits); with each shell having a

    characteristic binding energy for a given element.

    Table 3:  Important Atomic Terms & Concepts

    Atomic Number (Z) The number of protons and hence positive charges in a nucleus.

    “Elements”  are defined by their atomic number (regardless of theneutron number), so all atoms of a given element have the same Znumber. Since a neutral atom has a net zero charge, Z is also thenumber of electrons orbiting the nucleus.

    Neutron Number (N) The number of neutrons in a nucleus (N= A-Z).

    Nucleon Generic term for protons and neutrons.

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    Table 3:  Important Atomic Terms & Concepts Cont.

    Mass Number (A) The total number of nucleons in a given nuclide. It is always an in-teger (whole number) and should not be confused with the nuclide’sprecise mass, which is not a whole number. (A= N + Z)

    Atom SymbolizationAZX

    X is the  element symbol  - such as Sr for Strontium

    A is the  mass number  - such as 90 in Strontium 90   9038Sr

    Z is the  atomic number  - such as 38 for Strontium   9038Sr

    Isotope   Isotopes  are different forms of a given element; where each has thesame atomic number (Z) but different neutron numbers (N). Forexample, a   2H (deuterium - with 1 proton and 1 neutron) is anisotope of   1H (hydrogen - with 1 proton and 0 neutrons).

    Nuclide A nuclide is a generic term for any atomic nucleus specified by itsatomic number, mass number and charge. The term  “isotope”   isoften used loosely instead of  “nuclide”. Isotope is best used whenreferring to different atomic species of the same  element .

    Atomic Mass Units[Nuclear Mass Scale]

    Atomic mass units (amu)   provides the means for citing masses“relative” to   12C unbound, at rest, and in its ground state. Bydefinition  12C has 12amu; correspondingly one amu  equals the massin 1/12 of a   12C atom. The actual mass of one  amu  is based on the6 protons, 6 neutrons, and 6 electrons in one   12C atom and equals

    1.66 × 10−24

    g.

    An atom’s “atomic weight”  is its “amu number”; which is its mass“relative” to   12C or: atomic weight = 12 x (mass A / mass   12C)

    The atomic weight of an  “element”  is a weighted average, account-ing for the natural abundance of all the element’s isotopes.

    Moles andAvogadro’s Number

    One mole = atomic weight-g and contains Avogadro’s number of entities. Where: Avogadro’s number= 6.022 × 10 23 atoms (or molecules)

    Since one mole of an element is its  atomic weight  in grams and willcontain 6.022 × 1023 atoms, the number of atoms in any given masscan readily be computed. For example, since 12 g of   12C contains6.022 × 1023 atoms as does 235 g of   235U:

    100 g of   235U contains 100/235 × 6.022 × 1023 = 2.56 × 1023 atoms,and 100 g of  12C, 100/12 × 6.022 × 1023 atoms = 50.18 × 1023 atoms

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    1.4 Chemical Interactions

    Radioactive processes alter atomic nuclei, while chemical reactions involve changes in the arrange-ment of valence electrons, rather than nuclei. The chemical properties of an atom are determinedby characteristics of its outermost electrons, and formation of chemical compounds involve minorrearrangements of these electronic structures.

    Although chemical interactions do not affect the nucleus, the converse is not true. That is,ionizing radiation disrupts orbital electrons and radioactive decay often results in new elementsbeing formed (e.g. change in Z number).

    Table 4:   Basic Chemistry

    Electron Shells Extranuclear electrons ( e– ) can be conceptualized as “orbiting anucleus” like planets around the sun, except not in a fixed plane.Electrons arrange themselves in fixed orbitals (quantized energyshells) according to well-established laws. The closest electron or-

    bital is labeled K (and can only hold two electrons). The nextorbital is L (and can hold only 8 electrons). The outer most shellis called the “valence” shell. Electrons in the closer shells havinghigher binding energies, and those in the valence shells the least.

    Electronic Neutrality One of the basic physical laws of nature is that like charges repeland opposite charges attract. Thus, atoms move towards electronicneutrality and an ionized atom is very reactive.

    Full Valence Shells Another basic tendency is that towards a “full valence shell”. Thistendency plus that towards electric neutrality, govern the chemical

    behavior of elements. For example: Elemental fluorine (9

    F) hastwo electrons in its K- shell, and 7 in its L- shell. Thus, it onlyneeds one electron to “fill” its L-shell (i.e. 8 electrons). However,if it gained one electron, it would have a net negative charge sinceits nucleus has 9 protons. Elemental hydrogen (1H), on the otherhand, needs one electron to fill its valence shell. Thus, if a hydrogenatom forms a “bond” with a fluorine atom (HF), these two- basictendencies are satisfied for both elements.

    Ionization & Excitation When a sufficient amount of energy is imparted to an electron toremove it entirely from the electrical field of a nucleus, the atom

    becomes ionized. The “free electron” and positively charged atomtogether are called an “ion pair.” The ionization potential of anelement is the amount of energy necessary to ionize the atom byfreeing the least tightly bound electron.

    The orbital shell an electron normally occupies is called “groundstate.” Excitation refers to an electron that is still “bound” tothe atom but has moved to a higher-energy, less stable shell byabsorbing energy.

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    1.4.1 Modification to the Bohr Atomic Model

    Bohr’s atomic model (mathematical equations) explain the principal (ground state) electron or-bitals, but not the sub-levels within orbitals that are observed. For example, inspection of hy-drogen’s spectral lines using high resolving power spectroscopes, indicate the lines have a finestructure. That is, the spectral lines are in reality many lines very close together, which impliesthere are sub levels of energy within the principal orbital shells. These sublevels can be furtherexplained by assuming that within them, electrons orbit the nucleus in an elliptical rather thancircular pattern. The nucleus is at one of the foci and ellipses of different eccentricities have slightlydifferent energy levels which are restricted by quantum conditions. To adequately explain orbitalelectrons, four different “quantum numbers” need to be described involving angular momentum,elliptical momentum, spin and magnetic moment.

    1.4.2 Periodic Table of Elements

    The “Periodic Table” displays the elements in a tabular manner, arranging the elements in order of increasing atomic number (i.e. number of protons). There is a periodicity to the elements because:

    1) the number of electrons follows the number of protons, 2) no valence shell contains more thaneight electrons, and 3) electrons fill orbitals in an orderly, prescribed manner, as explained byBohr’s atomic model and by the Pauli Exclusion Principle. This principle indicates that no twoelectrons in any atom may have the same set of four quantum numbers. The horizontal rows inthe Periodic Table are called “periods” (of which there are seven) and the vertical rows are called“groups or families”. Families of elements behave similarly since they have the same valence shellstructure. For example, the noble gases (He, Ne, Ar, Kr, Xe & Rn) have full valence shells (eightelectrons) and chemically are very nonreactive. Some noteworthy points regarding the PeriodicTable of Elements:

    •  No valence shell has more than 8 electrons

    •  The first 20 elements successively add electrons to their outermost shells

    •  Transition elements (starting with Sc to Ni) add to the third orbital, instead of to the outerfourth orbital, to a maximum of 18 electrons. Elements from Y to Pd follow the same patternexcept add the fourth orbital, instead of the outer fifth orbital gets filled to a maximum of 18 electrons.

    •  The Lanthanides, also called the Rare Earths, (elements from Ce to Lu) differ from transitionelements in that the fourth and fifth shells contain essentially the same electronic structures,while the third shell gets filled as the atomic number increases.

    •  Actinides are elements starting with thorium. All isotopes of these elements are radioactive

    and this group includes the elements used to fuel nuclear reactors.

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    Figure 2:  The Periodic Table of the Elements

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    1.5 Mass & Energy Equivalency

    Einstein made the revolutionary proposal in his “Theory of Relativity” that mass and energy areequivalent and convertible, according to:

    E  = mc2 (1.1)

    Where:

    E    = ergs(g · cm2/s2)

    m0   = mass at rest(g)

    c   = speed of light in a vacuum (2.9979 × 1010 cm/s)

    (1.2)

    This mass-energy equivalency is startling when stated in actual numbers. For example, theenergy equivalency of 1 kg (2.2 lb) of matter (completely annihilated) is 1.977 × 1024 ergs (or25 × 109 kW h). This is 2,941,176,000 times the amount of energy that would be produced byburning the same amount of coal. With no real proof, at first Einstein’s equation created muchspeculation by philosophers, engineers, scientists and even comic strip developers. However, around1930, evidence supporting its validity began to emerge rapidly; and now this mass-energy relation-ship is accepted as a law of physics.

    Nuclear processes are normally measured in electron-volts (eV) defined as “the energy acquiredby an electron when it is accelerated through a potential difference of 1 volt (V)”. Often, elec-tron volts are expressed in terms of kilo (1000) or mega (1,000,000) electron volts, keV or MeV,respectively. There are 1.6022 × 10−6 ergs/MeV (1.6022 × 10−13 J/MeV).

    Example: The energy equivalence of an electron can be computed from its rest mass (m) asfollows:

    mc2 = 9.1095 × 10−28g × (2.9979 × 1010cm/s)2

    = 8.1861 × 10−7ergs

    = 8.1861 × 10−14J 

    divide by 1.6022 × 10−13J/MeV 8.1861 × 10−14J 

    1.6022

    ×10−13J/MeV 

      = 0.51093MeV  ≈ 0.511MeV 

    (1.3)

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    Example: The energy equivalence of one amu can be computed as follows:

    mc2 = 1.6605−24g × (2.9979 × 1010cm/s)2

    = 1.4924 × 10−3ergs

    = 1.4924 × 10−

    10J 

    divide by 1.6022 × 10−13J/MeV 1.4924 × 10−10J 

    1.6022 × 10−13J/MeV    = 931.47MeV/amu ≈ 931.5MeV/amu

    (1.4)

    1.6 Binding Energy

    The mass of an atom is always less than the sum of its constituent parts. That is the sum of anatom’s proton and neutron masses when computed by individual nucleon weights, will always bemore than the actual mass of the atom containing the same number of nucleons. This difference in

    mass is termed “mass defect.” Since energy and mass are equivalent and convertible, the energyequivalent of an atom’s mass defect can be determined; it is called “binding energy” since itrepresents the energy with which the nucleus is held together. Binding energy can also be thoughtof as: 1) the energy released when a nucleus is formed from its parts; or 2) the energy required tobreak down a nucleus into its components. The mass defect (∆) can be computed by the followingequation:

    ∆ = ZM  p + N M n + ZM e − M a   (1.5)Where:

    ∆  = mass defect 

    Z = atomic number 

    N = neutron number 

    M  p  = atomic mass one proton, amu 

    M n  = atomic mass one neutron, amu 

    M e  = atomic mass of one electron, amu 

    M a  = atomic mass of the bound atom, amu 

    The binding energy can then be computed from the mass defect by the previously establishedrelationship of 931.5 MeV/amu. The mass defect can also be used to compute the energy of emitted

    particulate radiation, as will be explained further in Section 2.

    Example: The mass defect (∆) and binding energy (Q) of   17O can be computed. Given it has8 protons and 9 neutrons, and:

    Atomic weight of   17O = 16.999133 amu

    Atomic weight of one proton = 1.0078252 amu

    Atomic weight of one neutron = 1.0086654 amu

    Atomic weight of one electron = 0.0005486 amu

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    !"!# !# "# $# %# # &!# &"# &$# &%# !## !!#

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    +,-.-/0 2 345.,-/0

       6  7  4  ,

      8  9  4   :   ;  /   <   ;  /  9   =  /  4  ,  9  >  ?  4  ,  /  5  @   A  4

      -  /   B   ;  /   C  4   D   E

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    Figure 3:  Avg. Nucleon Binding Energy vs Mass Number (No. of nucleons)

    ∆ = 8 ( 1.0078252 amu) + 9 (1.0086654 amu) + 8 (0.0005486 amu) − 16.999133 amu∆ = 0.145845 amu

    (1.6)

    The binding energy is then:

    931.5 MeV/ amu ×  0.145 845 amu = 135.85 MeV

    And, the binding energy per nucleon is

    135.85 / 17 = 7.99 MeV/ nucleon

    Figure-3  plots average binding energy per nucleon versus mass number. While total bindingenergy is an increasing function of the mass number, the average binding energy per nucleonincreases from mass numbers of 1 (hydrogen) to around 60 and then slowly decreases from there.Those elements represented by the highest average binding energies are the most stable since theyare the most tightly bound. The figure also indicates that stability is gained when two nuclei withlow mass combine into one element (e.g.   2H and   2H fusion) as well as when heavy nuclei split intotwo more tightly bound nuclei (e.g.   235U fission). Thus, both fission and fusion reactions result inthe release of energy.

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    Stable nuclides can exist for elements with Z numbers of 82 and below; all nuclides with Znumbers of 83 or greater are radioactive. When evaluating stable nuclides as a function of theratios of neutrons numbers (N) to proton number (Z) a few tendencies become evident:

    1. The ratio of neutron to protons for elements with Z numbers of 20 (calcium) or below stayfairly close to 1 (albeit the mean ratio deviates slightly above 1).

    2. The ratio of neutrons to protons for elements with Z numbers above 20 become increasinglyhigher.

    3. Certain combinations of neutrons and protons are more stable than others. For example,more stable nuclides exist when both neutrons and protons are even numbered than odd-even,or odd-odd pairs.

    •  Even N, Even Z - 159 stable nuclides

    •  Odd N, Even Z - 53 stable nuclides

    •  Even N, Odd Z - 50 stable nuclides

    •  Odd N, Odd Z - 5 stable nuclides

    4. There are certain neutron or proton “magic numbers” that are especially stable. These“magic numbers” are: 2, 8, 20, 50, 82 and 126 - etc. For example, all three natural decaychains end in stable lead (Z = 82). This “magic number” phenomenon suggests there may be“shells” within the nucleus somewhat analogous to the electron orbital shells; within certainnuclear shell configurations being more stable than others.

    5. Transuranic fission reactions result in neuron emissions since a lower neutron to proton ratiois necessary for stability in lower atomic mass nuclides.

    6. Figure-4  plots stable nuclides as a function of neutron and proton number. It graphicallyillustrates the relationship of the neutron to proton ratio and stability as a function of atomicnumber.

    1.7 Naturally Occurring Radionuclides

    The earth is naturally radioactive. The air we breathe, food we eat, rocks and soil we walk on, allcontain radionuclides. In addition, we are continually exposed to secondary cosmic radiation, andto gamma rays emitted by radionuclides all around us. In fact, around 340 naturally occurringradionuclides have been identified (“NORM” is an acronym for “Naturally Occurring Radioactive

    Material”). The sources of naturally occurring radiation can be categorized into three groups:

    •   Cosmic rays

    •  Cosmogenic radionuclides

    •  Primordial radionuclides

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    In addition to naturally occurring radiation, man-made radionuclides can contribute to back-ground levels. These man made radionuclides include those generated from weapons testing andnuclear power generation. Also, some technologies can enhance background levels, at least locally

    (e.g., coal burning).Levels of naturally occurring radiation can vary by over two orders of magnitude, depending on

    factors including type of adjacent rock, soil constituents, altitude, latitude, and even meteorologicalconditions. As an RSO it is essential to know when the radioactivity being encountered is morethan the levels naturally present at your location.

    1.7.1 Cosmic Rays

    Cosmic rays (also called galactic radiation) originate in outer space and impinge isotropically ontop of the earth’s atmosphere at around 15.5 mi (25 km) up. They consist of high energy particles:85% protons, 14% alpha particles and about 1% of nuclei with atomic numbers between 4 and

    26 (beryllium to iron). An outstanding characteristic of these cosmic rays is that even thoughthey are particulates, they are very penetrating due to their extreme energies. The average energyis 1 × 104 MeV, with maximum energies around 1 × 1013 MeV. In comparison, alpha particlesrarely exceed 8 MeV. Cosmic rays do not directly reach the earth’s surface, being intercepted byatmospheric gases. However, a small percentage of their secondary reaction products (gammarays, neutrons, protons, alpha particles, pions, electrons and muons) “rain down” upon the earth’ssurface. The dose rate from secondary cosmic radiation varies in different parts of the globe,based largely on geomagnetic fields and altitudes. Secondary cosmic radiation contributes fromabout 10% to 30% of the total annual dose delivered from all natural sources. Altitude has the

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    Table 5:  Cosmogenic Radionuclides

    CosmogenicRadionuclides

    Half-Life Avg Tropospheric Concentration (pCi/kg air)

    3H 12.3 years 3.2

    ×10−2

    7Be 53.6 days 0.28

    14C 5730 years 3.4

    22Na 2.6 years 3.0 × 10−5

    32P 14.3 days 3.4 × 10−3

    35S 2.87 hours 3.5 × 10−3

    36Cl 3.1×

    105 years 6.8×

    10−9

    From Eisenbud (1973).   Environmental Radioactivity .

    largest impact on the dose delivered from secondary cosmic radiation. For example, this dosecomponent is four times higher in Leadville, Colorado (at 10,000 ft elevation) than in Los Angeles,California, and the dose rate from cosmic radiation on airplanes is so high that according to theUnited Nations UNSCEAR 2000 Report, airline workers receive more dose on average than anyother type of worker.

    While the sun also emits particulate radiation (mostly protons), the energy spectrum is sig-nificantly lower than that from galactic origin. Solar particulates vary widely in intensity andspectrum, increasing in strength after some solar events such as solar flares. However, an increasein solar cosmic ray intensity is often followed by a decrease in the intensity of galactic rays imping-ing upon the earth’s atmosphere. This effect is called a “Forbush decrease”. This phenomenonis thought to occur from elevated solar winds expanding the sun’s magnetic field, and therebyproviding additional shielding against cosmic radiation.

    1.7.2 Cosmogenic Radionuclides

    Cosmogenic radionuclides are those that are formed by the interaction of cosmic rays with at-mospheric gases. These high energy interactions result in the liberation of neutrons from nuclei,which in turn are captured by atmospheric gases creating certain radionuclides (for example,   14N+ n →   14C + p). Essentially, almost all the dose delivered from cosmogenic radionuclides is dueto   14C. Nevertheless,   14C delivers only around 0.3% of the total annual background dose.

    Carbon-14 produced in the atmosphere quickly oxidizes to CO2. The equilibrium concentrationsof   14C in the atmosphere are controlled primarily by the exchange of CO2  between the atmosphereand the ocean; and oceans are the major sink for atmospheric removal of   14C. Table-5 lists a fewcosmogenic radionuclides.

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    1.7.3 Primordial Radionuclides

    Primordial radionuclides include those in the earth’s crust that have been around since it wasformed. The levels of primordial radionuclides vary within location, depending mostly on the typeof rock; and there are a few places on earth with exceptionally high concentrations. Primordialradionuclides are typically divided into two groups:

    •   Singly occurring radionuclides•  Decay chains

    Potassium-40   The most important “singly occurring” radionuclide is   40K; which exists asa constant fraction of stable potassium. It’s a beta and gamma emitter and decays to stable40Ar. Even though only 0.012 % of natural potassium is the seventh most abundant element in theearth’s crust and the sixth most abundant in the oceans. Potassium-40 behaves in the environmentthe same as other potassium isotopes, being assimilated into all plant and animal tissues throughnormal biological processes. Because of its relative abundance and energetic beta emission (1.3MeV),   40K is easily the predominant radioactive component in normal foods and human tissues.

    A 154-lb man contains around 140 g of potassium (and consequently ≈  0.1 µCi of   40K) mostly inmuscle tissue (which means over 200,000 atoms of   40K decay per minute). In all (externally andinternally),   40K generates about 10% of the total naturally occurring annual dose.

    Decay Chains   There are three long, ubiquitous naturally occurring parent-daughter decaychains. “Decay chains” form when an initial radionuclide (parent) decays (or transforms) into aradioactive daughter , which likewise transforms into a radionuclide, and so-on so-forth until gen-eration of a stable nuclide. Radioactive daughter nuclides may have different chemical properties,decay at different rates and emit different types and energies of radiation. The three naturallyoccurring chains start with   238U,   232Th and   235U, where:

    •   238U decays through 15 daughters to   206Pb,•   232Th decays through 10 daughters to   208Pb,

    •   235U decays through 12 daughters to   207Pb,

    •  Each chain decays through isotopes of radium and radon.

    Uranium   Three isotopes of uranium are found in nature (234, 235 and 238). Two areprimordial radionuclides (238U at 99.28% and   235U at 0.71%), where   234U is a daughter of   238U.Uranium concentrations vary in the different types of rocks and soil. Average concentrations varyfrom 0.03 ppm in ultrabasic igneous rocks to 120 ppms in Florida’s phosphate rocks. The high

    levels in phosphate rock result in correspondingly elevated uranium and daughter concentrationsin commercial phosphate fertilizers. Because uranium is found to some extent in all types of soil,uranium and daughter nuclides are also in food and subsequently, human tissues.

    Thorium   Thorium is also found throughout rocks and soil in varying concentrations (rangingfrom about 8 to 33 ppm.) However, thorium is less soluble than uranium and, thus, is not takenup by vegetation nearly as readily. Furthermore, thoron (220Rn) does not migrate as readily asradon (222Rn) because of its extremely short half life. Overall, thorium and daughters deliver amuch lower dose than that from the   238U decay series.

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    Table 6:   Naturally Occurring Decay Chains

    UraniumDecay Series

    ThoriumDecay Series

    ActiniumDecay Series

    Isotope H alf-Life Rad Isotope H alf-Life Rad Isotope H alf-Life Rad

    238U 4.47×109 yr   α   232Th 1.39×1010 yr   α   235U 7.13×108 yr   α↓ ↓ ↓

    234Th 24.1 days   β    228Ra 6.7 yr   β    231Th 25.6 hr   β 

    ↓ ↓ ↓234mPa 1.17 min   β    228Ac 6.13 hr   β    231Pa 3.48×104 yr   α

    ↓ ↓ ↓234U 2.45×105 yr   α   228Th 1.90 yr   α   227Ac 22 yr   β 

    ↓ ↓ ↓230Th 7.54×104 yr   α   224Ra 3.64 days   α   227Th 18 days   α↓ ↓ ↓

    226Ra 1.62×103yr   α   220Rn 54.5 sec   α   223Fr 22 min   β ↓ ↓ ↓

    222Rn 3.82 day   α   216Po 0.16 sec   α   223Ra 11.7 days   α

    ↓ ↓ ↓218Po 3.11 min   α   212Pb 10.6 hr   β    219Rn 4.0 sec   α

    ↓ ↓ ↓214Pb 26.8 min   β    212Bi 60.6 min   β    215Po  

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    Radium   Radium isotopes are found in all three naturally occurring decay chains. Radiumis chemically similar to calcium and thus, up-taken by plants in the same manner. Also, whenconsumed, radium is metabolized by the body similarly to calcium and deposits preferentially inbone matrices. Because of the considerable variability in soil, radium levels in food also fluctuates.An interesting bit of trivia is that due to radium, Brazil nuts tend to be much more radioactivethan most foods (on the order of 1000 times greater). This is because the extensive root system of 

    the Brazil nut tree concentrates barium, which is a cogener of radium (both are Group II on thePeriodic Table).

    Radon   (222Rn) is in the decay chain of   238U. It is an inert, noble gas with a half-life of 3.82days. Once formed by   226Ra decay, it readily migrates out of soil and collects inside buildings.Radon (and daughters) is by far the largest contributor to the dose received from all sources of naturally occurring radiation, generating around two-thirds of the total dose. It contributes sucha large fraction of the does because:

    •  It is a noble gas causing it to readily seep out of the ground and then mix with air,

    •  Its half-life is long enough to enable migration into air and become available for inhalation,

    •  It’s half-life is short enough to increase the probability of decay once inhaled,

    •   Radon’s daughter products are electrically charged solids that quickly adhere to airborneparticulates (e.g. dust) which can be inhaled,

    •  Radon is an energetic alpha emitter as well as the parent of five short lived daughters, threeof which also emit high energy alphas.

    Indoor radon levels have attracted much interest since the 1970s due to concerns about its abilityto potentially cause cancer. In the US, radon levels in homes average about 1.5 pCi/L (55Bq / m3),with an EPA action level of 4 pCi/L (148 Bq / m3. Nearly 1 in 15 US homes are estimated to exceed

    this EPA action level, and levels as high as 2700 pCi/L (100.000 Bq / m3

    ) have been measured.Correspondingly, thoron (220Rn) is thorium’s decay chain. Far lower concentrations of thoron arefound in air than radon. Its extremely short half-life (54.5 sec) precludes much migration out of the ground between birth and decay. Thoron decays through four very short-lived daughters to astable isotope of lead (208Pb).

    1.7.4 Areas of Unusually High Levels of NORM

    There are a few inhabited areas renown for their exceptionally high levels of terrestrial radionu-clides, they are:

    •  Ramsar, Iran

    •   Guarapari, Brazil

    •   Kerala, India

    •  Yanjian, China

    In some localizations near Ramsar, Iran, external dose rates can be 55 to 200 times higherthan normal. These elevated levels are primarily due to   226Ra having been concentrated at theearth’s surface by hot springs. The elevated regions in Brazil, India and China are mainly dueto monazite deposits and monazite beaches. Monazite is an insoluble rare earth mineral which

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    is rich in   232Th and its daughter products. Monazite beaches in Brazil can register dose rates ashigh as 5 mrem/hr (which if exposed to chronically would result in an annual external dose of 44rem/yr). Many mineral springs also contain relatively high concentrations of radium and radon.In fact, several hot springs have exploited these higher levels of radioactivity for “alleged curativepowers” (e.g. Bad Gastein in Austria). The levels of   226Ra in mineral waters can reach as high as100 pCi/L, about 1 million times higher than average values for public water supplies.

    1.7.5 Natural Reactor at Oklo

    In the 1970s, a discovery was made that suggests a self sustaining nuclear reaction occurred innature about 1.7 billion years ago at Oklo (in the West African Republic of Gabon). French scien-tists observed uranium samples extracted from the Oklo mine that had abnormally low percentagesof the   235U isotope. Uranium isotope ratios are normally consistent throughout nature (235U at0.711%,   238U at 99.28%).

    However, in these samples the percentage of  235U was less than half the normal amount. Becausesimilar ratios are found in spent nuclear fuel, the scientists surmised that a chain reaction processmust have occurred naturally within the Oklo mine. French scientists theorized that 1.7 billion

    years ago, the normal fraction of   235U would have been 3%; which is high enough to permitcritically, provided there is adequate moderation of fission neutrons. Water filtering down throughrock crevices could have provided the necessary moderation. Such a “natural reactor” would likelyhave cycled in that it would automatically quit when heat boiled the water to steam, therebyreducing moderation, and commencing once enough water condensed and re-accumulated. Aninteresting note is that, as in modern nuclear power plants, fission products and transuranicswould have been created. Investigations indicate that the transuranics created by this naturalreactor never moved far beyond their place of origin.

    1.7.6 Consumer Products

    Radionuclides have been used in various consumer products, such as:

    •   Watches and clocks sometimes contain a small quantity of   3H (tritium) or   147Pr for theirluminescent qualities. Older (for example, pre-1970) watches and clocks often used   226Ra.

    •   Smoke Detectors with   241Am alpha particles from   241Am ionize air. A steady amount of ionization occurs and is collected. However, if smoke appears, it will absorb alpha particlesreducing the amount of current collected and thereby trigger a smoke: alarm.

    •  Uranium in “Depression Glass” Depression glass (also called Vaseline Glass ) glass owes itsyellow-greenish color to its uranium content.

    •  Lantern Mantles with  232

    Th Thorium is added to lantern mantles because when heated thethorium emits an incandescent glow.

    •   Thorium in Camera Lenses In designing optical, it is often desirable to employ glass witha high index of refraction. By adding thorium to the glass, a high refractive index canbe achieved while maintaining a low dispersion. Older camera lenses (1950s-1970s) oftenemployed coatings of   232Th to alter the index of refraction.

    •  Uranium in ceramic glazes uranium added to ceramic glaze can result in vibrant colors (forexample the bright red-orange color in some vintage dishes).

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    1.8 Historical Highlights Related to Nuclear Science

    The earliest atomic hypotheses are attributed to ancient Greek philosophers. In the Fifth centuryB.C., Democritus believed that elementary substances (earth, water, fire and air) were formed byminute invisible particles called “atoms”. However, concrete evidence for this theory did not occuruntil the early 1800s when Dalton showed how to determine masses of different atoms relative toone another.

    Then the discovery of both x-rays and radioactivity in the 1890s began a period of intenseinvestigation and discovery, culminating just fifty years later with the creation of the first atomicbomb. The following table presents historical highlights from this remarkable era of nuclear science.

    1895 Wilhelm Roentgen When studying “cathode rays” (i.e. electrons), determined thatthe fluorescence glowing on a nearby screen resulted from invisiblerays being emitted from the Crookes tube. He named them “x-rays”. Took the first x-ray photo of his wife’s hand.

    1896 Henri Becquerel Discovered that uranium (U) emitted radiation, which he at first

    erroneously attributed to absorption of the sun’s energy by U andthen emission of this energy as x-rays.

    Becquerel later proved that the radiation he discovered could notbe x-rays since x-rays have no charge and cannot be bent in amagnetic field.

    1897 J. J. Thomson Identified the first subatomic particle (the electron), which hetermed “negative corpuscles” and thereby provided justificationfor the particulate theory of matter. He showed that the glowingbeam in a cathode-ray tube was not from light waves, but instead

    negatively charged particles. They could be deflected by an elec-tric field and bent into curved paths by a magnetic field. Theywere much lighter than hydrogen and were identical “whateverthe gas through which the discharge passed.” To honor Thomas’success the following was sung at the annual Cavendish dinner:“The corpuscle won the day, And in freedom went away, Andbecame a cathode ray.”

    1898 Pierre & MarieCurie

    Coined the term “radioactivity.” Discovered after chemical extrac-tion of U from ore, that the residual material was more “radioac-

    tive” than U; this led to the discovery of radium and polonium.It took four more years of processing tons of ore to isolate enoughof each element to determine their chemical properties.Marie Curie- “I have no dress except the one I wear every day. If you are going to be kind enough to give me one, please let it bepractical and dark so that I can put it on afterwards to go to thelaboratory.”

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    1900 Earnest Rutherford Reported the discovery of a radioactive gas (thoron) emanatingfrom thorium.

    1901 Max Planck In “quantum theory of heat radiation”, introduced the conceptof discrete amounts (quanta) of energy. This theory states that

    electromagnetic radiation must be emitted or absorbed in integralmultiples of these energy quanta. Planck- “A new scientific truthdoes not triumph by convincing its opponents and making themsee the light, but rather because its opponents eventually die, anda new generation grows up that is familiar with it.”

    1902 Charles Wilson Found that rain was radioactive and that this activity disappearedwithin a few hours

    1903 Sir WilliamCrookes and

    independently,Elster and Geitels

    Discover zinc sulfide crystals emit tiny flashes of visible light whenstruck with alpha particles.

    1903 Ernest Rutherfordand FrederickSoddy

    Develop laws of radioactive decay & proposed that radioactivityproduced changes within the atom. Published a paper “Radioac-tivity change” that offered the first informed calculations of theamount of energy released by radioactive decay. Rutherford- “If your result needs a statistician then you should design a betterexperiment.”

    1903 Hantaro Hagaoka Postulated a “Saturnian” model of the atom with electrons orbit-

    ing a nucleus in flat rings as the rings of Saturn.

    1904 J. J. Thomson Proposed the “plum pudding” atomic model. This model de-picted the atom as a homogeneous sphere of positive electric fluidimbedded with negatively charged electrons (analogous to plumssurrounded by pudding

    1905 Albert Einstein Published the “Theory of Relativity”; developed the mass energyequivalency equation;   E   =   mc2. Suggested that proof might befound be studying radioactive substances. Einstein- “Gravity can-not be held responsible for people falling in love.”

    1909 Frederick Soddy Wrote a book “Interpretation of Radium” which later influencedH.G. Wells to write a science fiction novel involving atomic bombs.Soddy- “Chemistry has been termed by the physicists as the messypart of physics, but the is no reason why the physicists should bepermitted to make a mess of chemistry when they invade it.”

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    1909 Ernest Rutherford From alpha scattering experiments developed a “planetary model”of an atom (apparently did not know of Hagaoka’s 1903 model).Bombarded a thin gold foil with alpha particles and the mannerin which they deflected suggested positive charges in atoms wereconfined to a very small nucleus. Rutherford- “Anyone who ex-

    pects a source of power from the transformation of the atom istalking moonshine”

    1910 Radiology Congress Chose the “curie” as the basic unit of radioactivity; which was theactivity in one gram of radium (later the definition of curie wasrefined to equal 3.7 × 1010 dps).

    1911 Robert Millikan Using oil droplets measured the electron charge.

    1913 Hans Geiger Unveiled a prototype gas-filled radiation detector.

    1913 Niels Bohr Coupled Rutherford’s atomic model with the newly proposedquantum theory and developed an updated “planetary-type”atomic model. Applied quantum theory to electron orbitals. Bohr-“If anybody says he can think about quantum physics without get-ting giddy, that only shows he has not understood the first thingabout them.”

    1914 H.G. Wells Published “The World Set Free” a science fiction novel that depictsatomic bombs. Wells claims his inspiration for the book came fromSoddy’s 1909 book “Interpretation of Radium”. The novel opens:“The history of mankind is the history an attainment of external

    power. Man is the tool-using, fire-making animal.” The atomicbombs depicted in this novel are unique in that they continue toexplode for days, although they have no more power than ordinaryhigh explosives.

    1916 ArnoldSommerfield

    Refined the quantum theory to account for discreet ellip tical electron orbits (in addition to circular orbits).

    1916 Gilbert Lewis Wrote an article “The Atom and the Molecule” which includeda rule of chemical behavior where atoms tend to hold even num-bers of electrons in an orbital shell and especially to hold eightelectrons.

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    1919 Francis Aston Developed first functional mass spectrograph by which to measurethe relative mass of elements. This invention led to the discoveryof isotopes. Aston- “It has been long known that the chemicalatomic weight of hydrogen was greater than one-quarter of thatof helium, but so long as fractional weights were general there

    was no particular need to explain this fact, nor could any definiteconclusions be drawn from it.”

    1919 Ernest Rutherford Demonstrated “artificial radioactivity” by bombarding nitrogen(14N) with alpha particles (4He), resulting in   17O and   1H.

    1923 Louis DeBroglie Postulated that matter (analogous to photons), in addition to be-ing “particulate” should also behave as a wave.

    1925 Wolfgang Pauli Building on Sommerfield’s 1916 (and other’s) views, formulatedthe “Pauli Exclusion Principle”. This principle was developed to

    explain some experimental results and how the periodic table isregulated by the electron structure of atoms. This explains whymatter occupies space exclusively for itself and does not allowother material objects to pass through it, while at the same timeallowing light and radiation to pass. It indicates that no twoelectrons may occupy the same quantum state simultaneously. Foratomic electrons, it means that no two electrons in a single atomcan have the same four quantum numbers at the same time; forexample, if n, l and ml are the same, ms must be different suchthat the electrons have opposite spins.

    1932 James Chadwick Discovers the neutrons by bombarding beryllium with alpha par-ticles. Chadwick (in 1941): “We had quite a lot of bombing raids.Practically all the windows in my laboratory were blown out, for-tunately very little damage was caused. The cyclotron was partlybelow ground it was in the basement, For about a week they wereblown in every direction in every night, and we put up cardboardshutters. Every night they would be blown in again. We’d justput them up in the morning and go on.”

    1933 Leo Szilard Influenced by H.G. Wells’s book “The World Set Free,” developed

    the concept of a nuclear chain reaction. Patented this concept thenext year.

    1933 Enrico Fermi Started neutron-bombardment experiments, which involved sys-tematically bombarding each element (including uranium) withneutrons. The results of the U irradiation produced unexpectedresults, various half-lives, which was first attributed to transuranicelements.

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    1934 Enrico Fermi By serendipity discovered neutron capture becomes more effectivewhen neutrons are slowed down, such as by hydrogenous materials.Fermi had made a last minute substitution of paraffin for lead inan experiment involving neutron activation, which produced theastonishing effect of enhancing the level of activation. Fermi and

    his team delivered a paper “Influence of Hydrogenous Substanceson the Radioactivity produced by Neutrons - I.”

    1938 Otto Hahn & FritzStrassman

    The “unexplained uranium” effects first observed by Fermi in 1933(upon neutron activation) were studied for the following severalyears by various investigators. Prevailing theories included thatthe various half-lives were transuranics and/or that double alphadecay produced radium isotopes.Hahn & Strassman set about chemically separating “radium” afterbombardment of U with neutrons, and discovered the separated

    material behaved like barium instead. Upon rechecking their re-sults and refining the techniques, they surmised that the radiumthat acted like barium, was in fact “barium”. They postulatedthat U must have split into two roughly equal parts. In reportingtheir results, they stated:

    •  “We come to the conclusion that our ‘radium isotopes’ havethe properties of barium. As chemists, we should actuallystate that the new products are not radium, but rather bar-ium itself. Other elements beside radium or barium are outof the question.”

    •  However, they were cautious in reporting these findings asthey stated, their findings went against the “previous lawsof nuclear physics”. For this reason they added a note totheir paper:

    •   “There could perhaps be a series of unusual coincidenceswhich has given us false indications.”

    1938 Lise Meitner &Otto Frisch

    Described the theoretical mechanisms of fission and calculated theamount of binding energy released in the process (on the order of 

    200 MeV). Termed the process of U splitting “fission”.

    1939 Albert Einstein Prompted by Fermi & Szilard, sent a letter to President FranklinD. Roosevelt informing him of German atomic research and thepotential for a bomb. This letter then prompted Roosevelt toform a special committee to investigate the military implicationsof atomic research.

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    1939 Enrico Fermi &Leo Szilard

    After learning about nuclear fission, concluded that uraniumwould be the element capable of sustaining a chain reaction. Con-ducted a simple experiment at Columbia and discovered signifi-cant neutron multiplication in uranium, proving that criticalitywas possible and opening the way to nuclear weapons.

    1939 Niels Bohr Proposed that fission was much more likely to occur in   235Uthan in   238U and that fission would occur more effectively withslow-moving neutrons than with fast neutrons. Published (withWheeler) a classical paper analyzing the fission process. The pa-per was published only two days before the “official” start date of WWII.

    1939 Otto Frisch &Rudolph Peierls

    Gave a major impetus to the concept of the atomic bomb in adocument called “the Frisch-Peierls Memorandum”. They pre-dicted that about 5 kg of pure   235U could make a very powerfulatomic bomb equivalent to several kilotons of dynamite. Theyalso suggested how to detonate such a bomb and how   235U mightbe enriched.

    1939 Francis Perrin Introduced the concept of the “critical mass” of U required toproduce a self-sustaining reaction. Showed that a chain reactioncould be sustained in a U and water mixture. Also demonstratedthe neutron absorbing material could be added to control neutronmultiplication.

    1940 Glen Seaborg,Arthur Wahl, &Joseph Kennedy

    Created plutonium by bombarding uranium oxide with high en-ergy deuterons at the Berkeley cyclotron.

    1942 Franklin Roosevelt Authorizes the formation of the Manhattan Project. This projectwas committed to secret, expedient research and production toproduce a viable atomic bomb before the Germans.

    1942 Enrico Fermi Created the first graphite moderated reactor called a pile in a labunder the squash court at the University of Chicago.

    1945 Harry Truman Ordered the dropping of the first atomic bombs on Japan. In pressrelease states: “Sixteen hours ago an American airplane droppedone bomb on Hiroshima, Japan, and destroyed its usefulness tothe enemy. That bomb had more power than 20,000 tons of TNT.It had more than 2000 times the blast power of the British GrandSlam, which is the largest bomb ever used yet in the history of warfare.”

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    Section 1 Exercise

    1. What is the isotope’s mass number and identification symbol that has 55 protons and 82neutrons.

    2. Calculate the number of atoms in one (1) gram of gold, given its atomic weight is 196.9665.

    3. Most stable isotopes have N values and Z values. (Odd or even).

    4. Which naturally occurring decay chain contributes the most to natural background radiation?

    5. The naturally occurring decay chains all end in what stable element(s)?

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    2 Radioactive Decay

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    RSO   Radioactive Decay - 2

    2.1 Radioactive Decay Kinetics

    Radioactive decay refers to the spontaneous disintegration of a radionuclide accompanied by theemission of ionizing radiation. Through decay a nuclide transforms into a different element, or toa lower energy state of the same nuclide. For example,   90Sr (parent) emits a beta particle andtransforms in   90Y (daughter). You cannot predict when any one radioactive atom will sponta-neously disintegrate. However, each radionuclide has its own unique decay probability, and thisprobability is independent of physical or chemical parameters (such as temperature). Thus, fora large population of atoms, statistical behavior(a) ensures that the decay process follows a welldescribed pattern (i.e. equation). The rate of decay is proportional to the concentration and sinceconcentration decreases with decay, the number remaining nuclei decreases exponentially withtime. Figure-5 (relative activity as a function of time) illustrates this concept for   131 I.

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    Figure 5:   For a large number of events, there is a tendency towards long-term stability of a randomvariable. Given a large sample of independent random variable