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College Physics for AP® Courses

31.4 Nuclear Decay and Conservation Laws

College Physics for AP® Courses31.4 Nuclear Decay and Conservation Laws
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  1. Preface
  2. 1 Introduction: The Nature of Science and Physics
    1. Connection for AP® Courses
    2. 1.1 Physics: An Introduction
    3. 1.2 Physical Quantities and Units
    4. 1.3 Accuracy, Precision, and Significant Figures
    5. 1.4 Approximation
    6. Glossary
    7. Section Summary
    8. Conceptual Questions
    9. Problems & Exercises
  3. 2 Kinematics
    1. Connection for AP® Courses
    2. 2.1 Displacement
    3. 2.2 Vectors, Scalars, and Coordinate Systems
    4. 2.3 Time, Velocity, and Speed
    5. 2.4 Acceleration
    6. 2.5 Motion Equations for Constant Acceleration in One Dimension
    7. 2.6 Problem-Solving Basics for One Dimensional Kinematics
    8. 2.7 Falling Objects
    9. 2.8 Graphical Analysis of One Dimensional Motion
    10. Glossary
    11. Section Summary
    12. Conceptual Questions
    13. Problems & Exercises
    14. Test Prep for AP® Courses
  4. 3 Two-Dimensional Kinematics
    1. Connection for AP® Courses
    2. 3.1 Kinematics in Two Dimensions: An Introduction
    3. 3.2 Vector Addition and Subtraction: Graphical Methods
    4. 3.3 Vector Addition and Subtraction: Analytical Methods
    5. 3.4 Projectile Motion
    6. 3.5 Addition of Velocities
    7. Glossary
    8. Section Summary
    9. Conceptual Questions
    10. Problems & Exercises
    11. Test Prep for AP® Courses
  5. 4 Dynamics: Force and Newton's Laws of Motion
    1. Connection for AP® Courses
    2. 4.1 Development of Force Concept
    3. 4.2 Newton's First Law of Motion: Inertia
    4. 4.3 Newton's Second Law of Motion: Concept of a System
    5. 4.4 Newton's Third Law of Motion: Symmetry in Forces
    6. 4.5 Normal, Tension, and Other Examples of Force
    7. 4.6 Problem-Solving Strategies
    8. 4.7 Further Applications of Newton's Laws of Motion
    9. 4.8 Extended Topic: The Four Basic Forces—An Introduction
    10. Glossary
    11. Section Summary
    12. Conceptual Questions
    13. Problems & Exercises
    14. Test Prep for AP® Courses
  6. 5 Further Applications of Newton's Laws: Friction, Drag, and Elasticity
    1. Connection for AP® Courses
    2. 5.1 Friction
    3. 5.2 Drag Forces
    4. 5.3 Elasticity: Stress and Strain
    5. Glossary
    6. Section Summary
    7. Conceptual Questions
    8. Problems & Exercises
    9. Test Prep for AP® Courses
  7. 6 Gravitation and Uniform Circular Motion
    1. Connection for AP® Courses
    2. 6.1 Rotation Angle and Angular Velocity
    3. 6.2 Centripetal Acceleration
    4. 6.3 Centripetal Force
    5. 6.4 Fictitious Forces and Non-inertial Frames: The Coriolis Force
    6. 6.5 Newton's Universal Law of Gravitation
    7. 6.6 Satellites and Kepler's Laws: An Argument for Simplicity
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  8. 7 Work, Energy, and Energy Resources
    1. Connection for AP® Courses
    2. 7.1 Work: The Scientific Definition
    3. 7.2 Kinetic Energy and the Work-Energy Theorem
    4. 7.3 Gravitational Potential Energy
    5. 7.4 Conservative Forces and Potential Energy
    6. 7.5 Nonconservative Forces
    7. 7.6 Conservation of Energy
    8. 7.7 Power
    9. 7.8 Work, Energy, and Power in Humans
    10. 7.9 World Energy Use
    11. Glossary
    12. Section Summary
    13. Conceptual Questions
    14. Problems & Exercises
    15. Test Prep for AP® Courses
  9. 8 Linear Momentum and Collisions
    1. Connection for AP® courses
    2. 8.1 Linear Momentum and Force
    3. 8.2 Impulse
    4. 8.3 Conservation of Momentum
    5. 8.4 Elastic Collisions in One Dimension
    6. 8.5 Inelastic Collisions in One Dimension
    7. 8.6 Collisions of Point Masses in Two Dimensions
    8. 8.7 Introduction to Rocket Propulsion
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  10. 9 Statics and Torque
    1. Connection for AP® Courses
    2. 9.1 The First Condition for Equilibrium
    3. 9.2 The Second Condition for Equilibrium
    4. 9.3 Stability
    5. 9.4 Applications of Statics, Including Problem-Solving Strategies
    6. 9.5 Simple Machines
    7. 9.6 Forces and Torques in Muscles and Joints
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  11. 10 Rotational Motion and Angular Momentum
    1. Connection for AP® Courses
    2. 10.1 Angular Acceleration
    3. 10.2 Kinematics of Rotational Motion
    4. 10.3 Dynamics of Rotational Motion: Rotational Inertia
    5. 10.4 Rotational Kinetic Energy: Work and Energy Revisited
    6. 10.5 Angular Momentum and Its Conservation
    7. 10.6 Collisions of Extended Bodies in Two Dimensions
    8. 10.7 Gyroscopic Effects: Vector Aspects of Angular Momentum
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  12. 11 Fluid Statics
    1. Connection for AP® Courses
    2. 11.1 What Is a Fluid?
    3. 11.2 Density
    4. 11.3 Pressure
    5. 11.4 Variation of Pressure with Depth in a Fluid
    6. 11.5 Pascal’s Principle
    7. 11.6 Gauge Pressure, Absolute Pressure, and Pressure Measurement
    8. 11.7 Archimedes’ Principle
    9. 11.8 Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action
    10. 11.9 Pressures in the Body
    11. Glossary
    12. Section Summary
    13. Conceptual Questions
    14. Problems & Exercises
    15. Test Prep for AP® Courses
  13. 12 Fluid Dynamics and Its Biological and Medical Applications
    1. Connection for AP® Courses
    2. 12.1 Flow Rate and Its Relation to Velocity
    3. 12.2 Bernoulli’s Equation
    4. 12.3 The Most General Applications of Bernoulli’s Equation
    5. 12.4 Viscosity and Laminar Flow; Poiseuille’s Law
    6. 12.5 The Onset of Turbulence
    7. 12.6 Motion of an Object in a Viscous Fluid
    8. 12.7 Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  14. 13 Temperature, Kinetic Theory, and the Gas Laws
    1. Connection for AP® Courses
    2. 13.1 Temperature
    3. 13.2 Thermal Expansion of Solids and Liquids
    4. 13.3 The Ideal Gas Law
    5. 13.4 Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature
    6. 13.5 Phase Changes
    7. 13.6 Humidity, Evaporation, and Boiling
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  15. 14 Heat and Heat Transfer Methods
    1. Connection for AP® Courses
    2. 14.1 Heat
    3. 14.2 Temperature Change and Heat Capacity
    4. 14.3 Phase Change and Latent Heat
    5. 14.4 Heat Transfer Methods
    6. 14.5 Conduction
    7. 14.6 Convection
    8. 14.7 Radiation
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  16. 15 Thermodynamics
    1. Connection for AP® Courses
    2. 15.1 The First Law of Thermodynamics
    3. 15.2 The First Law of Thermodynamics and Some Simple Processes
    4. 15.3 Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency
    5. 15.4 Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated
    6. 15.5 Applications of Thermodynamics: Heat Pumps and Refrigerators
    7. 15.6 Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy
    8. 15.7 Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  17. 16 Oscillatory Motion and Waves
    1. Connection for AP® Courses
    2. 16.1 Hooke’s Law: Stress and Strain Revisited
    3. 16.2 Period and Frequency in Oscillations
    4. 16.3 Simple Harmonic Motion: A Special Periodic Motion
    5. 16.4 The Simple Pendulum
    6. 16.5 Energy and the Simple Harmonic Oscillator
    7. 16.6 Uniform Circular Motion and Simple Harmonic Motion
    8. 16.7 Damped Harmonic Motion
    9. 16.8 Forced Oscillations and Resonance
    10. 16.9 Waves
    11. 16.10 Superposition and Interference
    12. 16.11 Energy in Waves: Intensity
    13. Glossary
    14. Section Summary
    15. Conceptual Questions
    16. Problems & Exercises
    17. Test Prep for AP® Courses
  18. 17 Physics of Hearing
    1. Connection for AP® Courses
    2. 17.1 Sound
    3. 17.2 Speed of Sound, Frequency, and Wavelength
    4. 17.3 Sound Intensity and Sound Level
    5. 17.4 Doppler Effect and Sonic Booms
    6. 17.5 Sound Interference and Resonance: Standing Waves in Air Columns
    7. 17.6 Hearing
    8. 17.7 Ultrasound
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  19. 18 Electric Charge and Electric Field
    1. Connection for AP® Courses
    2. 18.1 Static Electricity and Charge: Conservation of Charge
    3. 18.2 Conductors and Insulators
    4. 18.3 Conductors and Electric Fields in Static Equilibrium
    5. 18.4 Coulomb’s Law
    6. 18.5 Electric Field: Concept of a Field Revisited
    7. 18.6 Electric Field Lines: Multiple Charges
    8. 18.7 Electric Forces in Biology
    9. 18.8 Applications of Electrostatics
    10. Glossary
    11. Section Summary
    12. Conceptual Questions
    13. Problems & Exercises
    14. Test Prep for AP® Courses
  20. 19 Electric Potential and Electric Field
    1. Connection for AP® Courses
    2. 19.1 Electric Potential Energy: Potential Difference
    3. 19.2 Electric Potential in a Uniform Electric Field
    4. 19.3 Electrical Potential Due to a Point Charge
    5. 19.4 Equipotential Lines
    6. 19.5 Capacitors and Dielectrics
    7. 19.6 Capacitors in Series and Parallel
    8. 19.7 Energy Stored in Capacitors
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  21. 20 Electric Current, Resistance, and Ohm's Law
    1. Connection for AP® Courses
    2. 20.1 Current
    3. 20.2 Ohm’s Law: Resistance and Simple Circuits
    4. 20.3 Resistance and Resistivity
    5. 20.4 Electric Power and Energy
    6. 20.5 Alternating Current versus Direct Current
    7. 20.6 Electric Hazards and the Human Body
    8. 20.7 Nerve Conduction–Electrocardiograms
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  22. 21 Circuits, Bioelectricity, and DC Instruments
    1. Connection for AP® Courses
    2. 21.1 Resistors in Series and Parallel
    3. 21.2 Electromotive Force: Terminal Voltage
    4. 21.3 Kirchhoff’s Rules
    5. 21.4 DC Voltmeters and Ammeters
    6. 21.5 Null Measurements
    7. 21.6 DC Circuits Containing Resistors and Capacitors
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  23. 22 Magnetism
    1. Connection for AP® Courses
    2. 22.1 Magnets
    3. 22.2 Ferromagnets and Electromagnets
    4. 22.3 Magnetic Fields and Magnetic Field Lines
    5. 22.4 Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field
    6. 22.5 Force on a Moving Charge in a Magnetic Field: Examples and Applications
    7. 22.6 The Hall Effect
    8. 22.7 Magnetic Force on a Current-Carrying Conductor
    9. 22.8 Torque on a Current Loop: Motors and Meters
    10. 22.9 Magnetic Fields Produced by Currents: Ampere’s Law
    11. 22.10 Magnetic Force between Two Parallel Conductors
    12. 22.11 More Applications of Magnetism
    13. Glossary
    14. Section Summary
    15. Conceptual Questions
    16. Problems & Exercises
    17. Test Prep for AP® Courses
  24. 23 Electromagnetic Induction, AC Circuits, and Electrical Technologies
    1. Connection for AP® Courses
    2. 23.1 Induced Emf and Magnetic Flux
    3. 23.2 Faraday’s Law of Induction: Lenz’s Law
    4. 23.3 Motional Emf
    5. 23.4 Eddy Currents and Magnetic Damping
    6. 23.5 Electric Generators
    7. 23.6 Back Emf
    8. 23.7 Transformers
    9. 23.8 Electrical Safety: Systems and Devices
    10. 23.9 Inductance
    11. 23.10 RL Circuits
    12. 23.11 Reactance, Inductive and Capacitive
    13. 23.12 RLC Series AC Circuits
    14. Glossary
    15. Section Summary
    16. Conceptual Questions
    17. Problems & Exercises
    18. Test Prep for AP® Courses
  25. 24 Electromagnetic Waves
    1. Connection for AP® Courses
    2. 24.1 Maxwell’s Equations: Electromagnetic Waves Predicted and Observed
    3. 24.2 Production of Electromagnetic Waves
    4. 24.3 The Electromagnetic Spectrum
    5. 24.4 Energy in Electromagnetic Waves
    6. Glossary
    7. Section Summary
    8. Conceptual Questions
    9. Problems & Exercises
    10. Test Prep for AP® Courses
  26. 25 Geometric Optics
    1. Connection for AP® Courses
    2. 25.1 The Ray Aspect of Light
    3. 25.2 The Law of Reflection
    4. 25.3 The Law of Refraction
    5. 25.4 Total Internal Reflection
    6. 25.5 Dispersion: The Rainbow and Prisms
    7. 25.6 Image Formation by Lenses
    8. 25.7 Image Formation by Mirrors
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  27. 26 Vision and Optical Instruments
    1. Connection for AP® Courses
    2. 26.1 Physics of the Eye
    3. 26.2 Vision Correction
    4. 26.3 Color and Color Vision
    5. 26.4 Microscopes
    6. 26.5 Telescopes
    7. 26.6 Aberrations
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  28. 27 Wave Optics
    1. Connection for AP® Courses
    2. 27.1 The Wave Aspect of Light: Interference
    3. 27.2 Huygens's Principle: Diffraction
    4. 27.3 Young’s Double Slit Experiment
    5. 27.4 Multiple Slit Diffraction
    6. 27.5 Single Slit Diffraction
    7. 27.6 Limits of Resolution: The Rayleigh Criterion
    8. 27.7 Thin Film Interference
    9. 27.8 Polarization
    10. 27.9 *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light
    11. Glossary
    12. Section Summary
    13. Conceptual Questions
    14. Problems & Exercises
    15. Test Prep for AP® Courses
  29. 28 Special Relativity
    1. Connection for AP® Courses
    2. 28.1 Einstein’s Postulates
    3. 28.2 Simultaneity And Time Dilation
    4. 28.3 Length Contraction
    5. 28.4 Relativistic Addition of Velocities
    6. 28.5 Relativistic Momentum
    7. 28.6 Relativistic Energy
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  30. 29 Introduction to Quantum Physics
    1. Connection for AP® Courses
    2. 29.1 Quantization of Energy
    3. 29.2 The Photoelectric Effect
    4. 29.3 Photon Energies and the Electromagnetic Spectrum
    5. 29.4 Photon Momentum
    6. 29.5 The Particle-Wave Duality
    7. 29.6 The Wave Nature of Matter
    8. 29.7 Probability: The Heisenberg Uncertainty Principle
    9. 29.8 The Particle-Wave Duality Reviewed
    10. Glossary
    11. Section Summary
    12. Conceptual Questions
    13. Problems & Exercises
    14. Test Prep for AP® Courses
  31. 30 Atomic Physics
    1. Connection for AP® Courses
    2. 30.1 Discovery of the Atom
    3. 30.2 Discovery of the Parts of the Atom: Electrons and Nuclei
    4. 30.3 Bohr’s Theory of the Hydrogen Atom
    5. 30.4 X Rays: Atomic Origins and Applications
    6. 30.5 Applications of Atomic Excitations and De-Excitations
    7. 30.6 The Wave Nature of Matter Causes Quantization
    8. 30.7 Patterns in Spectra Reveal More Quantization
    9. 30.8 Quantum Numbers and Rules
    10. 30.9 The Pauli Exclusion Principle
    11. Glossary
    12. Section Summary
    13. Conceptual Questions
    14. Problems & Exercises
    15. Test Prep for AP® Courses
  32. 31 Radioactivity and Nuclear Physics
    1. Connection for AP® Courses
    2. 31.1 Nuclear Radioactivity
    3. 31.2 Radiation Detection and Detectors
    4. 31.3 Substructure of the Nucleus
    5. 31.4 Nuclear Decay and Conservation Laws
    6. 31.5 Half-Life and Activity
    7. 31.6 Binding Energy
    8. 31.7 Tunneling
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  33. 32 Medical Applications of Nuclear Physics
    1. Connection for AP® Courses
    2. 32.1 Medical Imaging and Diagnostics
    3. 32.2 Biological Effects of Ionizing Radiation
    4. 32.3 Therapeutic Uses of Ionizing Radiation
    5. 32.4 Food Irradiation
    6. 32.5 Fusion
    7. 32.6 Fission
    8. 32.7 Nuclear Weapons
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  34. 33 Particle Physics
    1. Connection for AP® Courses
    2. 33.1 The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited
    3. 33.2 The Four Basic Forces
    4. 33.3 Accelerators Create Matter from Energy
    5. 33.4 Particles, Patterns, and Conservation Laws
    6. 33.5 Quarks: Is That All There Is?
    7. 33.6 GUTs: The Unification of Forces
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  35. 34 Frontiers of Physics
    1. Connection for AP® Courses
    2. 34.1 Cosmology and Particle Physics
    3. 34.2 General Relativity and Quantum Gravity
    4. 34.3 Superstrings
    5. 34.4 Dark Matter and Closure
    6. 34.5 Complexity and Chaos
    7. 34.6 High-Temperature Superconductors
    8. 34.7 Some Questions We Know to Ask
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
  36. A | Atomic Masses
  37. B | Selected Radioactive Isotopes
  38. C | Useful Information
  39. D | Glossary of Key Symbols and Notation
  40. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
    14. Chapter 14
    15. Chapter 15
    16. Chapter 16
    17. Chapter 17
    18. Chapter 18
    19. Chapter 19
    20. Chapter 20
    21. Chapter 21
    22. Chapter 22
    23. Chapter 23
    24. Chapter 24
    25. Chapter 25
    26. Chapter 26
    27. Chapter 27
    28. Chapter 28
    29. Chapter 29
    30. Chapter 30
    31. Chapter 31
    32. Chapter 32
    33. Chapter 33
    34. Chapter 34
  41. Index

Learning Objectives

By the end of this section, you will be able to:

  • Define and discuss nuclear decay.
  • State the conservation laws.
  • Explain parent and daughter nucleus.
  • Calculate the energy emitted during nuclear decay.

The information presented in this section supports the following AP® learning objectives and science practices:

  • 5.B.8.1 The student is able to describe emission or absorption spectra associated with electronic or nuclear transitions as transitions between allowed energy states of the atom in terms of the principle of energy conservation, including characterization of the frequency of radiation emitted or absorbed. (S.P. 1.2, 7.2)
  • 5.C.1.1 The student is able to analyze electric charge conservation for nuclear and elementary particle reactions and make predictions related to such reactions based upon conservation of charge. (S.P. 6.4, 7.2)
  • 5.C.2.1 The student is able to predict electric charges on objects within a system by application of the principle of charge conservation within a system. (S.P. 6.4)
  • 5.G.1.1 The student is able to apply conservation of nucleon number and conservation of electric charge to make predictions about nuclear reactions and decays such as fission, fusion, alpha decay, beta decay, or gamma decay. (S.P. 6.4)

Nuclear decay has provided an amazing window into the realm of the very small. Nuclear decay gave the first indication of the connection between mass and energy, and it revealed the existence of two of the four basic forces in nature. In this section, we explore the major modes of nuclear decay; and, like those who first explored them, we will discover evidence of previously unknown particles and conservation laws.

Some nuclides are stable, apparently living forever. Unstable nuclides decay (that is, they are radioactive), eventually producing a stable nuclide after many decays. We call the original nuclide the parent and its decay products the daughters. Some radioactive nuclides decay in a single step to a stable nucleus. For example, 60Co60Co size 12{"" lSup { size 8{"60"} } "Co"} {} is unstable and decays directly to 60Ni60Ni size 12{"" lSup { size 8{"60"} } "Ni"} {}, which is stable. Others, such as 238U238U size 12{"" lSup { size 8{"238"} } U} {}, decay to another unstable nuclide, resulting in a decay series in which each subsequent nuclide decays until a stable nuclide is finally produced. The decay series that starts from 238U238U size 12{"" lSup { size 8{"238"} } U} {} is of particular interest, since it produces the radioactive isotopes 226Ra226Ra size 12{"" lSup { size 8{"226"} } "Ra"} {} and 210Po210Po size 12{"" lSup { size 8{"210"} } "Po"} {}, which the Curies first discovered (see Figure 31.16). Radon gas is also produced (222Rn222Rn size 12{"" lSup { size 8{"222"} } "Rn"} {} in the series), an increasingly recognized naturally occurring hazard. Since radon is a noble gas, it emanates from materials, such as soil, containing even trace amounts of 238U238U size 12{"" lSup { size 8{"238"} } U} {} and can be inhaled. The decay of radon and its daughters produces internal damage. The 238U238U size 12{"" lSup { size 8{"238"} } U} {} decay series ends with 206Pb206Pb size 12{"" lSup { size 8{"206"} } "Pb"} {}, a stable isotope of lead.

A graph is shown in which decay of alpha and beta is shown. Also half lives of each isotope are shown. Uranium decays in one mode but some isotopes decay by more than one mode. Finally a stable isotope of lead results.
Figure 31.16 The decay series produced by 238U238U size 12{"" lSup { size 8{"238"} } U} {}, the most common uranium isotope. Nuclides are graphed in the same manner as in the chart of nuclides. The type of decay for each member of the series is shown, as well as the half-lives. Note that some nuclides decay by more than one mode. You can see why radium and polonium are found in uranium ore. A stable isotope of lead is the end product of the series.

Note that the daughters of αα size 12{α} {} decay shown in Figure 31.16 always have two fewer protons and two fewer neutrons than the parent. This seems reasonable, since we know that αα size 12{α} {} decay is the emission of a 4He4He size 12{"" lSup { size 8{4} } "He"} {} nucleus, which has two protons and two neutrons. The daughters of ββ size 12{β} {} decay have one less neutron and one more proton than their parent. Beta decay is a little more subtle, as we shall see. No γγ size 12{γ} {} decays are shown in the figure, because they do not produce a daughter that differs from the parent.

Alpha Decay

In alpha decay, a 4He4He size 12{"" lSup { size 8{4} } "He"} {} nucleus simply breaks away from the parent nucleus, leaving a daughter with two fewer protons and two fewer neutrons than the parent (see Figure 31.17). One example of αα size 12{α} {} decay is shown in Figure 31.16 for 238U238U size 12{"" lSup { size 8{"238"} } U} {}. Another nuclide that undergoes αα size 12{α} {} decay is 239Pu239Pu size 12{"" lSup { size 8{"239"} } "Pu"} {}. The decay equations for these two nuclides are

238 U 234 Th 92 234 + 4 He 238 U 234 Th 92 234 + 4 He
31.13

and

239Pu235U+4He.239Pu235U+4He. size 12{"" lSup { size 8{"239"} } "Pu" rightarrow "" lSup { size 8{"235"} } U+"" lSup { size 8{4} } "He"} {}
31.14
The image shows conditions before and after alpha decay. Before alpha decay the nucleus is labeled parent and after decay the nucleus is labeled daughter.
Figure 31.17 Alpha decay is the separation of a 4He4He size 12{"" lSup { size 8{4} } "He"} {} nucleus from the parent. The daughter nucleus has two fewer protons and two fewer neutrons than the parent. Alpha decay occurs spontaneously only if the daughter and 4He4He size 12{"" lSup { size 8{4} } "He"} {} nucleus have less total mass than the parent.

If you examine the periodic table of the elements, you will find that Th has Z=90Z=90 size 12{Z="90"} {}, two fewer than U, which has Z=92Z=92 size 12{Z="92"} {}. Similarly, in the second decay equation, we see that U has two fewer protons than Pu, which has Z=94Z=94 size 12{Z="94"} {}. The general rule for αα size 12{α} {} decay is best written in the format ZAXNZAXN. If a certain nuclide is known to αα size 12{α} {} decay (generally this information must be looked up in a table of isotopes, such as in Table A1), its αα size 12{α} {} decay equation is

ZA XN Z2A4 YN2 + 24 He2 (αdecay) ZA XN Z2A4 YN2 + 24 He2 (αdecay) size 12{α} {}
31.15

where Y is the nuclide that has two fewer protons than X, such as Th having two fewer than U. So if you were told that 239Pu239Pu αα decays and were asked to write the complete decay equation, you would first look up which element has two fewer protons (an atomic number two lower) and find that this is uranium. Then since four nucleons have broken away from the original 239, its atomic mass would be 235.

It is instructive to examine conservation laws related to αα size 12{α} {} decay. You can see from the equation ZA XN Z2A4 YN2 + 24 He2 ZA XN Z2A4 YN2 + 24 He2 that total charge is conserved. Linear and angular momentum are conserved, too. Although conserved angular momentum is not of great consequence in this type of decay, conservation of linear momentum has interesting consequences. If the nucleus is at rest when it decays, its momentum is zero. In that case, the fragments must fly in opposite directions with equal-magnitude momenta so that total momentum remains zero. This results in the αα size 12{α} {} particle carrying away most of the energy, as a bullet from a heavy rifle carries away most of the energy of the powder burned to shoot it. Total mass–energy is also conserved: the energy produced in the decay comes from conversion of a fraction of the original mass. As discussed in Exercise 29.18, the general relationship is

E = ( Δm ) c 2 . E = ( Δm ) c 2 .
31.16

Here, EE size 12{E} {} is the nuclear reaction energy (the reaction can be nuclear decay or any other reaction), and ΔmΔm size 12{Δm} {} is the difference in mass between initial and final products. When the final products have less total mass, ΔmΔm size 12{Δm} {} is positive, and the reaction releases energy (is exothermic). When the products have greater total mass, the reaction is endothermic (ΔmΔm size 12{Δm} {} is negative) and must be induced with an energy input. For αα size 12{α} {} decay to be spontaneous, the decay products must have smaller mass than the parent.

Example 31.2 Alpha Decay Energy Found from Nuclear Masses

Find the energy emitted in the αα size 12{α} {} decay of 239Pu239Pu size 12{"" lSup { size 8{"239"} } "Pu"} {}.

Strategy

Nuclear reaction energy, such as released in α decay, can be found using the equation E=(Δm)c2E=(Δm)c2 size 12{E= \( Δm \) c"" lSup { size 8{2} } } {}. We must first find ΔmΔm size 12{Δm} {}, the difference in mass between the parent nucleus and the products of the decay. This is easily done using masses given in Exercise 34.31.

Solution

The decay equation was given earlier for 239Pu239Pu size 12{"" lSup { size 8{"239"} } "Pu"} {} ; it is

239Pu235U+4He.239Pu235U+4He.
31.17

Thus the pertinent masses are those of 239Pu239Pu, 235U235U, and the αα particle or 4He4He, all of which are listed in Exercise 34.31. The initial mass was m(239Pu)=239.052157 um(239Pu)=239.052157 u. The final mass is the sum m(235U) + m(4He) = 235.043924 u + 4.002602 u = 239.046526 um(235U) + m(4He) = 235.043924 u + 4.002602 u = 239.046526 u. Thus,

Δ m = m ( 239 Pu ) [ m ( 235 U ) + m ( 4 He ) ] = 239.052157 u 239.046526 u = 0.0005631 u. Δ m = m ( 239 Pu ) [ m ( 235 U ) + m ( 4 He ) ] = 239.052157 u 239.046526 u = 0.0005631 u.
31.18

Now we can find EE size 12{E} {} by entering ΔmΔm size 12{Δm} {} into the equation:

E=(Δm)c2=(0.005631 u)c2.E=(Δm)c2=(0.005631 u)c2.
31.19

We know 1 u=931.5 MeV/c21 u=931.5 MeV/c2 size 12{1" u =931" "." "5 MeV/"c rSup { size 8{2} } } {}, and so

E=(0.005631)(931.5 MeV/c2)(c2)=5.25 MeV.E=(0.005631)(931.5 MeV/c2)(c2)=5.25 MeV. size 12{E= \( 0 "." "005631" \) \( "931" "." 5" MeV"/c rSup { size 8{2} } \) \( c rSup { size 8{2} } \) =5 "." "25"" MeV"} {}
31.20

Discussion

The energy released in this αα size 12{α} {} decay is in the MeVMeV size 12{"MeV"} {} range, about 106106 size 12{"10" rSup { size 8{6} } } {} times as great as typical chemical reaction energies, consistent with many previous discussions. Most of this energy becomes kinetic energy of the αα size 12{α} {} particle (or 4He4He size 12{"" lSup { size 8{4} } "He"} {} nucleus), which moves away at high speed. The energy carried away by the recoil of the 235U235U size 12{"" lSup { size 8{"235"} } U} {} nucleus is much smaller in order to conserve momentum. The 235U235U size 12{"" lSup { size 8{"235"} } U} {} nucleus can be left in an excited state to later emit photons (γγ size 12{γ} {} rays). This decay is spontaneous and releases energy, because the products have less mass than the parent nucleus. The question of why the products have less mass will be discussed in Equation 31.59. Note that the masses given in Exercise 34.31 are atomic masses of neutral atoms, including their electrons. The mass of the electrons is the same before and after αα decay, and so their masses subtract out when finding ΔmΔm. In this case, there are 94 electrons before and after the decay.

Beta Decay

There are actually three types of beta decay. The first discovered was “ordinary” beta decay and is called ββ size 12{β rSup { size 8{ - {}} } } {} decay or electron emission. The symbol ββ size 12{β rSup { size 8{ - {}} } } {} represents an electron emitted in nuclear beta decay. Cobalt-60 is a nuclide that ββ size 12{β rSup { size 8{ - {}} } } {} decays in the following manner:

60Co60Ni+β+ neutrino.60Co60Ni+β+ neutrino. size 12{"" lSup { size 8{"60"} } "Co" rightarrow "" lSup { size 8{"60"} } "Ni"+β rSup { size 8{-{}} } +" neutrino"} {}
31.21

The neutrino is a particle emitted in beta decay that was unanticipated and is of fundamental importance. The neutrino was not even proposed in theory until more than 20 years after beta decay was known to involve electron emissions. Neutrinos are so difficult to detect that the first direct evidence of them was not obtained until 1953. Neutrinos are nearly massless, have no charge, and do not interact with nucleons via the strong nuclear force. Traveling approximately at the speed of light, they have little time to affect any nucleus they encounter. This is, owing to the fact that they have no charge (and they are not EM waves), they do not interact through the EM force. They do interact via the relatively weak and very short range weak nuclear force. Consequently, neutrinos escape almost any detector and penetrate almost any shielding. However, neutrinos do carry energy, angular momentum (they are fermions with half-integral spin), and linear momentum away from a beta decay. When accurate measurements of beta decay were made, it became apparent that energy, angular momentum, and linear momentum were not accounted for by the daughter nucleus and electron alone. Either a previously unsuspected particle was carrying them away, or three conservation laws were being violated. Wolfgang Pauli made a formal proposal for the existence of neutrinos in 1930. The Italian-born American physicist Enrico Fermi (1901–1954) gave neutrinos their name, meaning little neutral ones, when he developed a sophisticated theory of beta decay (see Figure 31.18). Part of Fermi’s theory was the identification of the weak nuclear force as being distinct from the strong nuclear force and in fact responsible for beta decay.

Photo of physicist Enrico Fermi.
Figure 31.18 Enrico Fermi was nearly unique among 20th-century physicists—he made significant contributions both as an experimentalist and a theorist. His many contributions to theoretical physics included the identification of the weak nuclear force. The fermi (fm) is named after him, as are an entire class of subatomic particles (fermions), an element (Fermium), and a major research laboratory (Fermilab). His experimental work included studies of radioactivity, for which he won the 1938 Nobel Prize in physics, and creation of the first nuclear chain reaction. (credit: United States Department of Energy, Office of Public Affairs)

The neutrino also reveals a new conservation law. There are various families of particles, one of which is the electron family. We propose that the number of members of the electron family is constant in any process or any closed system. In our example of beta decay, there are no members of the electron family present before the decay, but after, there is an electron and a neutrino. So electrons are given an electron family number of +1+1. The neutrino in ββ size 12{β rSup { size 8{ - {}} } } {} decay is an electron’s antineutrino, given the symbol ν¯eν¯e, where νν is the Greek letter nu, and the subscript e means this neutrino is related to the electron. The bar indicates this is a particle of antimatter. (All particles have antimatter counterparts that are nearly identical except that they have the opposite charge. Antimatter is almost entirely absent on Earth, but it is found in nuclear decay and other nuclear and particle reactions as well as in outer space.) The electron’s antineutrino ν¯eν¯e, being antimatter, has an electron family number of –1–1. The total is zero, before and after the decay. The new conservation law, obeyed in all circumstances, states that the total electron family number is constant. An electron cannot be created without also creating an antimatter family member. This law is analogous to the conservation of charge in a situation where total charge is originally zero, and equal amounts of positive and negative charge must be created in a reaction to keep the total zero.

If a nuclide ZAXNZAXN is known to ββ decay, then its ββ decay equation is

Z A X N Z + 1 A Y N 1 + β + ν - e ( β decay ) , Z A X N Z + 1 A Y N 1 + β + ν - e ( β decay ) , size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } rightarrow "" lSub { size 8{Z+1} } lSup { size 8{A} } Y rSub { size 8{N - 1} } +β rSup { size 8{ - {}} } + { bar {ν}} rSub { size 8{e} } ``` \( β rSup { size 8{ - {}} } `"decay" \) ,} {}
31.22

where Y is the nuclide having one more proton than X (see Figure 31.19). So if you know that a certain nuclide ββ decays, you can find the daughter nucleus by first looking up ZZ for the parent and then determining which element has atomic number Z+1Z+1. In the example of the ββ decay of 60Co60Co size 12{"" lSup { size 8{"60"} } "Co"} {} given earlier, we see that Z=27Z=27 for Co and Z=28Z=28 is Ni. It is as if one of the neutrons in the parent nucleus decays into a proton, electron, and neutrino. In fact, neutrons outside of nuclei do just that—they live only an average of a few minutes and ββ decay in the following manner:

n p + β + ν - e . n p + β + ν - e . size 12{n rightarrow p+β rSup { size 8{ - {}} } + { bar {ν}} rSub { size 8{e} } } {}
31.23
Image shows parent nucleus before beta decay and daughter nucleus after beta decay.
Figure 31.19 In ββ size 12{β rSup { size 8{ - {}} } } {} decay, the parent nucleus emits an electron and an antineutrino. The daughter nucleus has one more proton and one less neutron than its parent. Neutrinos interact so weakly that they are almost never directly observed, but they play a fundamental role in particle physics.

We see that charge is conserved in ββ decay, since the total charge is ZZ size 12{Z} {} before and after the decay. For example, in 60Co60Co decay, total charge is 27 before decay, since cobalt has Z=27Z=27. After decay, the daughter nucleus is Ni, which has Z=28Z=28, and there is an electron, so that the total charge is also 28 + (–1)28 + (–1) or 27. Angular momentum is conserved, but not obviously (you have to examine the spins and angular momenta of the final products in detail to verify this). Linear momentum is also conserved, again imparting most of the decay energy to the electron and the antineutrino, since they are of low and zero mass, respectively. Another new conservation law is obeyed here and elsewhere in nature. The total number of nucleons AA is conserved. In 60Co60Co decay, for example, there are 60 nucleons before and after the decay. Note that total AA is also conserved in αα decay. Also note that the total number of protons changes, as does the total number of neutrons, so that total ZZ size 12{Z} {} and total NN size 12{N} {} are not conserved in ββ size 12{β rSup { size 8{ - {}} } } {} decay, as they are in αα size 12{α} {} decay. Energy released in ββ size 12{β rSup { size 8{ - {}} } } {} decay can be calculated given the masses of the parent and products.

Example 31.3 ββ size 12{β rSup { size 8{ - {}} } } {} Decay Energy from Masses

Find the energy emitted in the ββ size 12{β rSup { size 8{ - {}} } } {} decay of 60Co60Co size 12{"" lSup { size 8{"60"} } "Co"} {}.

Strategy and Concept

As in the preceding example, we must first find ΔmΔm, the difference in mass between the parent nucleus and the products of the decay, using masses given in Exercise 34.31. Then the emitted energy is calculated as before, using E=(Δm)c2E=(Δm)c2. The initial mass is just that of the parent nucleus, and the final mass is that of the daughter nucleus and the electron created in the decay. The neutrino is massless, or nearly so. However, since the masses given in Exercise 34.31 are for neutral atoms, the daughter nucleus has one more electron than the parent, and so the extra electron mass that corresponds to the ββ is included in the atomic mass of Ni. Thus,

Δm=m(60Co )m(60Ni).Δm=m(60Co )m(60Ni). size 12{Δm=m \( "" lSup { size 8{"60"} } "Co" \) -m \( "" lSup { size 8{"60"} } "Ni" \) } {}
31.24

Solution

The ββ decay equation for 60Co60Co size 12{"" lSup { size 8{"60"} } "Co"} {} is

2760Co33 2860Ni32 + β +ν¯e.2760Co33 2860Ni32 + β +ν¯e.
31.25

As noticed,

Δm=m(60Co )m(60Ni).Δm=m(60Co )m(60Ni). size 12{Δm=m \( "" lSup { size 8{"60"} } "Co" \) -m \( "" lSup { size 8{"60"} } "Ni" \) } {}
31.26

Entering the masses found in Exercise 34.31 gives

Δm=59.933820 u59.930789 u=0.003031 u.Δm=59.933820 u59.930789 u=0.003031 u.
31.27

Thus,

E=(Δm)c2=(0.003031 u)c2.E=(Δm)c2=(0.003031 u)c2. size 12{E= \( Δm \) c rSup { size 8{2} } = \( 0 "." "003031" \) \( uc rSup { size 8{2} } \) } {}
31.28

Using 1 u=931.5 MeV/c21 u=931.5 MeV/c2, we obtain

E=(0.003031)(931.5 MeV/c2)(c2)=2.82 MeV.E=(0.003031)(931.5 MeV/c2)(c2)=2.82 MeV. size 12{E= \( 0 "." "003031" \) \( "931" "." 5" MeV"/c rSup { size 8{2} } \) \( c rSup { size 8{2} } \) =2 "." "82"" MeV"} {}
31.29

Discussion and Implications

Perhaps the most difficult thing about this example is convincing yourself that the ββ size 12{β rSup { size 8{ - {}} } } {} mass is included in the atomic mass of 60Ni60Ni. Beyond that are other implications. Again the decay energy is in the MeV range. This energy is shared by all of the products of the decay. In many 60Co60Co decays, the daughter nucleus 60Ni60Ni is left in an excited state and emits photons ( γγ size 12{g} {} rays). Most of the remaining energy goes to the electron and neutrino, since the recoil kinetic energy of the daughter nucleus is small. One final note: the electron emitted in ββ decay is created in the nucleus at the time of decay.

The second type of beta decay is less common than the first. It is β+β+ size 12{β rSup { size 8{+{}} } } {}decay. Certain nuclides decay by the emission of a positive electron. This is antielectron or positron decay (see Figure 31.20).

Image shows parent nucleus before beta plus decay and daughter nucleus after beta plus decay, which results in a positively charged electron called a positron.
Figure 31.20 β+β+ size 12{β rSup { size 8{+{}} } } {} decay is the emission of a positron that eventually finds an electron to annihilate, characteristically producing gammas in opposite directions.

The antielectron is often represented by the symbol e+e+ size 12{e rSup { size 8{+{}} } } {}, but in beta decay it is written as β+β+ size 12{β rSup { size 8{+{}} } } {} to indicate the antielectron was emitted in a nuclear decay. Antielectrons are the antimatter counterpart to electrons, being nearly identical, having the same mass, spin, and so on, but having a positive charge and an electron family number of –1–1. When a positron encounters an electron, there is a mutual annihilation in which all the mass of the antielectron-electron pair is converted into pure photon energy. (The reaction, e++eγ+γe++eγ+γ size 12{e rSup { size 8{+{}} } +e rSup { size 8{-{}} } rightarrow g+g} {}, conserves electron family number as well as all other conserved quantities.) If a nuclide ZAXNZAXN is known to β+β+ decay, then its β+β+ size 12{β rSup { size 8{+{}} } } {}decay equation is

ZA X N Z 1 A Y N + 1 + β + + ν e ( β + decay ) , ZA X N Z 1 A Y N + 1 + β + + ν e ( β + decay ) , size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } rightarrow "" lSub { size 8{Z - 1} } lSup { size 8{A} } Y rSub { size 8{N+1} } +β rSup { size 8{+{}} } +ν rSub { size 8{e} } ```` \( β rSup { size 8{+{}} } `"decay" \) ,} {}
31.30

where Y is the nuclide having one less proton than X (to conserve charge) and νeνe is the symbol for the electron’s neutrino, which has an electron family number of +1+1. Since an antimatter member of the electron family (the β+β+) is created in the decay, a matter member of the family (here the νeνe) must also be created. Given, for example, that 22Na22Na β+β+ size 12{β rSup { size 8{+{}} } } {} decays, you can write its full decay equation by first finding that Z=11Z=11 for 22Na22Na, so that the daughter nuclide will have Z=10Z=10 size 12{Z="10"} {}, the atomic number for neon. Thus the β+β+ size 12{β rSup { size 8{+{}} } } {} decay equation for 22Na22Na is

1122Na111022Ne12+β++νe.1122Na111022Ne12+β++νe.
31.31

In β+β+ size 12{β rSup { size 8{+{}} } } {} decay, it is as if one of the protons in the parent nucleus decays into a neutron, a positron, and a neutrino. Protons do not do this outside of the nucleus, and so the decay is due to the complexities of the nuclear force. Note again that the total number of nucleons is constant in this and any other reaction. To find the energy emitted in β+β+ size 12{β rSup { size 8{+{}} } } {} decay, you must again count the number of electrons in the neutral atoms, since atomic masses are used. The daughter has one less electron than the parent, and one electron mass is created in the decay. Thus, in β+β+ size 12{β rSup { size 8{+{}} } } {} decay,

Δm=m(parent)[m(daughter)+2me],Δm=m(parent)[m(daughter)+2me],
31.32

since we use the masses of neutral atoms.

Electron capture is the third type of beta decay. Here, a nucleus captures an inner-shell electron and undergoes a nuclear reaction that has the same effect as β+β+ size 12{β rSup { size 8{+{}} } } {} decay. Electron capture is sometimes denoted by the letters EC. We know that electrons cannot reside in the nucleus, but this is a nuclear reaction that consumes the electron and occurs spontaneously only when the products have less mass than the parent plus the electron. If a nuclide ZAXNZAXN is known to undergo electron capture, then its electron capture equation is

ZA X N + e Z 1 A Y N + 1 + ν e ( electron capture, or EC ) . ZA X N + e Z 1 A Y N + 1 + ν e ( electron capture, or EC ) . size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } +e rSup { size 8{ - {}} } rightarrow "" lSub { size 8{Z - 1} } lSup { size 8{A} } Y rSub { size 8{N+1} } +ν rSub { size 8{e} } ``` \( "electron capture, or EC" \) "." } {}
31.33

Any nuclide that can β+β+ size 12{β rSup { size 8{+{}} } } {} decay can also undergo electron capture (and often does both). The same conservation laws are obeyed for EC as for β+β+ size 12{β rSup { size 8{+{}} } } {} decay. It is good practice to confirm these for yourself.

All forms of beta decay occur because the parent nuclide is unstable and lies outside the region of stability in the chart of nuclides. Those nuclides that have relatively more neutrons than those in the region of stability will ββ size 12{β rSup { size 8{ - {}} } } {} decay to produce a daughter with fewer neutrons, producing a daughter nearer the region of stability. Similarly, those nuclides having relatively more protons than those in the region of stability will ββ size 12{β rSup { size 8{ - {}} } } {} decay or undergo electron capture to produce a daughter with fewer protons, nearer the region of stability.

Gamma Decay

Gamma decay is the simplest form of nuclear decay—it is the emission of energetic photons by nuclei left in an excited state by some earlier process. Protons and neutrons in an excited nucleus are in higher orbitals, and they fall to lower levels by photon emission (analogous to electrons in excited atoms). Nuclear excited states have lifetimes typically of only about 10141014 size 12{"10" rSup { size 8{ - "14"} } } {} s, an indication of the great strength of the forces pulling the nucleons to lower states. The γγ size 12{γ} {} decay equation is simply

ZA X N * Z A X N + γ 1 + γ 2 + ( γ decay ) ZA X N * Z A X N + γ 1 + γ 2 + ( γ decay ) size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } rSup { size 8{*} } rightarrow "" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } +γ rSub { size 8{1} } +γ rSub { size 8{2} } + dotsaxis ``` \( γ`"decay" \) } {}
31.34

where the asterisk indicates the nucleus is in an excited state. There may be one or more γγ s emitted, depending on how the nuclide de-excites. In radioactive decay, γγ emission is common and is preceded by γγ or ββ size 12{β} {} decay. For example, when 60Co60Co ββ size 12{β rSup { size 8{ - {}} } } {} decays, it most often leaves the daughter nucleus in an excited state, written 60Ni*60Ni*. Then the nickel nucleus quickly γγ size 12{γ} {} decays by the emission of two penetrating γγ size 12{γ} {} s:

60Ni*60Ni+γ1+γ2.60Ni*60Ni+γ1+γ2. size 12{"" lSup { size 8{"60"} } "Ni" rSup { size 8{*} } rightarrow "" lSup { size 8{"60"} } "Ni"+γ rSub { size 8{1} } +γ rSub { size 8{2} } } {}
31.35

These are called cobalt γγ size 12{γ} {} rays, although they come from nickel—they are used for cancer therapy, for example. It is again constructive to verify the conservation laws for gamma decay. Finally, since γγ size 12{γ} {} decay does not change the nuclide to another species, it is not prominently featured in charts of decay series, such as that in Figure 31.16.

There are other types of nuclear decay, but they occur less commonly than αα, ββ, and γγ size 12{γ} {} decay. Spontaneous fission is the most important of the other forms of nuclear decay because of its applications in nuclear power and weapons. It is covered in the next chapter.

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