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College Physics

33.4 Particles, Patterns, and Conservation Laws

College Physics33.4 Particles, Patterns, and Conservation Laws
  1. Preface
  2. 1 Introduction: The Nature of Science and Physics
    1. Introduction to Science and the Realm of Physics, Physical Quantities, and Units
    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. Introduction to One-Dimensional Kinematics
    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
  4. 3 Two-Dimensional Kinematics
    1. Introduction to Two-Dimensional Kinematics
    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
  5. 4 Dynamics: Force and Newton's Laws of Motion
    1. Introduction to Dynamics: Newton’s Laws of Motion
    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 Forces
    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
  6. 5 Further Applications of Newton's Laws: Friction, Drag, and Elasticity
    1. Introduction: Further Applications of Newton’s Laws
    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
  7. 6 Uniform Circular Motion and Gravitation
    1. Introduction to Uniform Circular Motion and Gravitation
    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
  8. 7 Work, Energy, and Energy Resources
    1. Introduction to Work, Energy, and Energy Resources
    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
  9. 8 Linear Momentum and Collisions
    1. Introduction to Linear Momentum and Collisions
    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
  10. 9 Statics and Torque
    1. Introduction to Statics and Torque
    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
  11. 10 Rotational Motion and Angular Momentum
    1. Introduction to Rotational Motion and Angular Momentum
    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
  12. 11 Fluid Statics
    1. Introduction to Fluid Statics
    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
  13. 12 Fluid Dynamics and Its Biological and Medical Applications
    1. Introduction to Fluid Dynamics and Its Biological and Medical Applications
    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
  14. 13 Temperature, Kinetic Theory, and the Gas Laws
    1. Introduction to Temperature, Kinetic Theory, and the Gas Laws
    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
  15. 14 Heat and Heat Transfer Methods
    1. Introduction to Heat and Heat Transfer Methods
    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
  16. 15 Thermodynamics
    1. Introduction to Thermodynamics
    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
  17. 16 Oscillatory Motion and Waves
    1. Introduction to Oscillatory Motion and Waves
    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
  18. 17 Physics of Hearing
    1. Introduction to the Physics of Hearing
    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
  19. 18 Electric Charge and Electric Field
    1. Introduction to Electric Charge and Electric Field
    2. 18.1 Static Electricity and Charge: Conservation of Charge
    3. 18.2 Conductors and Insulators
    4. 18.3 Coulomb’s Law
    5. 18.4 Electric Field: Concept of a Field Revisited
    6. 18.5 Electric Field Lines: Multiple Charges
    7. 18.6 Electric Forces in Biology
    8. 18.7 Conductors and Electric Fields in Static Equilibrium
    9. 18.8 Applications of Electrostatics
    10. Glossary
    11. Section Summary
    12. Conceptual Questions
    13. Problems & Exercises
  20. 19 Electric Potential and Electric Field
    1. Introduction to Electric Potential and Electric Energy
    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
  21. 20 Electric Current, Resistance, and Ohm's Law
    1. Introduction to Electric Current, Resistance, and Ohm's Law
    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
  22. 21 Circuits and DC Instruments
    1. Introduction to Circuits and DC Instruments
    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
  23. 22 Magnetism
    1. Introduction to Magnetism
    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
  24. 23 Electromagnetic Induction, AC Circuits, and Electrical Technologies
    1. Introduction to Electromagnetic Induction, AC Circuits and Electrical Technologies
    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
  25. 24 Electromagnetic Waves
    1. Introduction to Electromagnetic Waves
    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
  26. 25 Geometric Optics
    1. Introduction to Geometric Optics
    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
  27. 26 Vision and Optical Instruments
    1. Introduction to Vision and Optical Instruments
    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
  28. 27 Wave Optics
    1. Introduction to Wave Optics
    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
  29. 28 Special Relativity
    1. Introduction to Special Relativity
    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
  30. 29 Introduction to Quantum Physics
    1. Introduction to Quantum Physics
    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
  31. 30 Atomic Physics
    1. Introduction to Atomic Physics
    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
  32. 31 Radioactivity and Nuclear Physics
    1. Introduction to Radioactivity and Nuclear Physics
    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
  33. 32 Medical Applications of Nuclear Physics
    1. Introduction to Applications of Nuclear Physics
    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
  34. 33 Particle Physics
    1. Introduction to Particle Physics
    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
  35. 34 Frontiers of Physics
    1. Introduction to Frontiers of Physics
    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. Index

In the early 1930s only a small number of subatomic particles were known to exist—the proton, neutron, electron, photon and, indirectly, the neutrino. Nature seemed relatively simple in some ways, but mysterious in others. Why, for example, should the particle that carries positive charge be almost 2000 times as massive as the one carrying negative charge? Why does a neutral particle like the neutron have a magnetic moment? Does this imply an internal structure with a distribution of moving charges? Why is it that the electron seems to have no size other than its wavelength, while the proton and neutron are about 1 fermi in size? So, while the number of known particles was small and they explained a great deal of atomic and nuclear phenomena, there were many unexplained phenomena and hints of further substructures.

Things soon became more complicated, both in theory and in the prediction and discovery of new particles. In 1928, the British physicist P.A.M. Dirac (see Figure 33.12) developed a highly successful relativistic quantum theory that laid the foundations of quantum electrodynamics (QED). His theory, for example, explained electron spin and magnetic moment in a natural way. But Dirac’s theory also predicted negative energy states for free electrons. By 1931, Dirac, along with Oppenheimer, realized this was a prediction of positively charged electrons (or positrons). In 1932, American physicist Carl Anderson discovered the positron in cosmic ray studies. The positron, or e+e+ size 12{e rSup { size 8{+{}} } } {} , is the same particle as emitted in β+β+ size 12{e rSup { size 8{+{}} } } {} decay and was the first antimatter that was discovered. In 1935, Yukawa predicted pions as the carriers of the strong nuclear force, and they were eventually discovered. Muons were discovered in cosmic ray experiments in 1937, and they seemed to be heavy, unstable versions of electrons and positrons. After World War II, accelerators energetic enough to create these particles were built. Not only were predicted and known particles created, but many unexpected particles were observed. Initially called elementary particles, their numbers proliferated to dozens and then hundreds, and the term “particle zoo” became the physicist’s lament at the lack of simplicity. But patterns were observed in the particle zoo that led to simplifying ideas such as quarks, as we shall soon see.

A photo of a young Paul Dirac.
Figure 33.12 P.A.M. Dirac’s theory of relativistic quantum mechanics not only explained a great deal of what was known, it also predicted antimatter. (credit: Cambridge University, Cavendish Laboratory)

Matter and Antimatter

The positron was only the first example of antimatter. Every particle in nature has an antimatter counterpart, although some particles, like the photon, are their own antiparticles. Antimatter has charge opposite to that of matter (for example, the positron is positive while the electron is negative) but is nearly identical otherwise, having the same mass, intrinsic spin, half-life, and so on. When a particle and its antimatter counterpart interact, they annihilate one another, usually totally converting their masses to pure energy in the form of photons as seen in Figure 33.13. Neutral particles, such as neutrons, have neutral antimatter counterparts, which also annihilate when they interact. Certain neutral particles are their own antiparticle and live correspondingly short lives. For example, the neutral pion π0π0 size 12{π rSup { size 8{0} } } {} is its own antiparticle and has a half-life about 108108 size 12{"10" rSup { size 8{ - 8} } } {} shorter than π+π+ size 12{π rSup { size 8{+{}} } } {} and ππ size 12{π rSup { size 8{ - {}} } } {}, which are each other’s antiparticles. Without exception, nature is symmetric—all particles have antimatter counterparts. For example, antiprotons and antineutrons were first created in accelerator experiments in 1956 and the antiproton is negative. Antihydrogen atoms, consisting of an antiproton and antielectron, were observed in 1995 at CERN, too. It is possible to contain large-scale antimatter particles such as antiprotons by using electromagnetic traps that confine the particles within a magnetic field so that they don't annihilate with other particles. However, particles of the same charge repel each other, so the more particles that are contained in a trap, the more energy is needed to power the magnetic field that contains them. It is not currently possible to store a significant quantity of antiprotons. At any rate, we now see that negative charge is associated with both low-mass (electrons) and high-mass particles (antiprotons) and the apparent asymmetry is not there. But this knowledge does raise another question—why is there such a predominance of matter and so little antimatter? Possible explanations emerge later in this and the next chapter.

Hadrons and Leptons

Particles can also be revealingly grouped according to what forces they feel between them. All particles (even those that are massless) are affected by gravity, since gravity affects the space and time in which particles exist. All charged particles are affected by the electromagnetic force, as are neutral particles that have an internal distribution of charge (such as the neutron with its magnetic moment). Special names are given to particles that feel the strong and weak nuclear forces. Hadrons are particles that feel the strong nuclear force, whereas leptons are particles that do not. The proton, neutron, and the pions are examples of hadrons. The electron, positron, muons, and neutrinos are examples of leptons, the name meaning low mass. Leptons feel the weak nuclear force. In fact, all particles feel the weak nuclear force. This means that hadrons are distinguished by being able to feel both the strong and weak nuclear forces.

Table 33.2 lists the characteristics of some of the most important subatomic particles, including the directly observed carrier particles for the electromagnetic and weak nuclear forces, all leptons, and some hadrons. Several hints related to an underlying substructure emerge from an examination of these particle characteristics. Note that the carrier particles are called gauge bosons. First mentioned in Patterns in Spectra Reveal More Quantization, a boson is a particle with zero or an integer value of intrinsic spin (such as s=0, 1, 2, ...s=0, 1, 2, ... size 12{s=0,`1,`2,` "." "." "." } {}), whereas a fermion is a particle with a half-integer value of intrinsic spin (s=1/2,3/2,...s=1/2,3/2,... size 12{s=1/2,`3/2,` "." "." "." } {}). Fermions obey the Pauli exclusion principle whereas bosons do not. All the known and conjectured carrier particles are bosons.

The upper image shows an electron and positron colliding head-on. The lower image shows a starburst image from which two photons are emerging in opposite directions.
Figure 33.13 When a particle encounters its antiparticle, they annihilate, often producing pure energy in the form of photons. In this case, an electron and a positron convert all their mass into two identical energy rays, which move away in opposite directions to keep total momentum zero as it was before. Similar annihilations occur for other combinations of a particle with its antiparticle, sometimes producing more particles while obeying all conservation laws.
Category Particle name Symbol Antiparticle Rest mass ( MeV / c 2 ) ( MeV / c 2 ) B B L e L e L μ L μ L τ L τ size 12{L rSub { size 8{τ} } } {} S S size 12{S} {} Lifetime5 (s)
Gauge Photon γ γ size 12{γ} {} Self 0 0 0 0 0 0 Stable
Bosons W W size 12{W} {} W + W + size 12{W rSup { size 8{+{}} } } {} W W size 12{W rSup { size 8{ - {}} } } {} 80 . 39 × 10 3 80 . 39 × 10 3 size 12{"80" "." "22" times "10" rSup { size 8{3} } } {} 0 0 0 0 0 1.6 × 10 25 1.6 × 10 25 size 12{3 times "10" rSup { size 8{ - "25"} } } {}
Z Z size 12{Z} {} Z 0 Z 0 size 12{Z rSup { size 8{0} } } {} Self 91 . 19 × 10 3 91 . 19 × 10 3 size 12{"91" "." "19" times "10" rSup { size 8{3} } } {} 0 0 0 0 0 1.32 × 10 25 1.32 × 10 25 size 12{3 times "10" rSup { size 8{ - "25"} } } {}
Leptons Electron e e size 12{e rSup { size 8{ - {}} } } {} e + e + size 12{e rSup { size 8{ - {}} } } {} 0.511 0 ± 1 ± 1 size 12{ +- 1} {} 0 0 0 Stable
Neutrino (e) ν e ν e size 12{e rSup { size 8{ - {}} } } {} v ¯ e v ¯ e size 12{ { bar {v}} rSub { size 8{e} } } {} 0 7 . 0 eV 0 7 . 0 eV size 12{0` left (<7 "." 0`"eV" right )} {} 6 0 ± 1 ± 1 size 12{ +- 1} {} 0 0 0 Stable
Muon μ μ size 12{μ rSup { size 8{ - {}} } } {} μ + μ + size 12{μ rSup { size 8{+{}} } } {} 105.7 0 0 ± 1 ± 1 size 12{ +- 1} {} 0 0 2 . 20 × 10 6 2 . 20 × 10 6 size 12{2 "." "20" times "10" rSup { size 8{ - 6} } } {}
Neutrino (μ)(μ size 12{μ} {}) v μ v μ size 12{v rSub { size 8{μ} } } {} v - μ v - μ size 12{v rSub { size 8{μ} } } {} 0 ( < 0.27 ) 0(<0.27) 0 0 ± 1 ± 1 size 12{ +- 1} {} 0 0 Stable
Tau τ τ size 12{τ rSup { size 8{ - {}} } } {} τ + τ + size 12{τ rSup { size 8{+{}} } } {} 1777 0 0 0 ± 1 ± 1 size 12{ +- 1} {} 0 2 . 91 × 10 13 2 . 91 × 10 13 size 12{2 "." "29" times "10" rSup { size 8{ - "13"} } } {}
Neutrino (τ)(τ size 12{τ} {}) v τ v τ size 12{v rSub { size 8{τ} } } {} v - τ v - τ size 12{ { bar {v}} rSub { size 8{τ} } } {} 0 ( < 31 ) 0(<31) 0 0 0 ± 1 ± 1 size 12{ +- 1} {} 0 Stable
Hadrons (selected)
  Mesons Pion π + π + size 12{π rSup { size 8{+{}} } } {} π π size 12{π rSup { size 8{ - {}} } } {} 139.6 0 0 0 0 0 2.60 × 10 −8
π 0 π 0 size 12{π rSup { size 8{0} } } {} Self 135.0 0 0 0 0 0 8.4 × 10 −17
Kaon K + K + size 12{K rSup { size 8{+{}} } } {} K K size 12{K rSup { size 8{ - {}} } } {} 493.7 0 0 0 0 ± 1 ± 1 size 12{ +- 1} {} 1.24 × 10 −8
K 0 K 0 size 12{K rSup { size 8{0} } } {} K - 0 K - 0 size 12{ { bar {K}} rSup { size 8{0} } } {} 497.6 0 0 0 0 ± 1 ± 1 size 12{ +- 1} {} 0.90 × 10 −10
Eta η 0 η 0 size 12{η rSup { size 8{0} } } {} Self 547.9 0 0 0 0 0 2.53 × 10 −19
(many other mesons known)
  Baryons Proton p p size 12{p} {} p - p - size 12{ { bar {p}}} {} 938.3 ± 1 0 0 0 0 Stable7
Neutron n n size 12{n} {} n - n - size 12{ { bar {n}}} {} 939.6 ± 1 0 0 0 0 882
Lambda Λ 0 Λ 0 size 12{Λ rSup { size 8{0} } } {} Λ - 0 Λ - 0 size 12{ { bar {Λ}} rSup { size 8{0} } } {} 1115.7 ± 1 0 0 0 1 1 size 12{ -+ 1} {} 2.63 × 10 −10
Sigma Σ + Σ + size 12{Σ rSup { size 8{+{}} } } {} Σ - Σ - size 12{ { bar {Σ}} rSup { size 8{ - {}} } } {} 1189.4 ± 1 0 0 0 1 1 size 12{ -+ 1} {} 0.80 × 10 −10
Σ 0 Σ 0 size 12{Σ rSup { size 8{0} } } {} Σ - 0 Σ - 0 size 12{ { bar {Σ}} rSup { size 8{0} } } {} 1192.6 ± 1 0 0 0 1 1 size 12{ -+ 1} {} 7.4 × 10 −20
Σ Σ size 12{Σ rSup { size 8{ - {}} } } {} Σ - + Σ - + size 12{ { bar {Σ}} rSup { size 8{+{}} } } {} 1197.4 ± 1 0 0 0 1 1 size 12{ -+ 1} {} 1.48 × 10 −10
Xi Ξ 0 Ξ 0 size 12{Ξ rSup { size 8{0} } } {} Ξ - 0 Ξ - 0 size 12{ { bar {Ξ}} rSup { size 8{0} } } {} 1314.9 ± 1 0 0 0 2 2 size 12{ -+ 2} {} 2.90 × 10 −10
Ξ Ξ size 12{Ξ rSup { size 8{ - {}} } } {} Ξ + Ξ + size 12{Ξ rSup { size 8{+{}} } } {} 1321.7 ± 1 0 0 0 2 2 size 12{ -+ 2} {} 1.64 × 10 −10
Omega Ω Ω size 12{ %OMEGA rSup { size 8{ - {}} } } {} Ω + Ω + size 12{ %OMEGA rSup { size 8{+{}} } } {} 1672.5 ± 1 0 0 0 3 3 size 12{ -+ 3} {} 0.82 × 10 −10
(many other baryons known)
Table 33.2 Selected Particle Characteristics4

All known leptons are listed in the table given above. There are only six leptons (and their antiparticles), and they seem to be fundamental in that they have no apparent underlying structure. Leptons have no discernible size other than their wavelength, so that we know they are pointlike down to about 1018m1018m size 12{"10" rSup { size 8{ - "18"} } m} {}. The leptons fall into three families, implying three conservation laws for three quantum numbers. One of these was known from ββ size 12{β} {} decay, where the existence of the electron’s neutrino implied that a new quantum number, called the electron family number LeLe size 12{L rSub { size 8{e} } } {} is conserved. Thus, in ββ size 12{β} {} decay, an antielectron’s neutrino v-ev-e size 12{ { bar {v}} rSub { size 8{e} } } {} must be created with Le=1Le=1 size 12{L rSub { size 8{e} } = - 1} {} when an electron with Le=+1Le=+1 size 12{L rSub { size 8{e} } "=+"1} {} is created, so that the total remains 0 as it was before decay.

Once the muon was discovered in cosmic rays, its decay mode was found to be

μe+v-e+vμ,μe+v-e+vμ, size 12{μ rSup { size 8{ - {}} } rightarrow e rSup { size 8{ - {}} } + { bar {v}} rSub { size 8{e} } +v rSub { size 8{μ} } ","} {}
33.7

which implied another “family” and associated conservation principle. The particle vμvμ size 12{L rSub { size 8{μ} } } {} is a muon’s neutrino, and it is created to conserve muon family numberLμLμ size 12{L rSub { size 8{μ} } } {}. So muons are leptons with a family of their own, and conservation of total LμLμ size 12{L rSub { size 8{μ} } } {} also seems to be obeyed in many experiments.

More recently, a third lepton family was discovered when ττ size 12{τ} {} particles were created and observed to decay in a manner similar to muons. One principal decay mode is

τμ+v-μ+vτ.τμ+v-μ+vτ. size 12{τ rSup { size 8{ - {}} } rightarrow μ rSup { size 8{ - {}} } + { bar {v}} rSub { size 8{u} } +v rSub { size 8{τ} } "."} {}
33.8

Conservation of total LτLτ size 12{L rSub { size 8{μ} } } {} seems to be another law obeyed in many experiments. In fact, particle experiments have found that lepton family number is not universally conserved, due to neutrino “oscillations,” or transformations of neutrinos from one family type to another.

Mesons and Baryons

Now, note that the hadrons in the table given above are divided into two subgroups, called mesons (originally for medium mass) and baryons (the name originally meaning large mass). The division between mesons and baryons is actually based on their observed decay modes and is not strictly associated with their masses. Mesons are hadrons that can decay to leptons and leave no hadrons, which implies that mesons are not conserved in number. Baryons are hadrons that always decay to another baryon. A new physical quantity called baryon number BB size 12{B} {} seems to always be conserved in nature and is listed for the various particles in the table given above. Mesons and leptons have B=0B=0 size 12{B=0} {} so that they can decay to other particles with B=0B=0 size 12{B=0} {}. But baryons have B=+1B=+1 size 12{B"=+"1} {} if they are matter, and B=1B=1 size 12{B= - 1} {} if they are antimatter. The conservation of total baryon number is a more general rule than first noted in nuclear physics, where it was observed that the total number of nucleons was always conserved in nuclear reactions and decays. That rule in nuclear physics is just one consequence of the conservation of the total baryon number.

Forces, Reactions, and Reaction Rates

The forces that act between particles regulate how they interact with other particles. For example, pions feel the strong force and do not penetrate as far in matter as do muons, which do not feel the strong force. (This was the way those who discovered the muon knew it could not be the particle that carries the strong force—its penetration or range was too great for it to be feeling the strong force.) Similarly, reactions that create other particles, like cosmic rays interacting with nuclei in the atmosphere, have greater probability if they are caused by the strong force than if they are caused by the weak force. Such knowledge has been useful to physicists while analyzing the particles produced by various accelerators.

The forces experienced by particles also govern how particles interact with themselves if they are unstable and decay. For example, the stronger the force, the faster they decay and the shorter is their lifetime. An example of a nuclear decay via the strong force is 8 Beα+α 8 Beα+α size 12{"" lSup { size 8{8} } "Be" rightarrow α+α} {} with a lifetime of about 1016s1016s size 12{"10" rSup { size 8{ - "16"} } `s} {}. The neutron is a good example of decay via the weak force. The process np+e+v-enp+e+v-e size 12{n rightarrow p+e rSup { size 8{ - {}} } + { bar {v}} rSub { size 8{e} } } {} has a longer lifetime of 882 s. The weak force causes this decay, as it does all ββ size 12{β} {} decay. An important clue that the weak force is responsible for ββ size 12{β} {} decay is the creation of leptons, such as ee size 12{e rSup { size 8{ - {}} } } {} and v-ev-e size 12{ { bar {v}} rSub { size 8{e} } } {}. None would be created if the strong force was responsible, just as no leptons are created in the decay of 8Be8Be size 12{"" lSup { size 8{8} } "Be"} {}. The systematics of particle lifetimes is a little simpler than nuclear lifetimes when hundreds of particles are examined (not just the ones in the table given above). Particles that decay via the weak force have lifetimes mostly in the range of 10161016 size 12{"10" rSup { size 8{ - "16"} } } {} to 10121012 size 12{"10" rSup { size 8{ - "12"} } } {} s, whereas those that decay via the strong force have lifetimes mostly in the range of 10161016 size 12{"10" rSup { size 8{ - "16"} } } {} to 10231023 size 12{"10" rSup { size 8{ - "23"} } } {} s. Turning this around, if we measure the lifetime of a particle, we can tell if it decays via the weak or strong force.

Yet another quantum number emerges from decay lifetimes and patterns. Note that the particles Λ,Σ,ΞΛ,Σ,Ξ size 12{Λ,`Σ,`Ξ} {}, and ΩΩ size 12{ %OMEGA } {} decay with lifetimes on the order of 10101010 size 12{"10" rSup { size 8{ - "10"} } } {} s (the exception is Σ0Σ0 size 12{Σ rSup { size 8{0} } } {}, whose short lifetime is explained by its particular quark substructure.), implying that their decay is caused by the weak force alone, although they are hadrons and feel the strong force. The decay modes of these particles also show patterns—in particular, certain decays that should be possible within all the known conservation laws do not occur. Whenever something is possible in physics, it will happen. If something does not happen, it is forbidden by a rule. All this seemed strange to those studying these particles when they were first discovered, so they named a new quantum number strangeness, given the symbol SS size 12{S} {} in the table given above. The values of strangeness assigned to various particles are based on the decay systematics. It is found that strangeness is conserved by the strong force, which governs the production of most of these particles in accelerator experiments. However, strangeness is not conserved by the weak force. This conclusion is reached from the fact that particles that have long lifetimes decay via the weak force and do not conserve strangeness. All of this also has implications for the carrier particles, since they transmit forces and are thus involved in these decays.

Example 33.3 Calculating Quantum Numbers in Two Decays

(a) The most common decay mode of the ΞΞ size 12{Ξ rSup { size 8{ - {}} } } {} particle is ΞΛ0+πΞΛ0+π size 12{Ξ rSup { size 8{ - {}} } rightarrow Λ rSup { size 8{0} } +π rSup { size 8{ - {}} } } {}. Using the quantum numbers in the table given above, show that strangeness changes by 1, baryon number and charge are conserved, and lepton family numbers are unaffected.

(b) Is the decay K+μ++νμK+μ++νμ size 12{K rSup { size 8{+{}} } rightarrow μ rSup { size 8{+{}} } +ν rSub { size 8{μ} } } {} allowed, given the quantum numbers in the table given above?

Strategy

In part (a), the conservation laws can be examined by adding the quantum numbers of the decay products and comparing them with the parent particle. In part (b), the same procedure can reveal if a conservation law is broken or not.

Solution for (a)

Before the decay, the ΞΞ has strangeness S=2S=2 size 12{S= - 2} {}. After the decay, the total strangeness is –1 for the Λ0Λ0 size 12{Λ rSup { size 8{0} } } {}, plus 0 for the ππ. Thus, total strangeness has gone from –2 to –1 or a change of +1. Baryon number for the ΞΞ is B=+1B=+1 before the decay, and after the decay the Λ0Λ0 has B=+1B=+1 and the ππ has B=0B=0 size 12{B=0} {} so that the total baryon number remains +1. Charge is –1 before the decay, and the total charge after is also 01=101=1 size 12{0 - 1= - 1} {}. Lepton numbers for all the particles are zero, and so lepton numbers are conserved.

Discussion for (a)

The ΞΞ size 12{Ξ rSup { size 8{ - {}} } } {} decay is caused by the weak interaction, since strangeness changes, and it is consistent with the relatively long 1.64×1010-s1.64×1010-s size 12{1 "." "64" times "10" rSup { size 8{ - "10"} } "-s"} {} lifetime of the ΞΞ size 12{Ξ rSup { size 8{ - {}} } } {}.

Solution for (b)

The decay K+μ++νμK+μ++νμ size 12{K rSup { size 8{+{}} } rightarrow μ rSup { size 8{+{}} } +ν rSub { size 8{μ} } } {} is allowed if charge, baryon number, mass-energy, and lepton numbers are conserved. Strangeness can change due to the weak interaction. Charge is conserved as sdsd size 12{s rightarrow d} {}. Baryon number is conserved, since all particles have B=0B=0 size 12{B=0} {}. Mass-energy is conserved in the sense that the K+K+ size 12{K rSup { size 8{+{}} } } {} has a greater mass than the products, so that the decay can be spontaneous. Lepton family numbers are conserved at 0 for the electron and tau family for all particles. The muon family number is Lμ=0Lμ=0 size 12{L rSub { size 8{μ} } =0} {} before and Lμ=1+1=0Lμ=1+1=0 size 12{L rSub { size 8{μ} } = - 1+1=0} {} after. Strangeness changes from +1 before to 0 + 0 after, for an allowed change of 1. The decay is allowed by all these measures.

Discussion for (b)

This decay is not only allowed by our reckoning, it is, in fact, the primary decay mode of the K+K+ size 12{K rSup { size 8{+{}} } } {} meson and is caused by the weak force, consistent with the long 1.24×108-s1.24×108-s size 12{1 "." "24" times "10" rSup { size 8{ - 8} } "-s"} {} lifetime.

There are hundreds of particles, all hadrons, not listed in Table 33.2, most of which have shorter lifetimes. The systematics of those particle lifetimes, their production probabilities, and decay products are completely consistent with the conservation laws noted for lepton families, baryon number, and strangeness, but they also imply other quantum numbers and conservation laws. There are a finite, and in fact relatively small, number of these conserved quantities, however, implying a finite set of substructures. Additionally, some of these short-lived particles resemble the excited states of other particles, implying an internal structure. All of this jigsaw puzzle can be tied together and explained relatively simply by the existence of fundamental substructures. Leptons seem to be fundamental structures. Hadrons seem to have a substructure called quarks. Quarks: Is That All There Is? explores the basics of the underlying quark building blocks.

The image shows a picture of physicist Murray Gell Mann, who looks like a pleasant white-haired gentleman.
Figure 33.14 Murray Gell-Mann (b. 1929) proposed quarks as a substructure of hadrons in 1963 and was already known for his work on the concept of strangeness. Although quarks have never been directly observed, several predictions of the quark model were quickly confirmed, and their properties explain all known hadron characteristics. Gell-Mann was awarded the Nobel Prize in 1969. (credit: Luboš Motl)

Footnotes

  • 4 The lower of the size 12{ -+ {}} {} or ±± size 12{ +- {}} {} symbols are the values for antiparticles.
  • 5 Lifetimes are traditionally given as t1/2/0.693t1/2/0.693 (which is 1/λ1/λ size 12{ {1} slash {λ} } {}, the inverse of the decay constant).
  • 6 Neutrino masses may be zero. Experimental upper limits are given in parentheses.
  • 7 Experimental lower limit is >5×1032>5×1032 size 12{>5 times "10" rSup { size 8{"32"} } } {} for proposed mode of decay.
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