8.12 Symmetries and Conservation Laws

Comments

Please login to add a comment.

Don't have an account? Register now!

Where to Move

Move chapter:

• ☰ 1 Mathematical Foundations of Physics
  • ☰ 1.1 Physical Quantities and Units
    • ☰ 1.1.1 Physical Quantities
    • ☰ 1.1.2 SI Base Units
    • ☰ 1.1.3 Derived Units
    • ☰ 1.1.4 Unit Conversions
    • ☰ 1.1.5 Scientific Notation
    • ☰ 1.1.6 Orders of Magnitude
    • ☰ 1.1.7 Dimensional Analysis
    • ☰ 1.1.8 Significant Figures
    • ☰ 1.1.9 Measurement Uncertainty
  • ☰ 1.2 Scalars and Vectors
    • ☰ 1.2.1 Scalars and Vectors
    • ☰ 1.2.2 Vector Notation
    • ☰ 1.2.3 Vector Addition and Subtraction
    • ☰ 1.2.4 Vector Components
    • ☰ 1.2.5 Unit Vectors
    • ☰ 1.2.6 Dot Product
    • ☰ 1.2.7 Cross Product
    • ☰ 1.2.8 Applications of Vectors in Physics
  • ☰ 1.3 Coordinate Systems
    • ☰ 1.3.1 Cartesian Coordinates
    • ☰ 1.3.2 Polar Coordinates
    • ☰ 1.3.3 Cylindrical Coordinates
    • ☰ 1.3.4 Spherical Coordinates
    • ☰ 1.3.5 Coordinate Transformations
  • ☰ 1.4 Calculus for Physics
    • ☰ 1.4.1 Functions and Graphs
    • ☰ 1.4.2 Derivatives
    • ☰ 1.4.3 Physical Meaning of Derivatives
    • ☰ 1.4.4 Partial Derivatives
    • ☰ 1.4.5 Integrals
    • ☰ 1.4.6 Physical Meaning of Integrals
    • ☰ 1.4.7 Differential Equations
    • ☰ 1.4.8 Taylor Series and Approximations
• ☰ 2 Part I: Classical Mechanics
  • ☰ 2.1 Kinematics
    • ☰ 2.1.1 Motion in One Dimension
      • ☰ 2.1.1.1 Position
      • ☰ 2.1.1.2 Distance and Displacement
      • ☰ 2.1.1.3 Speed and Velocity
      • ☰ 2.1.1.4 Average Velocity
      • ☰ 2.1.1.5 Instantaneous Velocity
      • ☰ 2.1.1.6 Acceleration
    • ☰ 2.1.2 Motion with Constant Acceleration
      • ☰ 2.1.2.1 Kinematic Equations
      • ☰ 2.1.2.2 Free Fall
      • ☰ 2.1.2.3 Vertical Motion
      • ☰ 2.1.2.4 Position-Time Graphs
      • ☰ 2.1.2.5 Velocity-Time Graphs
      • ☰ 2.1.2.6 Acceleration-Time Graphs
    • ☰ 2.1.3 Motion in Two and Three Dimensions
      • ☰ 2.1.3.1 Position Vectors
      • ☰ 2.1.3.2 Velocity Vectors
      • ☰ 2.1.3.3 Acceleration Vectors
      • ☰ 2.1.3.4 Relative Motion
    • ☰ 2.1.4 Projectile Motion
      • ☰ 2.1.4.1 Horizontal Projection
      • ☰ 2.1.4.2 Oblique Projection
      • ☰ 2.1.4.3 Maximum Height
      • ☰ 2.1.4.4 Time of Flight
      • ☰ 2.1.4.5 Projectile Range
      • ☰ 2.1.4.6 Trajectory Equation
    • ☰ 2.1.5 Circular Motion
      • ☰ 2.1.5.1 Angular Position
      • ☰ 2.1.5.2 Angular Velocity
      • ☰ 2.1.5.3 Angular Acceleration
      • ☰ 2.1.5.4 Uniform Circular Motion
      • ☰ 2.1.5.5 Centripetal Acceleration
  • ☰ 2.2 Newton's Laws of Motion
    • ☰ 2.2.1 Force
      • ☰ 2.2.1.1 Concept of Force
      • ☰ 2.2.1.2 Fundamental Forces
      • ☰ 2.2.1.3 Contact Forces
      • ☰ 2.2.1.4 Free-Body Diagrams
    • ☰ 2.2.2 Newton's First Law
      • ☰ 2.2.2.1 Inertia
      • ☰ 2.2.2.2 Inertial Reference Frames
      • ☰ 2.2.2.3 Equilibrium
    • ☰ 2.2.3 Newton's Second Law
      • ☰ 2.2.3.1 Force, Mass, and Acceleration
      • ☰ 2.2.3.2 Net Force
      • ☰ 2.2.3.3 Applications of F = ma
    • ☰ 2.2.4 Newton's Third Law
      • ☰ 2.2.4.1 Action-Reaction Pairs
      • ☰ 2.2.4.2 Interaction Forces
    • ☰ 2.2.5 Common Forces
      • ☰ 2.2.5.1 Weight
      • ☰ 2.2.5.2 Normal Force
      • ☰ 2.2.5.3 Tension
      • ☰ 2.2.5.4 Spring Force
      • ☰ 2.2.5.5 Static Friction
      • ☰ 2.2.5.6 Kinetic Friction
      • ☰ 2.2.5.7 Drag Force
    • ☰ 2.2.6 Applications of Newton's Laws
      • ☰ 2.2.6.1 Connected Objects
      • ☰ 2.2.6.2 Pulley Systems
      • ☰ 2.2.6.3 Inclined Planes
      • ☰ 2.2.6.4 Elevators
      • ☰ 2.2.6.5 Circular Motion
  • ☰ 2.3 Work and Energy
    • ☰ 2.3.1 Work
      • ☰ 2.3.1.1 Work Done by a Constant Force
      • ☰ 2.3.1.2 Work Done by a Variable Force
      • ☰ 2.3.1.3 Work from Force-Position Graphs
    • ☰ 2.3.2 Kinetic Energy
      • ☰ 2.3.2.1 Translational Kinetic Energy
      • ☰ 2.3.2.2 Work-Energy Theorem
    • ☰ 2.3.3 Potential Energy
      • ☰ 2.3.3.1 Gravitational Potential Energy
      • ☰ 2.3.3.2 Elastic Potential Energy
      • ☰ 2.3.3.3 Potential-Energy Curves
    • ☰ 2.3.4 Conservation of Energy
      • ☰ 2.3.4.1 Mechanical Energy
      • ☰ 2.3.4.2 Conservative Forces
      • ☰ 2.3.4.3 Non-Conservative Forces
      • ☰ 2.3.4.4 Conservation of Mechanical Energy
      • ☰ 2.3.4.5 Energy Dissipation
    • ☰ 2.3.5 Power
      • ☰ 2.3.5.1 Average Power
      • ☰ 2.3.5.2 Instantaneous Power
      • ☰ 2.3.5.3 Efficiency
  • ☰ 2.4 Momentum and Collisions
    • ☰ 2.4.1 Linear Momentum
      • ☰ 2.4.1.1 Momentum
      • ☰ 2.4.1.2 Momentum and Force
    • ☰ 2.4.2 Impulse
      • ☰ 2.4.2.1 Impulse
      • ☰ 2.4.2.2 Impulse-Momentum Theorem
      • ☰ 2.4.2.3 Force-Time Graphs
    • ☰ 2.4.3 Conservation of Momentum
      • ☰ 2.4.3.1 Isolated Systems
      • ☰ 2.4.3.2 Center-of-Mass Motion
    • ☰ 2.4.4 Collisions
      • ☰ 2.4.4.1 Elastic Collisions
      • ☰ 2.4.4.2 Inelastic Collisions
      • ☰ 2.4.4.3 Perfectly Inelastic Collisions
      • ☰ 2.4.4.4 One-Dimensional Collisions
      • ☰ 2.4.4.5 Two-Dimensional Collisions
    • ☰ 2.4.5 Center of Mass
      • ☰ 2.4.5.1 Center of Mass of Particles
      • ☰ 2.4.5.2 Center of Mass of Continuous Objects
    • ☰ 2.4.6 Rocket Motion
      • ☰ 2.4.6.1 Variable-Mass Systems
      • ☰ 2.4.6.2 Rocket Equation
  • ☰ 2.5 Rotational Motion
    • ☰ 2.5.1 Rotational Kinematics
      • ☰ 2.5.1.1 Angular Displacement
      • ☰ 2.5.1.2 Angular Velocity
      • ☰ 2.5.1.3 Angular Acceleration
    • ☰ 2.5.2 Torque
      • ☰ 2.5.2.1 Torque
      • ☰ 2.5.2.2 Lever Arm
      • ☰ 2.5.2.3 Vector Definition of Torque
    • ☰ 2.5.3 Moment of Inertia
      • ☰ 2.5.3.1 Rotational Inertia
      • ☰ 2.5.3.2 Common Moments of Inertia
      • ☰ 2.5.3.3 Parallel-Axis Theorem
    • ☰ 2.5.4 Rotational Dynamics
      • ☰ 2.5.4.1 Newton's Second Law for Rotation
      • ☰ 2.5.4.2 Rotational Kinetic Energy
      • ☰ 2.5.4.3 Work and Power in Rotation
    • ☰ 2.5.5 Angular Momentum
      • ☰ 2.5.5.1 Angular Momentum
      • ☰ 2.5.5.2 Conservation of Angular Momentum
    • ☰ 2.5.6 Rolling Motion
      • ☰ 2.5.6.1 Rolling Without Slipping
      • ☰ 2.5.6.2 Translational and Rotational Energy
    • ☰ 2.5.7 Static Equilibrium
      • ☰ 2.5.7.1 Conditions for Equilibrium
      • ☰ 2.5.7.2 Center of Gravity
      • ☰ 2.5.7.3 Stability
  • ☰ 2.6 Gravitation
    • ☰ 2.6.1 Newton's Law of Gravitation
      • ☰ 2.6.1.1 Universal Gravitation
      • ☰ 2.6.1.2 Gravitational Constant
      • ☰ 2.6.1.3 Superposition
    • ☰ 2.6.2 Gravitational Field
      • ☰ 2.6.2.1 Gravitational Field Strength
      • ☰ 2.6.2.2 Field of Spherical Bodies
    • ☰ 2.6.3 Gravitational Potential
      • ☰ 2.6.3.1 Gravitational Potential Energy
      • ☰ 2.6.3.2 Gravitational Potential
    • ☰ 2.6.4 Planetary Motion
      • ☰ 2.6.4.1 Kepler's Laws
      • ☰ 2.6.4.2 Circular Orbits
      • ☰ 2.6.4.3 Orbital Velocity
      • ☰ 2.6.4.4 Orbital Period
    • ☰ 2.6.5 Satellites and Spaceflight
      • ☰ 2.6.5.1 Geostationary Satellites
      • ☰ 2.6.5.2 Escape Velocity
      • ☰ 2.6.5.3 Orbital Energy
• ☰ 3 Part II: Oscillations, Waves, and Fluids
  • ☰ 3.1 Oscillations
    • ☰ 3.1.1 Simple Harmonic Motion
      • ☰ 3.1.1.1 Periodic Motion
      • ☰ 3.1.1.2 Amplitude
      • ☰ 3.1.1.3 Frequency and Period
      • ☰ 3.1.1.4 Angular Frequency
      • ☰ 3.1.1.5 SHM Equation
    • ☰ 3.1.2 Mass-Spring Systems
      • ☰ 3.1.2.1 Hooke's Law
      • ☰ 3.1.2.2 Spring Oscillations
      • ☰ 3.1.2.3 Energy in SHM
    • ☰ 3.1.3 Pendulums
      • ☰ 3.1.3.1 Simple Pendulum
      • ☰ 3.1.3.2 Physical Pendulum
    • ☰ 3.1.4 Damped Oscillations
      • ☰ 3.1.4.1 Damping
      • ☰ 3.1.4.2 Critical Damping
    • ☰ 3.1.5 Forced Oscillations and Resonance
      • ☰ 3.1.5.1 Driving Force
      • ☰ 3.1.5.2 Resonance
      • ☰ 3.1.5.3 Natural Frequency
  • ☰ 3.2 Mechanical Waves
    • ☰ 3.2.1 Fundamentals of Waves
      • ☰ 3.2.1.1 Transverse Waves
      • ☰ 3.2.1.2 Longitudinal Waves
      • ☰ 3.2.1.3 Wavelength
      • ☰ 3.2.1.4 Frequency
      • ☰ 3.2.1.5 Wave Speed
      • ☰ 3.2.1.6 Amplitude
    • ☰ 3.2.2 Mathematical Description of Waves
      • ☰ 3.2.2.1 Wave Function
      • ☰ 3.2.2.2 Phase
      • ☰ 3.2.2.3 Wave Equation
    • ☰ 3.2.3 Superposition
      • ☰ 3.2.3.1 Interference
      • ☰ 3.2.3.2 Constructive Interference
      • ☰ 3.2.3.3 Destructive Interference
    • ☰ 3.2.4 Standing Waves
      • ☰ 3.2.4.1 Nodes and Antinodes
      • ☰ 3.2.4.2 Strings
      • ☰ 3.2.4.3 Pipes
      • ☰ 3.2.4.4 Harmonics
    • ☰ 3.2.5 Sound Waves
      • ☰ 3.2.5.1 Speed of Sound
      • ☰ 3.2.5.2 Sound Intensity
      • ☰ 3.2.5.3 Decibels
      • ☰ 3.2.5.4 Beats
      • ☰ 3.2.5.5 Doppler Effect
  • ☰ 3.3 Fluid Mechanics
    • ☰ 3.3.1 Properties of Fluids
      • ☰ 3.3.1.1 Density
      • ☰ 3.3.1.2 Pressure
      • ☰ 3.3.1.3 Compressibility
    • ☰ 3.3.2 Fluid Statics
      • ☰ 3.3.2.1 Hydrostatic Pressure
      • ☰ 3.3.2.2 Pascal's Principle
    • ☰ 3.3.3 Buoyancy
      • ☰ 3.3.3.1 Archimedes' Principle
      • ☰ 3.3.3.2 Floating and Sinking
    • ☰ 3.3.4 Fluid Dynamics
      • ☰ 3.3.4.1 Flow Rate
      • ☰ 3.3.4.2 Continuity Equation
      • ☰ 3.3.4.3 Bernoulli's Equation
    • ☰ 3.3.5 Viscosity
      • ☰ 3.3.5.1 Laminar Flow
      • ☰ 3.3.5.2 Turbulent Flow
      • ☰ 3.3.5.3 Poiseuille's Law
      • ☰ 3.3.5.4 Reynolds Number
• ☰ 4 Part III: Thermodynamics
  • ☰ 4.1 Temperature and Heat
    • ☰ 4.1.1 Temperature and Thermal Equilibrium
    • ☰ 4.1.2 Zeroth Law of Thermodynamics
    • ☰ 4.1.3 Temperature Scales
    • ☰ 4.1.4 Thermal Expansion
    • ☰ 4.1.5 Heat and Internal Energy
    • ☰ 4.1.6 Specific Heat Capacity
    • ☰ 4.1.7 Calorimetry
    • ☰ 4.1.8 Phase Changes
    • ☰ 4.1.9 Latent Heat
    • ☰ 4.1.10 Heat Transfer
  • ☰ 4.2 Kinetic Theory of Gases
    • ☰ 4.2.1 Ideal Gas Law
    • ☰ 4.2.2 Molecular Interpretation of Pressure
    • ☰ 4.2.3 Temperature and Molecular Kinetic Energy
    • ☰ 4.2.4 RMS Molecular Speed
    • ☰ 4.2.5 Maxwell-Boltzmann Distribution
    • ☰ 4.2.6 Mean Free Path
  • ☰ 4.3 Thermodynamics
    • ☰ 4.3.1 Thermodynamic Systems
    • ☰ 4.3.2 First Law of Thermodynamics
    • ☰ 4.3.3 Isothermal Processes
    • ☰ 4.3.4 Isobaric Processes
    • ☰ 4.3.5 Isochoric Processes
    • ☰ 4.3.6 Adiabatic Processes
    • ☰ 4.3.7 Heat Engines
    • ☰ 4.3.8 Carnot Cycle
    • ☰ 4.3.9 Refrigerators
    • ☰ 4.3.10 Second Law of Thermodynamics
    • ☰ 4.3.11 Entropy
    • ☰ 4.3.12 Reversible and Irreversible Processes
• ☰ 5 Part IV: Electricity and Magnetism
  • ☰ 5.1 Electric Charge and Electric Field
    • ☰ 5.1.1 Electric Charge
    • ☰ 5.1.2 Conductors and Insulators
    • ☰ 5.1.3 Coulomb's Law
    • ☰ 5.1.4 Superposition
    • ☰ 5.1.5 Electric Field
    • ☰ 5.1.6 Electric Field Lines
    • ☰ 5.1.7 Electric Dipoles
    • ☰ 5.1.8 Electric Flux
    • ☰ 5.1.9 Gauss's Law
  • ☰ 5.2 Electric Potential
    • ☰ 5.2.1 Electric Potential Energy
    • ☰ 5.2.2 Electric Potential
    • ☰ 5.2.3 Equipotential Surfaces
    • ☰ 5.2.4 Relationship Between Potential and Field
    • ☰ 5.2.5 Potential of Continuous Charge Distributions
  • ☰ 5.3 Capacitance
    • ☰ 5.3.1 Capacitors
    • ☰ 5.3.2 Parallel-Plate Capacitor
    • ☰ 5.3.3 Series and Parallel Capacitors
    • ☰ 5.3.4 Energy Stored in Capacitors
    • ☰ 5.3.5 Dielectrics
    • ☰ 5.3.6 Polarization
  • ☰ 5.4 Electric Current and Resistance
    • ☰ 5.4.1 Electric Current
    • ☰ 5.4.2 Current Density
    • ☰ 5.4.3 Drift Velocity
    • ☰ 5.4.4 Resistance
    • ☰ 5.4.5 Ohm's Law
    • ☰ 5.4.6 Resistivity
    • ☰ 5.4.7 Electrical Energy
    • ☰ 5.4.8 Electric Power
    • ☰ 5.4.9 Electromotive Force
  • ☰ 5.5 DC Circuits
    • ☰ 5.5.1 Kirchhoff's Laws
    • ☰ 5.5.2 Multi-Loop Circuits
    • ☰ 5.5.3 RC Circuits
    • ☰ 5.5.4 Measuring Instruments
  • ☰ 5.6 Magnetism
    • ☰ 5.6.1 Magnetic Fields
    • ☰ 5.6.2 Lorentz Force
    • ☰ 5.6.3 Motion of Charged Particles
    • ☰ 5.6.4 Force on Current-Carrying Wires
    • ☰ 5.6.5 Torque on Current Loops
    • ☰ 5.6.6 Biot-Savart Law
    • ☰ 5.6.7 Ampère's Law
    • ☰ 5.6.8 Solenoids
    • ☰ 5.6.9 Magnetic Materials
  • ☰ 5.7 Electromagnetic Induction
    • ☰ 5.7.1 Magnetic Flux
    • ☰ 5.7.2 Faraday's Law
    • ☰ 5.7.3 Lenz's Law
    • ☰ 5.7.4 Motional EMF
    • ☰ 5.7.5 Self-Inductance
    • ☰ 5.7.6 Mutual Inductance
    • ☰ 5.7.7 RL Circuits
    • ☰ 5.7.8 LC Oscillations
  • ☰ 5.8 Alternating Current
    • ☰ 5.8.1 AC Voltage and Current
    • ☰ 5.8.2 RMS Quantities
    • ☰ 5.8.3 Resistors in AC Circuits
    • ☰ 5.8.4 Capacitors in AC Circuits
    • ☰ 5.8.5 Inductors in AC Circuits
    • ☰ 5.8.6 RLC Circuits
    • ☰ 5.8.7 Impedance
    • ☰ 5.8.8 Resonance
    • ☰ 5.8.9 Transformers
  • ☰ 5.9 Maxwell's Equations and Electromagnetic Waves
    • ☰ 5.9.1 Gauss's Law for Electricity
    • ☰ 5.9.2 Gauss's Law for Magnetism
    • ☰ 5.9.3 Faraday's Law
    • ☰ 5.9.4 Ampère-Maxwell Law
    • ☰ 5.9.5 Electromagnetic Waves
    • ☰ 5.9.6 Speed of Light
    • ☰ 5.9.7 Electromagnetic Spectrum
    • ☰ 5.9.8 Poynting Vector
    • ☰ 5.9.9 Radiation Pressure
• ☰ 6 Part V: Optics
  • ☰ 6.1 Geometrical Optics
    • ☰ 6.1.1 Nature of Light
    • ☰ 6.1.2 Reflection
    • ☰ 6.1.3 Plane Mirrors
    • ☰ 6.1.4 Refraction
    • ☰ 6.1.5 Snell's Law
    • ☰ 6.1.6 Total Internal Reflection
    • ☰ 6.1.7 Spherical Mirrors
    • ☰ 6.1.8 Thin Lenses
    • ☰ 6.1.9 Mirror Equation
    • ☰ 6.1.10 Lens Equation
    • ☰ 6.1.11 Magnification
    • ☰ 6.1.12 Ray Diagrams
    • ☰ 6.1.13 Optical Instruments
  • ☰ 6.2 Wave Optics
    • ☰ 6.2.1 Interference
    • ☰ 6.2.2 Young's Double-Slit Experiment
    • ☰ 6.2.3 Diffraction
    • ☰ 6.2.4 Single-Slit Diffraction
    • ☰ 6.2.5 Diffraction Gratings
    • ☰ 6.2.6 Polarization
    • ☰ 6.2.7 Malus's Law
    • ☰ 6.2.8 Brewster's Angle
    • ☰ 6.2.9 Rayleigh Criterion
    • ☰ 6.2.10 Optical Resolution
• ☰ 7 Part VI: Modern Physics
  • ☰ 7.1 Special Relativity
    • ☰ 7.1.1 Galilean Relativity
    • ☰ 7.1.2 Michelson-Morley Experiment
    • ☰ 7.1.3 Einstein's Postulates
    • ☰ 7.1.4 Lorentz Transformations
    • ☰ 7.1.5 Relativity of Simultaneity
    • ☰ 7.1.6 Time Dilation
    • ☰ 7.1.7 Length Contraction
    • ☰ 7.1.8 Relativistic Velocity Addition
    • ☰ 7.1.9 Relativistic Momentum
    • ☰ 7.1.10 Relativistic Energy
    • ☰ 7.1.11 Mass-Energy Equivalence
    • ☰ 7.1.12 Energy-Momentum Relation
    • ☰ 7.1.13 Spacetime Diagrams
    • ☰ 7.1.14 Light Cones
  • ☰ 7.2 Introduction to Quantum Physics
    • ☰ 7.2.1 Blackbody Radiation
    • ☰ 7.2.2 Planck's Hypothesis
    • ☰ 7.2.3 Photoelectric Effect
    • ☰ 7.2.4 Photon Energy
    • ☰ 7.2.5 Photon Momentum
    • ☰ 7.2.6 Compton Scattering
    • ☰ 7.2.7 de Broglie Wavelength
    • ☰ 7.2.8 Matter Waves
    • ☰ 7.2.9 Wave-Particle Duality
    • ☰ 7.2.10 Double-Slit Experiment
    • ☰ 7.2.11 Heisenberg Uncertainty Principle
  • ☰ 7.3 Quantum Mechanics
    • ☰ 7.3.1 Wave Function
    • ☰ 7.3.2 Probability Interpretation
    • ☰ 7.3.3 Normalization
    • ☰ 7.3.4 Schrödinger Equation
    • ☰ 7.3.5 Operators and Observables
    • ☰ 7.3.6 Expectation Values
    • ☰ 7.3.7 Particle in a Box
    • ☰ 7.3.8 Finite Potential Wells
    • ☰ 7.3.9 Quantum Tunneling
    • ☰ 7.3.10 Quantum Harmonic Oscillator
    • ☰ 7.3.11 Hydrogen Atom
    • ☰ 7.3.12 Quantum Numbers
    • ☰ 7.3.13 Angular Momentum
    • ☰ 7.3.14 Spin
    • ☰ 7.3.15 Stern-Gerlach Experiment
    • ☰ 7.3.16 Pauli Exclusion Principle
  • ☰ 7.4 Atomic Physics
    • ☰ 7.4.1 Thomson Atomic Model
    • ☰ 7.4.2 Rutherford Atomic Model
    • ☰ 7.4.3 Bohr Model
    • ☰ 7.4.4 Atomic Spectra
    • ☰ 7.4.5 Hydrogen Spectrum
    • ☰ 7.4.6 Electron Shells
    • ☰ 7.4.7 Orbitals
    • ☰ 7.4.8 Electron Configurations
    • ☰ 7.4.9 X-Ray Spectra
    • ☰ 7.4.10 Atomic Transitions
    • ☰ 7.4.11 Lasers
    • ☰ 7.4.12 Stimulated Emission
• ☰ 8 Part VII: Nuclear and Particle Physics
  • ☰ 8.1 Nuclear Structure
    • ☰ 8.1.1 The Atomic Nucleus
      • ☰ 8.1.1.1 Protons and Neutrons
      • ☰ 8.1.1.2 Atomic Number
      • ☰ 8.1.1.3 Mass Number
      • ☰ 8.1.1.4 Isotopes
      • ☰ 8.1.1.5 Isotones
      • ☰ 8.1.1.6 Isobars
    • ☰ 8.1.2 Nuclear Size and Density
      • ☰ 8.1.2.1 Nuclear Radius
      • ☰ 8.1.2.2 Nuclear Density
      • ☰ 8.1.2.3 Nuclear Charge Distribution
    • ☰ 8.1.3 Nuclear Forces
      • ☰ 8.1.3.1 Strong Nuclear Force
      • ☰ 8.1.3.2 Properties of Nuclear Forces
      • ☰ 8.1.3.3 Proton-Neutron Interaction
      • ☰ 8.1.3.4 Nuclear Stability
    • ☰ 8.1.4 Mass and Binding Energy
      • ☰ 8.1.4.1 Atomic Mass Units
      • ☰ 8.1.4.2 Mass Defect
      • ☰ 8.1.4.3 Binding Energy
      • ☰ 8.1.4.4 Binding Energy per Nucleon
      • ☰ 8.1.4.5 Binding-Energy Curve
    • ☰ 8.1.5 Nuclear Models
      • ☰ 8.1.5.1 Liquid-Drop Model
      • ☰ 8.1.5.2 Semi-Empirical Mass Formula
      • ☰ 8.1.5.3 Nuclear Shell Model
      • ☰ 8.1.5.4 Magic Numbers
      • ☰ 8.1.5.5 Collective Model
    • ☰ 8.1.6 Nuclear Spin and Magnetic Moments
      • ☰ 8.1.6.1 Nuclear Angular Momentum
      • ☰ 8.1.6.2 Nuclear Spin
      • ☰ 8.1.6.3 Nuclear Magnetic Moment
  • ☰ 8.2 Radioactivity and Nuclear Decay
    • ☰ 8.2.1 Radioactive Decay
      • ☰ 8.2.1.1 Nuclear Instability
      • ☰ 8.2.1.2 Random Nature of Decay
      • ☰ 8.2.1.3 Decay Constant
    • ☰ 8.2.2 Radioactive Decay Law
      • ☰ 8.2.2.1 Exponential Decay
      • ☰ 8.2.2.2 Activity
      • ☰ 8.2.2.3 Half-Life
      • ☰ 8.2.2.4 Mean Lifetime
    • ☰ 8.2.3 Alpha Decay
      • ☰ 8.2.3.1 Alpha Particles
      • ☰ 8.2.3.2 Energy of Alpha Decay
    • ☰ 8.2.4 Beta Decay
      • ☰ 8.2.4.1 Beta-Minus Decay
      • ☰ 8.2.4.2 Beta-Plus Decay
      • ☰ 8.2.4.3 Electron Capture
      • ☰ 8.2.4.4 Neutrinos
      • ☰ 8.2.4.5 Energy Spectrum
    • ☰ 8.2.5 Gamma Decay
      • ☰ 8.2.5.1 Nuclear Excited States
      • ☰ 8.2.5.2 Gamma-Ray Emission
      • ☰ 8.2.5.3 Internal Conversion
    • ☰ 8.2.6 Decay Chains
      • ☰ 8.2.6.1 Parent and Daughter Nuclei
      • ☰ 8.2.6.2 Secular Equilibrium
      • ☰ 8.2.6.3 Natural Radioactive Series
  • ☰ 8.3 Interaction of Radiation with Matter
    • ☰ 8.3.1 Charged Particle Interactions
      • ☰ 8.3.1.1 Ionization
      • ☰ 8.3.1.2 Excitation
      • ☰ 8.3.1.3 Energy Loss
      • ☰ 8.3.1.4 Stopping Power
      • ☰ 8.3.1.5 Range
    • ☰ 8.3.2 Heavy Charged Particles
      • ☰ 8.3.2.1 Alpha Particles
      • ☰ 8.3.2.2 Bragg Curve
      • ☰ 8.3.2.3 Bragg Peak
    • ☰ 8.3.3 Electron Interactions
      • ☰ 8.3.3.1 Collisional Energy Loss
      • ☰ 8.3.3.2 Bremsstrahlung
      • ☰ 8.3.3.3 Electron Range
    • ☰ 8.3.4 Photon Interactions
      • ☰ 8.3.4.1 Pair Production
      • ☰ 8.3.4.2 Rayleigh Scattering
    • ☰ 8.3.5 Attenuation of Radiation
      • ☰ 8.3.5.1 Linear Attenuation Coefficient
      • ☰ 8.3.5.2 Mass Attenuation Coefficient
      • ☰ 8.3.5.3 Exponential Attenuation
      • ☰ 8.3.5.4 Half-Value Layer
    • ☰ 8.3.6 Neutron Interactions
      • ☰ 8.3.6.1 Elastic Scattering
      • ☰ 8.3.6.2 Inelastic Scattering
      • ☰ 8.3.6.3 Neutron Capture
      • ☰ 8.3.6.4 Neutron Moderation
  • ☰ 8.4 Radiation Detection and Measurement
    • ☰ 8.4.1 Principles of Radiation Detection
      • ☰ 8.4.1.1 Energy Deposition
      • ☰ 8.4.1.2 Detector Efficiency
      • ☰ 8.4.1.3 Energy Resolution
      • ☰ 8.4.1.4 Timing Resolution
      • ☰ 8.4.1.5 Dead Time
    • ☰ 8.4.2 Gas-Filled Detectors
      • ☰ 8.4.2.1 Ionization Chambers
      • ☰ 8.4.2.2 Proportional Counters
      • ☰ 8.4.2.3 Geiger-Müller Counters
    • ☰ 8.4.3 Scintillation Detectors
      • ☰ 8.4.3.1 Scintillation Process
      • ☰ 8.4.3.2 Organic Scintillators
      • ☰ 8.4.3.3 Inorganic Scintillators
      • ☰ 8.4.3.4 Photomultiplier Tubes
      • ☰ 8.4.3.5 Silicon Photomultipliers
    • ☰ 8.4.4 Semiconductor Detectors
      • ☰ 8.4.4.1 Silicon Detectors
      • ☰ 8.4.4.2 Germanium Detectors
      • ☰ 8.4.4.3 Electron-Hole Pair Creation
    • ☰ 8.4.5 Gamma-Ray Spectroscopy
      • ☰ 8.4.5.1 Photopeak
      • ☰ 8.4.5.2 Compton Continuum
      • ☰ 8.4.5.3 Compton Edge
      • ☰ 8.4.5.4 Escape Peaks
    • ☰ 8.4.6 Coincidence Measurements
      • ☰ 8.4.6.1 Coincidence Detection
      • ☰ 8.4.6.2 Timing Windows
      • ☰ 8.4.6.3 True Coincidences
      • ☰ 8.4.6.4 Random Coincidences
  • ☰ 8.5 Nuclear Reactions
    • ☰ 8.5.1 Principles of Nuclear Reactions
      • ☰ 8.5.1.1 Reaction Notation
      • ☰ 8.5.1.2 Conservation Laws
      • ☰ 8.5.1.3 Reaction Energetics
    • ☰ 8.5.2 Q-Value
      • ☰ 8.5.2.1 Exothermic Reactions
      • ☰ 8.5.2.2 Endothermic Reactions
      • ☰ 8.5.2.3 Reaction Thresholds
    • ☰ 8.5.3 Reaction Cross Section
      • ☰ 8.5.3.1 Cross Section
      • ☰ 8.5.3.2 Reaction Probability
      • ☰ 8.5.3.3 Energy Dependence
    • ☰ 8.5.4 Types of Nuclear Reactions
      • ☰ 8.5.4.1 Elastic Scattering
      • ☰ 8.5.4.2 Inelastic Scattering
      • ☰ 8.5.4.3 Capture Reactions
      • ☰ 8.5.4.4 Transfer Reactions
      • ☰ 8.5.4.5 Charge-Exchange Reactions
    • ☰ 8.5.5 Compound Nucleus
      • ☰ 8.5.5.1 Formation
      • ☰ 8.5.5.2 Decay Channels
      • ☰ 8.5.5.3 Resonances
  • ☰ 8.6 Nuclear Fission and Fusion
    • ☰ 8.6.1 Nuclear Fission
      • ☰ 8.6.1.1 Fission Process
      • ☰ 8.6.1.2 Fission Fragments
      • ☰ 8.6.1.3 Energy Release
      • ☰ 8.6.1.4 Neutron Production
    • ☰ 8.6.2 Chain Reactions
      • ☰ 8.6.2.1 Criticality
      • ☰ 8.6.2.2 Multiplication Factor
      • ☰ 8.6.2.3 Critical Mass
    • ☰ 8.6.3 Nuclear Reactors
      • ☰ 8.6.3.1 Reactor Components
      • ☰ 8.6.3.2 Fuel
      • ☰ 8.6.3.3 Moderator
      • ☰ 8.6.3.4 Control Rods
      • ☰ 8.6.3.5 Coolant
    • ☰ 8.6.4 Nuclear Fusion
      • ☰ 8.6.4.1 Fusion Reactions
      • ☰ 8.6.4.2 Coulomb Barrier
    • ☰ 8.6.5 Stellar Fusion
      • ☰ 8.6.5.1 Proton-Proton Chain
      • ☰ 8.6.5.2 CNO Cycle
      • ☰ 8.6.5.3 Nucleosynthesis
    • ☰ 8.6.6 Controlled Fusion
      • ☰ 8.6.6.1 Magnetic Confinement
      • ☰ 8.6.6.2 Tokamaks
      • ☰ 8.6.6.3 Inertial Confinement
  • ☰ 8.7 Particle Physics Foundations
    • ☰ 8.7.1 From Atoms to Elementary Particles
      • ☰ 8.7.1.1 Discovery of the Electron
      • ☰ 8.7.1.2 Discovery of the Nucleus
      • ☰ 8.7.1.3 Discovery of the Neutron
      • ☰ 8.7.1.4 Discovery of Antimatter
    • ☰ 8.7.2 Classification of Particles
      • ☰ 8.7.2.1 Elementary Particles
      • ☰ 8.7.2.2 Composite Particles
      • ☰ 8.7.2.3 Fermions
      • ☰ 8.7.2.4 Bosons
    • ☰ 8.7.3 Antiparticles
      • ☰ 8.7.3.1 Matter and Antimatter
      • ☰ 8.7.3.2 Pair Production
      • ☰ 8.7.3.3 Annihilation
    • ☰ 8.7.4 Relativistic Particle Kinematics
      • ☰ 8.7.4.1 Four-Momentum
      • ☰ 8.7.4.2 Invariant Mass
    • ☰ 8.7.5 Particle Decays
      • ☰ 8.7.5.1 Decay Width
      • ☰ 8.7.5.2 Lifetime
      • ☰ 8.7.5.3 Branching Ratio
      • ☰ 8.7.5.4 Conservation Laws
  • ☰ 8.8 Quarks and Hadrons
    • ☰ 8.8.1 Quarks
      • ☰ 8.8.1.1 Up Quark
      • ☰ 8.8.1.2 Down Quark
      • ☰ 8.8.1.3 Strange Quark
      • ☰ 8.8.1.4 Charm Quark
      • ☰ 8.8.1.5 Top Quark
      • ☰ 8.8.1.6 Bottom Quark
    • ☰ 8.8.2 Quark Properties
      • ☰ 8.8.2.1 Mass
      • ☰ 8.8.2.2 Flavor
      • ☰ 8.8.2.3 Color Charge
    • ☰ 8.8.3 Hadrons
      • ☰ 8.8.3.1 Baryons
      • ☰ 8.8.3.2 Mesons
    • ☰ 8.8.4 Baryon Structure
      • ☰ 8.8.4.1 Proton Quark Structure
      • ☰ 8.8.4.2 Neutron Quark Structure
      • ☰ 8.8.4.3 Other Baryons
    • ☰ 8.8.5 Meson Structure
      • ☰ 8.8.5.1 Pions
      • ☰ 8.8.5.2 Kaons
      • ☰ 8.8.5.3 Heavy Mesons
    • ☰ 8.8.6 Confinement
      • ☰ 8.8.6.1 Color Confinement
      • ☰ 8.8.6.2 Hadronization
      • ☰ 8.8.6.3 Jets
  • ☰ 8.9 Leptons and Neutrinos
    • ☰ 8.9.1 Charged Leptons
      • ☰ 8.9.1.1 Electron
      • ☰ 8.9.1.2 Muon
      • ☰ 8.9.1.3 Tau
    • ☰ 8.9.2 Neutrinos
      • ☰ 8.9.2.1 Electron Neutrino
      • ☰ 8.9.2.2 Muon Neutrino
      • ☰ 8.9.2.3 Tau Neutrino
    • ☰ 8.9.3 Neutrino Interactions
      • ☰ 8.9.3.1 Weak Interactions
      • ☰ 8.9.3.2 Neutrino Detection
    • ☰ 8.9.4 Neutrino Oscillations
      • ☰ 8.9.4.1 Neutrino Flavor
      • ☰ 8.9.4.2 Flavor Oscillation
      • ☰ 8.9.4.3 Neutrino Mass
  • ☰ 8.10 Fundamental Interactions
    • ☰ 8.10.1 Four Fundamental Interactions
      • ☰ 8.10.1.1 Electromagnetism
      • ☰ 8.10.1.2 Strong Interaction
      • ☰ 8.10.1.3 Weak Interaction
    • ☰ 8.10.2 Exchange Particles
      • ☰ 8.10.2.1 Photons
      • ☰ 8.10.2.2 Gluons
      • ☰ 8.10.2.3 W Bosons
      • ☰ 8.10.2.4 Z Boson
    • ☰ 8.10.3 Electromagnetic Interaction
      • ☰ 8.10.3.1 Photon Exchange
    • ☰ 8.10.4 Strong Interaction
      • ☰ 8.10.4.1 Color Charge
      • ☰ 8.10.4.2 Gluons
      • ☰ 8.10.4.3 Quantum Chromodynamics
    • ☰ 8.10.5 Weak Interaction
      • ☰ 8.10.5.1 Beta Decay
      • ☰ 8.10.5.2 W and Z Bosons
      • ☰ 8.10.5.3 Flavor-Changing Processes
  • ☰ 8.11 The Standard Model
    • ☰ 8.11.1 Overview of the Standard Model
      • ☰ 8.11.1.1 Matter Particles
      • ☰ 8.11.1.2 Force Carriers
      • ☰ 8.11.1.3 Particle Generations
    • ☰ 8.11.2 Fermions
      • ☰ 8.11.2.1 Quarks
      • ☰ 8.11.2.2 Leptons
    • ☰ 8.11.3 Gauge Bosons
      • ☰ 8.11.3.1 Photon
      • ☰ 8.11.3.2 Gluons
      • ☰ 8.11.3.3 W Bosons
      • ☰ 8.11.3.4 Z Boson
    • ☰ 8.11.4 Higgs Field and Higgs Boson
      • ☰ 8.11.4.1 Higgs Field
      • ☰ 8.11.4.2 Spontaneous Symmetry Breaking
      • ☰ 8.11.4.3 Particle Masses
      • ☰ 8.11.4.4 Higgs Boson
    • ☰ 8.11.5 Standard Model Interactions
      • ☰ 8.11.5.1 Electroweak Theory
      • ☰ 8.11.5.2 Quantum Chromodynamics
    • ☰ 8.11.6 Limitations of the Standard Model
      • ☰ 8.11.6.1 Gravity
      • ☰ 8.11.6.2 Dark Matter
      • ☰ 8.11.6.3 Neutrino Masses
      • ☰ 8.11.6.4 Matter-Antimatter Asymmetry
  • ☰ 8.12 Symmetries and Conservation Laws
    • ☰ 8.12.1 Conservation Laws
      • ☰ 8.12.1.1 Energy
    • ☰ 8.12.2 Particle Quantum Numbers
      • ☰ 8.12.2.1 Baryon Number
      • ☰ 8.12.2.2 Lepton Number
      • ☰ 8.12.2.3 Strangeness
      • ☰ 8.12.2.4 Charm
      • ☰ 8.12.2.5 Isospin
    • ☰ 8.12.3 Symmetries
      • ☰ 8.12.3.1 Charge Conjugation
      • ☰ 8.12.3.2 Parity
      • ☰ 8.12.3.3 Time Reversal
    • ☰ 8.12.4 CP Symmetry
      • ☰ 8.12.4.1 CP Conservation
      • ☰ 8.12.4.2 CP Violation
      • ☰ 8.12.4.3 Matter-Antimatter Asymmetry
  • ☰ 8.13 Particle Accelerators
    • ☰ 8.13.1 Principles of Acceleration
      • ☰ 8.13.1.1 Electric-Field Acceleration
      • ☰ 8.13.1.2 Magnetic-Field Steering
    • ☰ 8.13.2 Linear Accelerators
      • ☰ 8.13.2.1 LINACs
      • ☰ 8.13.2.2 Radio-Frequency Acceleration
    • ☰ 8.13.3 Cyclotrons
      • ☰ 8.13.3.1 Cyclotron Principle
      • ☰ 8.13.3.2 Cyclotron Frequency
      • ☰ 8.13.3.3 Limitations
    • ☰ 8.13.4 Synchrotrons
      • ☰ 8.13.4.1 Circular Accelerators
      • ☰ 8.13.4.2 Magnetic Focusing
      • ☰ 8.13.4.3 RF Cavities
    • ☰ 8.13.5 Colliders
      • ☰ 8.13.5.1 Fixed-Target Experiments
      • ☰ 8.13.5.2 Collider Experiments
      • ☰ 8.13.5.3 Center-of-Mass Energy
    • ☰ 8.13.6 Major Particle Accelerators
      • ☰ 8.13.6.1 Large Hadron Collider
      • ☰ 8.13.6.2 Electron-Positron Colliders
      • ☰ 8.13.6.3 Heavy-Ion Colliders
  • ☰ 8.14 Particle Detectors
    • ☰ 8.14.1 Principles of Particle Detection
      • ☰ 8.14.1.1 Ionization
      • ☰ 8.14.1.2 Excitation
      • ☰ 8.14.1.3 Energy Deposition
      • ☰ 8.14.1.4 Particle Identification
    • ☰ 8.14.2 Tracking Detectors
      • ☰ 8.14.2.1 Cloud Chambers
      • ☰ 8.14.2.2 Bubble Chambers
      • ☰ 8.14.2.3 Wire Chambers
      • ☰ 8.14.2.4 Silicon Trackers
    • ☰ 8.14.3 Calorimeters
      • ☰ 8.14.3.1 Electromagnetic Calorimeters
      • ☰ 8.14.3.2 Hadronic Calorimeters
      • ☰ 8.14.3.3 Shower Development
    • ☰ 8.14.4 Cherenkov Detectors
      • ☰ 8.14.4.1 Cherenkov Radiation
      • ☰ 8.14.4.2 Particle Velocity Measurement
    • ☰ 8.14.5 Time-of-Flight Detectors
      • ☰ 8.14.5.1 Timing Measurements
      • ☰ 8.14.5.2 Particle Identification
    • ☰ 8.14.6 Modern Detector Systems
      • ☰ 8.14.6.1 Tracking
      • ☰ 8.14.6.2 Muon Systems
      • ☰ 8.14.6.3 Trigger Systems
• ☰ 9 Part VIII: Condensed Matter and Applied Physics
  • ☰ 9.1 Solid-State Physics
    • ☰ 9.1.1 Crystal Structure
      • ☰ 9.1.1.1 Crystal Lattices
      • ☰ 9.1.1.2 Unit Cells
      • ☰ 9.1.1.3 Bravais Lattices
    • ☰ 9.1.2 Electronic Properties
      • ☰ 9.1.2.1 Energy Bands
      • ☰ 9.1.2.2 Conductors
      • ☰ 9.1.2.3 Insulators
      • ☰ 9.1.2.4 Semiconductors
    • ☰ 9.1.3 Semiconductor Physics
      • ☰ 9.1.3.1 Intrinsic Semiconductors
      • ☰ 9.1.3.2 Doping
      • ☰ 9.1.3.3 p-Type Materials
      • ☰ 9.1.3.4 n-Type Materials
      • ☰ 9.1.3.5 p-n Junctions
    • ☰ 9.1.4 Superconductivity
      • ☰ 9.1.4.1 Zero Resistance
      • ☰ 9.1.4.2 Meissner Effect
      • ☰ 9.1.4.3 Critical Temperature
  • ☰ 9.2 Electronics
    • ☰ 9.2.1 Semiconductor Diodes
      • ☰ 9.2.1.1 p-n Junction
      • ☰ 9.2.1.2 Diode Characteristics
      • ☰ 9.2.1.3 Rectifiers
    • ☰ 9.2.2 Transistors
      • ☰ 9.2.2.1 Bipolar Junction Transistors
      • ☰ 9.2.2.2 Field-Effect Transistors
    • ☰ 9.2.3 Operational Amplifiers
      • ☰ 9.2.3.1 Ideal Op-Amp
      • ☰ 9.2.3.2 Amplifiers
      • ☰ 9.2.3.3 Comparators
    • ☰ 9.2.4 Digital Electronics
      • ☰ 9.2.4.1 Binary Numbers
      • ☰ 9.2.4.2 Logic Gates
      • ☰ 9.2.4.3 Boolean Algebra
      • ☰ 9.2.4.4 Basic Digital Circuits
• ☰ 10 Part IX: Astrophysics and Cosmology
  • ☰ 10.1 Astrophysics
    • ☰ 10.1.1 Measuring the Universe
      • ☰ 10.1.1.1 Astronomical Distances
      • ☰ 10.1.1.2 Parallax
      • ☰ 10.1.1.3 Luminosity
      • ☰ 10.1.1.4 Apparent Brightness
    • ☰ 10.1.2 Stars
      • ☰ 10.1.2.1 Stellar Spectra
      • ☰ 10.1.2.2 Hertzsprung-Russell Diagram
      • ☰ 10.1.2.3 Stellar Evolution
    • ☰ 10.1.3 Stellar Remnants
      • ☰ 10.1.3.1 White Dwarfs
      • ☰ 10.1.3.2 Neutron Stars
      • ☰ 10.1.3.3 Black Holes
    • ☰ 10.1.4 Galaxies
      • ☰ 10.1.4.1 Structure of Galaxies
      • ☰ 10.1.4.2 Milky Way
      • ☰ 10.1.4.3 Galaxy Classification
  • ☰ 10.2 Cosmology
    • ☰ 10.2.1 Expanding Universe
      • ☰ 10.2.1.1 Hubble's Law
      • ☰ 10.2.1.2 Cosmological Redshift
    • ☰ 10.2.2 Big Bang Cosmology
      • ☰ 10.2.2.1 Early Universe
      • ☰ 10.2.2.2 Cosmic Microwave Background
      • ☰ 10.2.2.3 Primordial Nucleosynthesis
    • ☰ 10.2.3 Dark Matter
      • ☰ 10.2.3.1 Evidence for Dark Matter