Foundations oF Physics

Cover Half-Title Title Copyright Dedication Contents Preface Chapter 1: The Language of Physics 1.0 Introduction 1.1 The SI System of Units 1.1.1 Derived Units 1.1.2 Energy 1.1.3 Viscosity 1.2 Dimensions 1.2.1 Method of Dimensions 1.3 Scientific Notation, Prefixes, and Significant Figures 1.4 Uncertainties 1.4.1 Types of Uncertainty 1.4.2 Combining Uncertainties 1.5 Dealing with Random and Systematic Experimental Errors 1.5.1 Random Errors 1.5.2 Systematic Errors 1.6 Differential Calculus 1.6.1 Derivatives and Rates of Change 1.6.1.1 Second Derivatives 1.6.2 Maximum and Minimum Values 1.7 Differential Equations 1.8 Integral Calculus 1.9 Vectors and Scalars 1.9.1 Adding Vectors 1.9.2 Resolving Vectors into Components 1.9.3 Multiplying Vectors 1.9.3.1 Scalar Product 1.9.3.2 Vector Product 1.10 Symmetry Principles 1.11 Exercises Chapter 2: Representing and Analyzing Data 2.0 Introduction 2.1 Experimental Variables 2.2 Recording Data 2.3 Straight-Line Graphs 2.3.1 Interpreting Straight-Line Graphs 2.3.2 Analyzing Straight-Line Graphs 2.4 Plotting Graphs and Using Error Bars 2.4.1 Plotting Graphs by Hand 2.4.2 Finding a Gradient from a Straight-Line Graph 2.4.3 Using a Spreadsheet Program (e.g., Excel) 2.4.4 Using Error Bars 2.5 Logarithms 2.5.1 Logarithmic Scales and Logarithms 2.5.2 Using Logarithms 2.6 Testing Mathematical Relationships between Variables 2.6.1 Direct Proportion 2.6.2 Inverse Proportion 2.6.3 Inverse-Square Law 2.6.4 Power Law 2.6.5 Exponential Decay or Growth 2.7 Exercises Chapter 3: Capturing, Displaying, and Analyzing Motion 3.0 Introduction 3.1 Motion Terminology 3.2 Graphs of Motion 3.3 Equations of Motion for Constant Acceleration: The Suvat Equations 3.3.1 Derivation 1: From Graphs of Motion 3.3.2 Derivation 2: Using Calculus 3.4 Projectile Motion 3.4.1 Independence of Horizontal and Vertical Components of Motion 3.4.2 Parabolic Paths 3.4.3 The Range of a Projectile 3.5 Equation of Motion 3.6 Methods to Capture and Display Graphs of Motion 3.6.1 Motion Sensors and Dataloggers 3.6.2 Light Gates 3.6.3 Mobile Phones and Tablets 3.6.3.1 Accelerometer Sensor 3.6.3.2 Video Capture 3.7 Exercises Chapter 4: Forces and Equilibrium 4.1 Force as a Vector 4.1.1 Free-Body Diagrams 4.1.2 Resolving Forces 4.1.3 Finding a Resultant Force 4.2 Mass, Weight, and Center of Gravity 4.2.1 Mass 4.2.2 Weight 4.2.3 Center of Gravity 4.3 Equilibrium of Coplanar Forces 4.3.1 Using the Triangle of Forces to Solve Equilibrium Problems 4.3.2 Resolving Forces to Solve Equilibrium Problems 4.4 Turning Effects of a Force: Moments, Torques, and Couples 4.4.1 Moments and Torques 4.4.2 Resultant Moment 4.4.3 Couples 4.4.4 The Principle of Moments 4.5 Stability 4.5.1 Types of Mechanical Equilibrium 4.5.2 Degrees of Stability 4.6 Frictional Forces 4.6.1 The Origin of Frictional Forces Between Surfaces in Contact 4.6.2 Static and Dynamic (Kinetic) Friction 4.6.3 The Coefficients of Friction 4.6.4 Measuring the Coefficient of Static Friction 4.6.5 Measuring the Coefficient of Dynamic (Kinetic) Friction 4.7 Exercises Chapter 5: Newtonian Mechanics 5.0 Introduction 5.1 Newton’s Laws of Motion 5.1.1 Newton’s First Law of Motion 5.1.2 Galilean Relativity 5.1.3 Newton’s Second Law of Motion 5.1.4 Free Fall 5.1.5 Newton’s Third Law of Motion 5.2 Linear Momentum 5.2.1 Newton’s Second Law in Terms of Linear Momentum 5.2.2 Impulse and Change of Momentum 5.2.3 Conservation of Linear Momentum 5.3 Work Energy and Power 5.3.1 Work 5.3.2 Gravitational Potential Energy Changes (Uniform Field) 5.3.3 Kinetic Energy 5.3.4 The Law of Conservation of Energy 5.3.5 Energy and Momentum in a 2D Collision 5.3.6 Energy Transfers 5.3.7 Power 5.4 Energy Resources 5.5 Propulsion Systems 5.5.1 Jet Propulsion 5.5.2 Rockets 5.5.3 Radiation Pressure 5.6 Frames of Reference 5.6.1 The Center of Mass Frame 5.6.2 The Galilean Transformation 5.7 Theoretical Mechanics 5.7.1 Force and Energy 5.7.2 Lagrangian Mechanics 5.8 Exercises Chapter 6: Fluids 6.0 Introduction 6.1 Hydrostatic Pressure 6.1.1 Excess Pressure Caused by a Column of Fluid 6.1.2 Atmospheric Pressure 6.1.3 Using a Manometer to Measure Pressure Differences 6.1.4 Barometers 6.1.5 Dams 6.2 Buoyancy and Archimedes Principle 6.2.1 Buoyancy Forces 6.2.2 Archimedes’ Principle 6.2.3 Flotation 6.3 Viscosity 6.3.1 The Coefficient of Viscosity 6.4 Fluid Flow 6.4.1 Laminar and Turbulent Flow 6.4.2 The Equation of Continuity 6.4.3 Drag Forces in a Fluid 6.4.4 Stokes’ Law 6.4.5 Turbulent Drag 6.4.6 The Bernoulli Equation 6.4.7 The Bernoulli Effect 6.4.8 Viscous Flow Through a Horizontal Pipe – The Poiseuille Equation 6.4.9 Measuring the Coefficient of Viscosity 6.5 Measuring Fluid Flow Rates 6.5.1 A Venturi Meter 6.5.2 A Pitot Tube 6.6 Exercises Chapter 7: Mechanical Properties 7.1 Density 7.2 Inter-atomic Forces 7.3 Stretching Springs 7.3.1 The Spring Constant 7.3.2 Springs in Series and in Parallel 7.3.3 Elastic Potential Energy (Strain Energy) 7.4 Stress and Strain 7.4.1 The Young’s Modulus 7.4.2 Experimental Measurement of Young’s Modulus for a Metal Wire 7.4.3 Stress Versus Strain Graph for a Ductile Metal 7.4.4 Rubber Hysteresis 7.5 Material Terminology 7.6 Material Types 7.7 Exercises Chapter 8: Thermal Physics 8.0 Introduction 8.1 Thermal Equilibrium 8.2 Measuring Temperature 8.3 Temperature Scales 8.4 Heat Transfer Mechanisms 8.4.1 Conduction 8.4.2 Convection 8.4.3 Radiation 8.5 Black Body Radiation 8.6 Heat Capacities 8.6.1 Specific Heat Capacity 8.6.2 Molar Heat Capacities of Gases 8.6.3 Measuring Specific Heat Capacity 8.7 Specific Latent Heat 8.8 Exercises Chapter 9: Gases 9.1 The Gas Laws 9.1.0 Introduction 9.1.1 Boyle’s Law 9.1.2 Charles’s Law 9.1.3 Gay Lussac’s Law (The Pressure Law) 9.2 The Ideal Gas Equation 9.3 The Kinetic Theory of Gases 9.3.1 Assumptions of the Kinetic Theory 9.3.2 Explaining Gas Pressure 9.3.3 Molecular Kinetic Energy and Temperature 9.3.4 Molar Heat Capacities of an Ideal Monatomic Gas 9.3.5 Equipartition of Energy 9.3.6 The Law of Dulong and Petit 9.3.7 Graham’s Law of Diffusion 9.3.8 The Speed of Sound in a Gas 9.4 The Maxwell Distribution 9.5 The Boltzmann Factor and Activation Processes 9.6 The First Law of Thermodynamics 9.6.1 Internal Energy 9.6.2 Heating, Working, and the First Law of Thermodynamics 9.6.3 Work Done by an Ideal Gas 9.6.4 Thermodynamic Changes 9.7 Heat Engines and Indicator Diagrams 9.7.1 What Is a Heat Engine? 9.7.2 Indicator Diagrams 9.7.3 The Otto Cycle 9.7.4 The Diesel Cycle 9.8 Exercises Chapter 10: Statistical Thermodynamics and the Second Law 10.0 Introduction 10.1 Reversible and Irreversible Processes 10.2 The Second Law of Thermodynamics as a Macroscopic Principle 10.2.1 Macroscopic Statements of the Second Law 10.2.2 Heat Transfer and Entropy 10.2.3 Entropy and Maximum Efficiency of a Heat Engine 10.3 Entropy and Number of Ways 10.3.1 Macro-state and Micro-states 10.3.2 Entropy and Number of Ways 10.3.3 Poincaré Recurrence 10.4 What Is Temperature? 10.5 Absolute Zero and Absolute Entropy 10.5.1 Entropy at Absolute Zero 10.5.2 Calculating Absolute Entropy 10.5.3 Entropy Changes for an Ideal Gas 10.6 Refrigerators and Heat Pumps 10.6.1 Refrigerators 10.6.2 Heat Pumps 10.7 Implications of the Second Law 10.7.1 The Second Law, the Arrow of Time, and the Universe 10.7.2 The Second Law and Living Things 10.7.3 Entropy and Energy Availability 10.8 Exercises Chapter 11: Oscillations 11.0 Oscillations 11.1 Capturing and Displaying Oscillatory Motion 11.1.1 Graphs and Equations of Displacement, Velocity, and Acceleration 11.1.2 Phase and Phase Difference 11.2 Simple Harmonic Motion 11.2.1 Equation of Motion for Simple Harmonic Motion 11.2.2 Physical Conditions for Simple Harmonic Motion 11.3 The Mass-Spring Oscillator 11.4 The Simple Pendulum 11.5 Energy in Simple Harmonic Motion 11.5.1 Variation of Energy with Time 11.5.2 Variation of Energy with Position 11.5.3 Damping 11.6 Forced Oscillations and Resonance 11.7 Exercises Chapter 12: Rotational Dynamics 12.0 Introduction 12.1 Angles 12.1.1 Measuring Angles in Radians 12.1.2 Small Angle Approximations 12.2 Describing Uniform Circular Motion 12.2.1 Angular Displacement, Angular Velocity, and Angular Acceleration 12.3 Centripetal Acceleration and Centripetal Force 12.3.1 Centripetal Acceleration 12.3.2 Centripetal Force 12.3.3 Centripetal Not Centrifugal 12.3.4 Moving in Uniform Circular Motion 12.4 Circular Motion, Simple Harmonic Motion, and Phasors 12.5 Rotational Kinematics 12.5.1 Equations for Uniform Angular Acceleration 12.5.2 Rotational Kinetic Energy 12.5.3 Angular Momentum 12.5.4 The Second Law of Motion for Rotation. 12.5.5 Conservation of Angular Momentum 12.6 Deriving Expressions for Moments of Inertia 12.6.1 Moment of Inertia of One or More Point Masses 12.6.2 Moment of Inertia of a Rod 12.6.3 Moment of Inertia of a Cylindrical Shell and a Uniform Cylinder 12.6.4 Moment of Inertia of a Uniform Sphere 12.7 Torque Work and Power 12.8 Rotational Oscillations, the Compound Pendulum 12.9 Exercises Chapter 13: Waves 13.0 Introduction 13.1 Describing and Representing Waves 13.1.1 Basic Wave Terminology 13.1.2 Transverse and Longitudinal Waves 13.1.3 Graphs of Wave Motion 13.1.4 Equation for a One-Dimensional Traveling Wave 13.1.5 Amplitude and Intensity 13.2 Reflection 13.3 Refraction 13.3.1 Refraction at a Boundary Between Two Different Media 13.3.2 Snell’s Law of Refraction 13.3.3 Absolute and Relative Refractive Indices 13.3.4 Total Internal Reflection 13.3.5 Optical Fibers 13.3.6 Dispersion 13.4 Polarization 13.4.1 What Is Polarization? 13.4.2 Polarizing Filters 13.4.3 Rotation of the Plane of Polarization 13.4.4 Polarization by Reflection and Scattering 13.5 Exercises Chapter 14: Light 14.1 Light as an Electromagnetic Wave 14.1.1 Waves or Particles? 14.1.2 Electromagnetism 14.1.3 Electromagnetic Waves 14.1.4 Measuring the Speed of Light 14.1.5 Maxwell’s Equations and the Speed of Light 14.1.6 Defining Speed, Time, and Distance 14.2 Ray Optics 14.2.1 Thin Lenses 14.2.2 Predictable Rays for Thin Lenses 14.2.3 Images 14.2.4 Image Formation with a Convex Lens 14.2.5 Image Formation with a Concave Lens 14.2.6 Object at Infinity 14.2.7 The Lens Equation 14.2.8 Virtual Image Formed by a Plane Mirror 14.2.9 Real and Apparent Depth 14.3 Optical Instruments 14.3.1 An Astronomical Refracting Telescope 14.3.2 An Astronomical Reflecting Telescope (Newtonian Telescope) 14.3.3 A Compound Microscope 14.4 The Doppler Effect 14.4.1 The Doppler Effect for Electromagnetic Waves 14.4.2 “Red Shift” and “Blue Shift” 14.5 Exercises Chapter 15: Superposition Effects 15.0 Superposition Effects 15.1 Two-Source Interference 15.1.1 Demonstrating Superposition Effects with Sound 15.1.2 Demonstrating Superposition Effects with Light 15.1.3 Using the Double Slit Experiment to Find the Wavelength of Light 15.1.4 Superposition of Harmonic Waves 15.2 Diffraction Gratings 15.2.1 The Diffraction Grating Formula 15.2.2 Spectroscopy 15.2.3 Spectrometers 15.3 Diffraction by Slits and Holes 15.3.1 Diffraction by a Narrow Slit 15.3.2 Analysis of the Single Slit Diffraction Pattern 15.3.3 Diffraction Through a Circular Hole 15.3.4 Resolving Power and the Rayleigh Criterion 15.4 Standing (Stationary) Waves 15.4.1 Standing Waves on a String (Melde’s Experiment) 15.4.2 The Mathematics of Standing Waves 15.5 Exercises Chapter 16: Sound 16.1 The Nature and Speed of Sound 16.2 The Decibel Scale 16.3 Standing Waves in Air Columns 16.4 Measuring the Speed of Sound 16.5 Ultrasound 16.6 Analysis and Synthesis of Sound 16.7 Exercises Chapter 17: Electric Charge and Electric Fields 17.1 Electric Charge 17.2 Electrostatics 17.2.1 Charging by Friction 17.2.2 The Gold Leaf Electroscope 17.2.3 Using a Coulomb Meter 17.3 Electrostatic Forces 17.3.1 Coulomb’s Law 17.3.2 Investigating Electrostatic Forces 17.4 The Electric Field 17.4.1 Electric Field Strength 17.4.2 Electric Field Strength of a Point Charge 17.4.3 Gauss’s Law 17.4.4 Using Gauss’s Theorem 17.5 Electric Potential Energy and Electric Potential 17.5.1 Electric Potential and Potential Difference 17.5.2 Electric Potential Gradient and Electric Field Strength 17.5.3 Accelerating Charged Particles in an Electric Field 17.5.4 Deflecting Charged Particles in an Electric Field 17.5.5 The Absolute Electric Potential of a Point Charge 17.6 Exercises Chapter 18: DC Electric Circuits 18.0 Direct Current (DC) Circuits and Conventional Current 18.1 Charge and Current 18.1.1 Charge Carriers and Charge Carrier Density 18.1.2 Measuring Current 18.1.3 Currents in Circuits – Kirchhoff’s First Law 18.2 Measuring Potential Difference 18.2.1 EMF Potential Difference and Voltage 18.2.2 Kirchhoff’s Second Law 18.3 Resistance 18.3.1 Measuring Resistance 18.3.2 Current–Voltage Characteristics 18.3.3 Resistors in Series and in Parallel 18.3.4 Resistivity 18.4 Electrical Energy and Power 18.4.1 EMF and Internal Resistance of a Real Cell 18.4.2 Measuring the Internal Resistance and emf of a Cell 18.4.3 Power Transfer from a Real Cell to a Load Resistor 18.5 Resistance Networks 18.5.1 Potential Dividers 18.5.2 Using Kirchhoff’s Laws to Solve Resistance Networks 18.6 Semiconductors and Superconductors 18.6.1 Semiconductors 18.6.2 Variation of Resistance of a Metal with Temperature 18.7 Exercises Chapter 19: Capacitance 19.1 What Is a Capacitor? 19.1.1 Capacitors and Charge 19.1.2 Capacitance 19.1.3 Energy Stored on a Charged Capacitor 19.1.4 Efficiency of Charging a Capacitor 19.2 The Parallel Plate Capacitor 19.3 Capacitor Charging and Discharging 19.3.1 Equations for Capacitor Discharge 19.3.2 Equations for Capacitor Charging 19.4 Capacitors in Series and Parallel 19.4.1 Capacitance of Capacitors in Series 19.4.2 Capacitors in Parallel 19.5 The Capacitance of a Charged Sphere 19.6 Exercises Chapter 20: Magnetic Fields 20.0 The Magnetic Field 20.1 Permanent Magnets 20.2 Magnetic Forces on Electric Currents and Moving Charges 20.2.1 The Magnetic Force on an Electric Current 20.2.2 The Force on a Moving Charge 20.2.3 The Path of a Moving Charged Particle in a Magnetic Field 20.2.4 The Velocity-Selector: Crossed Electric and Magnetic Fields 20.3 The Magnetic Fields Created by Electric Currents 20.3.1 The Biot–Savart Law 20.3.2 The Magnetic Field at the Center of a Narrow Coil 20.3.3 The Magnetic Field of a Long Straight Current-Carrying Wire 20.3.4 The Magnetic Field Along the Axis of a Solenoid 20.3.5 Ampère’s Theorem 20.4 Electric Motors 20.4.1 The Turning Effect on a Coil in a Uniform Magnetic Field 20.4.2 A Simple DC Electric Motor 20.5 Exercises Chapter 21: Electromagnetic Induction 21.1 Induced emfs 21.1.1 What Is Electromagnetic Induction? 21.1.2 Electromagnetic Induction Experiments 21.2 The Laws of Electromagnetic Induction 21.2.1 Magnetic Flux and Magnetic Flux Linkage 21.2.2 Faraday’s Law of Electromagnetic Induction 21.2.3 Changing the Flux-Linkage in a Coil 21.3 Inductance 21.3.1 Self-inductance 21.3.2 The Rise of Current in an Inductor 21.3.3 The Energy Stored in an Inductor 21.3.4 Mutual Inductance 21.4 Transformers 21.4.1 An Ideal Transformer 21.4.2 Transmission of Electrical Energy 21.4.3 Real Transformers 21.5 A Simple AC Generator 21.6 Electromagnetic Damping 21.7 Induction Motors 21.8 Exercises Chapter 22: AC 22.1 AC and DC 22.1.1 AC Power and rms Values 22.2 Resistance and Reactance 22.2.1 Resistors in AC Circuits 22.2.2 Capacitors in AC Circuits 22.2.3 Inductors in AC Circuits 22.3 Resistance, Reactance, and Impedance 22.3.1 Phasor Diagrams for AC Series Circuits 22.3.2 Impedance 22.4 AC Series Circuits 22.4.1 RC Series Circuit 22.4.2 RL Series Circuit 22.4.3 RCL Series Circuit 22.4.4 Parallel Circuits Containing Resistors, Capacitors, and Inductors 22.5 Electric Oscillators 22.5.1 A Mechanical Analogy 22.6 Exercises Chapter 23: The Gravitational Field 23.1 Gravitational Forces and Gravitational Field Strength 23.1.1 Newton’s Law of Gravitation 23.1.2 Gravitational Field Strength 23.1.3 The Gravitational Field Strength of the Earth 23.2 Gravitational Potential Energy and Gravitational Potential 23.2.1 Change in Gravitational Potential Energy 23.2.2 Gravitational Potential 23.2.3 Gravitational Field Lines and Equipotentials 23.2.4 Gravitational Potential Energy in the Earth’s Field 23.2.5 Escape Velocity 23.3 Orbital Motion 23.3.1 Early Ideas About Planetary Motion 23.3.2 Circular Orbits 23.3.3 Artificial Satellites 23.4 Tidal Forces 23.4.1 The Origin of Tidal Forces 23.4.2 The Earth’s Ocean Tides 23.5 Einstein’s Theory of Gravitation 23.5.1 Space–Time Curvature 23.5.2 The Equivalence Principle 23.5.3 Gravitational Time Dilation 23.5.4 Gravitational Waves 23.6 Exercises Chapter 24: Special Relativity 24.1 The Postulates of Special Relativity 24.1.1 Absolute Space 24.1.2 Einstein’s Ideas About the Laws of Physics 24.2 Time in Special Relativity 24.2.1 Time Dilation 24.2.2 The “Twin Paradox” 24.2.3 The Relativity of Simultaneity 24.3 Length Contraction 24.4 The Lorentz Transformation 24.4.1 The Lorentz Transformation Equations 24.4.2 The Velocity Addition Equation 24.5 Mass, Velocity, and Energy 24.5.1 Mass and Velocity 24.5.2 Mass and Energy 24.6 Special Relativity and Geometry 24.6.1 Invariants 24.6.2 Space–Time 24.6.3 Mass, Energy, and Momentum 24.7 Exercises Chapter 25: Atomic Structure and Radioactivity 25.1 The Nuclear Atom 25.1.1 The Rutherford Scattering Experiment 25.1.2 Closest Approach and Nuclear Size 25.1.3 Using Electron Diffraction to Measure Nuclear Diameter 25.1.4 The Nuclear Atom 25.2 Ionizing Radiation 25.2.1 Types of Ionizing Radiation Emitted by Radioactive Sources 25.3 Attenuation of Ionizing Radiation 25.3.1 Inverse-Square Law of Absorption 25.3.2 Exponential Absorption and the Attenuation Coefficient 25.3.3 Absorption of Beta Radiation 25.3.4 Absorption of Alpha Particles 25.4 The Biological Effects of Ionizing Radiation 25.4.1 The Natural Background Radiation 25.4.2 Measuring Radiation Dose 25.4.3 The Effect of Radiation Dose on Human Health 25.4.4 Reducing Risks in the Laboratory 25.5 Radioactive Decay and Half-Life 25.6 Nuclear Transformations 25.6.1 Alpha Decay 25.6.2 Beta-Minus Decay 25.6.3 Gamma Emission 25.6.4 Beta-Plus Emission 25.6.5 Electron-Capture 25.7 Radiation Detectors 25.7.1 The Spark Counter 25.7.2 The Geiger Counter 25.7.3 Using a Geiger Counter to Measure Count Rates 25.8 Using Radioactive Sources 25.8.1 Radiological Dating 25.8.2 Radiological Dating of Rocks 25.9 Exercises Chapter 26: Nuclear Physics 26.1 Nuclear Energy Changes 26.1.1 Nuclear Binding Energy 26.1.2 Atomic Mass Units (amu) 26.1.3 Energy Released by Nuclear Decays 26.2 Nuclear Stability 26.2.1 Nuclear Configuration and Stability 26.2.2 Nuclear Binding Energy and Stability 26.3 Nuclear Fission and Nuclear Fusion 26.3.1 Nuclear Fission 26.3.2 The Principle of the Atomic Bomb 26.3.3 Nuclear Reactors 26.3.4 Plutonium 26.3.5 Nuclear Fusion 26.3.6 Nucleosynthesis 26.3.7 Thermonuclear Weapons 26.3.8 Fusion Reactors 26.4 Particle Physics 26.4.1 Leptons 26.4.2 Hadrons and Quarks 26.4.3 The Fundamental Interactions 26.4.4 The Conservation Laws 26.4.5 The Standard Model 26.4.6 Dark Matter and Dark Energy 26.5 Exercises Chapter 27: Quantum Theory 27.1 Problems in Classical Physics 27.1.1 Planck and the Black Body Radiation Spectrum 27.1.2 Explaining Heat Capacities 27.1.3 Explaining the Photoelectric Effect 27.1.4 Characteristics of Photoelectric Emission 27.1.5 Measuring the Planck Constant 27.2 Matter Waves 27.2.1 The de Broglie Relation 27.2.2 Electron Diffraction 27.2.3 The Compton Effect 27.3 Wave-Particle Duality 27.3.1 Young’s Double Slit Experiment Revisited 27.3.2 Interpreting Wave-Particle Duality 27.3.3 The Schrödinger Equation 27.4 The Quantum Atom 27.4.1 Bohr’s Model of the Hydrogen Atom 27.4.2 Explaining the Hydrogen Line Spectrum 27.4.3 Electron Waves in Atoms 27.4.4 The Schrödinger Atom 27.5 Interpretations of Quantum Theory 27.5.1 The Copenhagen Interpretation 27.5.2 Heisenberg’s Uncertainty (Indeterminacy) Principle 27.5.3 The Sum-Over-Histories Approach 27.5.4 The Many-Worlds Theory 27.5.5 Schrödinger’s Cat 27.6 Exercises Chapter 28: Astrophysics 28.0 Physics Astrophysics and Cosmology 28.1 Stars 28.1.1 Mass 28.1.2 Stars as Black Bodies 28.1.3 Stellar Spectra and the Hertzsprung–Russell Diagram 28.2 Distances 28.2.1 Trigonometric Parallax 28.2.2 The Inverse-Square Law and Cepheid Variables 28.2.3 Hubble’s Law 28.3 Cosmology 28.3.1 The Origin and Age of the Universe 28.3.2 Evidence for the Big Bang 28.4 Exercises Chapter 29: Medical Physics 29.1 Ultrasound 29.1.1 Overview of Ultrasound 29.1.2 Ultrasound and the Eye 29.1.3 Doppler Ultrasound for Blood Flow Measurements 29.1.4 Using Ultrasound to Break Kidney Stones 29.2 X-rays 29.2.1 Overview of Medical X-rays 29.2.2 Generating X-Rays 29.2.3 Attenuation of X-Rays in Matter 29.2.4 Creating X-Ray Images 29.3 Magnetic Resonance Imaging (MRI) 29.3.1 Overview of MRI 29.3.2 The Physics of MRI 29.4 Radioactive Tracers 29.4.1 Overview of the Use of Radioactive Tracers 29.4.2 The Gamma-Camera 29.5 Positron Emission Tomography (PET Scans) 29.5.1 The Physics of PET Scans 29.6 Exercises Appendix A: Estimations and Fermi Questions A.0 Fermi and the Trinity Test A.1 Making Estimations A.1.1 How Many Air Molecules in the Earth’s Atmosphere? A.1.2 What Is the Minimum Area for a Parachute? A.2 Useful Values A.3 Fermi Questions A.4 The Drake Equation A.5 Try These: Estimates and Fermi Questions Appendix B: Experimental Investigations B.0 Introduction: The Nature of Science B.1 Carrying Out an Experiment B.1.1 Variables B.1.2 Selecting Measuring Equipment B.1.3 Planning a Procedure B.1.4 Risk Assessments B.1.5 Writing Up an Experiment B.2 Investigations Appendix C: Units, Constants, and Equations C.1 SI Units C.2 Simple Approximate Combinations of Uncertainties C.3 Useful Derivatives C.4 Differential Equations C.5 Differentials and Integrals C.6 Equations C.7 Constants Appendix D: Solutions to Exercises Glossary Index