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University Physics Volume 3

Key Equations

University Physics Volume 3Key Equations
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Table of contents
  1. Preface
  2. Optics
    1. 1 The Nature of Light
      1. Introduction
      2. 1.1 The Propagation of Light
      3. 1.2 The Law of Reflection
      4. 1.3 Refraction
      5. 1.4 Total Internal Reflection
      6. 1.5 Dispersion
      7. 1.6 Huygens’s Principle
      8. 1.7 Polarization
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 2 Geometric Optics and Image Formation
      1. Introduction
      2. 2.1 Images Formed by Plane Mirrors
      3. 2.2 Spherical Mirrors
      4. 2.3 Images Formed by Refraction
      5. 2.4 Thin Lenses
      6. 2.5 The Eye
      7. 2.6 The Camera
      8. 2.7 The Simple Magnifier
      9. 2.8 Microscopes and Telescopes
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    3. 3 Interference
      1. Introduction
      2. 3.1 Young's Double-Slit Interference
      3. 3.2 Mathematics of Interference
      4. 3.3 Multiple-Slit Interference
      5. 3.4 Interference in Thin Films
      6. 3.5 The Michelson Interferometer
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 4 Diffraction
      1. Introduction
      2. 4.1 Single-Slit Diffraction
      3. 4.2 Intensity in Single-Slit Diffraction
      4. 4.3 Double-Slit Diffraction
      5. 4.4 Diffraction Gratings
      6. 4.5 Circular Apertures and Resolution
      7. 4.6 X-Ray Diffraction
      8. 4.7 Holography
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  3. Modern Physics
    1. 5 Relativity
      1. Introduction
      2. 5.1 Invariance of Physical Laws
      3. 5.2 Relativity of Simultaneity
      4. 5.3 Time Dilation
      5. 5.4 Length Contraction
      6. 5.5 The Lorentz Transformation
      7. 5.6 Relativistic Velocity Transformation
      8. 5.7 Doppler Effect for Light
      9. 5.8 Relativistic Momentum
      10. 5.9 Relativistic Energy
      11. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    2. 6 Photons and Matter Waves
      1. Introduction
      2. 6.1 Blackbody Radiation
      3. 6.2 Photoelectric Effect
      4. 6.3 The Compton Effect
      5. 6.4 Bohr’s Model of the Hydrogen Atom
      6. 6.5 De Broglie’s Matter Waves
      7. 6.6 Wave-Particle Duality
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    3. 7 Quantum Mechanics
      1. Introduction
      2. 7.1 Wave Functions
      3. 7.2 The Heisenberg Uncertainty Principle
      4. 7.3 The Schrӧdinger Equation
      5. 7.4 The Quantum Particle in a Box
      6. 7.5 The Quantum Harmonic Oscillator
      7. 7.6 The Quantum Tunneling of Particles through Potential Barriers
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 8 Atomic Structure
      1. Introduction
      2. 8.1 The Hydrogen Atom
      3. 8.2 Orbital Magnetic Dipole Moment of the Electron
      4. 8.3 Electron Spin
      5. 8.4 The Exclusion Principle and the Periodic Table
      6. 8.5 Atomic Spectra and X-rays
      7. 8.6 Lasers
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    5. 9 Condensed Matter Physics
      1. Introduction
      2. 9.1 Types of Molecular Bonds
      3. 9.2 Molecular Spectra
      4. 9.3 Bonding in Crystalline Solids
      5. 9.4 Free Electron Model of Metals
      6. 9.5 Band Theory of Solids
      7. 9.6 Semiconductors and Doping
      8. 9.7 Semiconductor Devices
      9. 9.8 Superconductivity
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    6. 10 Nuclear Physics
      1. Introduction
      2. 10.1 Properties of Nuclei
      3. 10.2 Nuclear Binding Energy
      4. 10.3 Radioactive Decay
      5. 10.4 Nuclear Reactions
      6. 10.5 Fission
      7. 10.6 Nuclear Fusion
      8. 10.7 Medical Applications and Biological Effects of Nuclear Radiation
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    7. 11 Particle Physics and Cosmology
      1. Introduction
      2. 11.1 Introduction to Particle Physics
      3. 11.2 Particle Conservation Laws
      4. 11.3 Quarks
      5. 11.4 Particle Accelerators and Detectors
      6. 11.5 The Standard Model
      7. 11.6 The Big Bang
      8. 11.7 Evolution of the Early Universe
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  4. A | Units
  5. B | Conversion Factors
  6. C | Fundamental Constants
  7. D | Astronomical Data
  8. E | Mathematical Formulas
  9. F | Chemistry
  10. G | The Greek Alphabet
  11. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  12. Index

Key Equations

Wien’s displacement law λmaxT=2.898×10−3m⋅KλmaxT=2.898×10−3m⋅K
Stefan’s law P(T)=σAT4P(T)=σAT4
Planck’s constant h=6.626×10−34J⋅s=4.136×10−15eV⋅sh=6.626×10−34J⋅s=4.136×10−15eV⋅s
Energy quantum of radiation ΔE=hfΔE=hf
Planck’s blackbody radiation law I(λ,T)=2πhc2λ51ehc/λkBT−1I(λ,T)=2πhc2λ51ehc/λkBT−1
Maximum kinetic energy
of a photoelectron		 Kmax=eΔVsKmax=eΔVs
Energy of a photon Ef=hfEf=hf
Energy balance for photoelectron Kmax=hf−ϕKmax=hf−ϕ
Cut-off frequency fc=ϕhfc=ϕh
Relativistic invariant
energy equation		 E2=p2c2+m02c4E2=p2c2+m02c4
Energy-momentum relation
for photon		 pf=Efcpf=Efc
Energy of a photon Ef=hf=hcλEf=hf=hcλ
Magnitude of photon’s momentum pf=hλpf=hλ
Photon’s linear
momentum vector		 p→f=ℏk→p→f=ℏk→
The Compton wavelength
of an electron		 λc=hm0c=0.00243nmλc=hm0c=0.00243nm
The Compton shift Δλ=λc(1−cosθ)Δλ=λc(1−cosθ)
The Balmer formula 1λ=RH(122−1n2)1λ=RH(122−1n2)
The Rydberg formula 1λ=RH(1nf2−1ni2),ni=nf+1,nf+2,…1λ=RH(1nf2−1ni2),ni=nf+1,nf+2,…
Bohr’s first quantization condition Ln=nℏ,n=1,2,…Ln=nℏ,n=1,2,…
Bohr’s second quantization condition hf=|En−Em|hf=|En−Em|
Bohr’s radius of hydrogen a0=4πε0ℏ2mee2=0.529Åa0=4πε0ℏ2mee2=0.529Å
Bohr’s radius of the nth orbit rn=a0n2rn=a0n2
Ground-state energy value,
ionization limit		 E0=18ε02mee4h2=13.6eVE0=18ε02mee4h2=13.6eV
Electron’s energy in
the nth orbit		 En=−E01n2En=−E01n2
Ground state energy of
hydrogen		 E1=−E0=−13.6eVE1=−E0=−13.6eV
The nth orbit of
hydrogen-like ion		 rn=a0Zn2rn=a0Zn2
The nth energy
of hydrogen-like ion		 En=−Z2E01n2En=−Z2E01n2
Energy of a matter wave E=hfE=hf
The de Broglie wavelength λ=hpλ=hp
The frequency-wavelength relation
for matter waves		 λf=cβλf=cβ
Heisenberg’s uncertainty principle ΔxΔp≥12ℏΔxΔp≥12ℏ
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