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  1. Preface
  2. Unit 1. 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. Unit 2. 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

Check Your Understanding

7.1

(3+4i)(34i)=916i2=25(3+4i)(34i)=916i2=25

7.2

A=2/LA=2/L

7.3

(1/21/π)/2=9%(1/21/π)/2=9%

7.4

4.1×10−8eV4.1×10−8eV; 1.1×10−5nm1.1×10−5nm

7.5

0.5mω2x2ψ(x)*ψ(x)0.5mω2x2ψ(x)*ψ(x)

7.6

None. The first function has a discontinuity; the second function is double-valued; and the third function diverges so is not normalizable.

7.7

a. 9.1%; b. 25%

7.8

a. 295 N/m; b. 0.277 eV

7.9

x=0x=0

7.10

Lproton/Lelectron=me/mp=2.3%Lproton/Lelectron=me/mp=2.3%

Conceptual Questions

1.

1/L,1/L, where L=lengthL=length; 1/L, where L=lengthL=length

3.

The wave function does not correspond directly to any measured quantity. It is a tool for predicting the values of physical quantities.

5.

The average value of the physical quantity for a large number of particles with the same wave function.

7.

Yes, if its position is completely unknown. Yes, if its momentum is completely unknown.

9.

No. According to the uncertainty principle, if the uncertainty on the particle’s position is small, the uncertainty on its momentum is large. Similarly, if the uncertainty on the particle’s position is large, the uncertainty on its momentum is small.

11.

No, it means that predictions about the particle (expressed in terms of probabilities) are time-independent.

13.

No, because the probability of the particle existing in a narrow (infinitesimally small) interval at the discontinuity is undefined.

15.

No. For an infinite square well, the spacing between energy levels increases with the quantum number n. The smallest energy measured corresponds to the transition from n = 2 to 1, which is three times the ground state energy. The largest energy measured corresponds to a transition from n=n= to 1, which is infinity. (Note: Even particles with extremely large energies remain bound to an infinite square well—they can never “escape”)

17.

No. This energy corresponds to n=0.25n=0.25, but n must be an integer.

19.

Because the smallest allowed value of the quantum number n for a simple harmonic oscillator is 0. No, because quantum mechanics and classical mechanics agree only in the limit of large nn.

21.

Yes, within the constraints of the uncertainty principle. If the oscillating particle is localized, the momentum and therefore energy of the oscillator are distributed.

23.

doubling the barrier width

25.

No, the restoring force on the particle at the walls of an infinite square well is infinity.

Problems

27.

|ψ(x)|2sin2ωt|ψ(x)|2sin2ωt

29.

(a) and (e), can be normalized

31.

a. A=2α/πA=2α/π; b. probability=29.3%probability=29.3%; c. x=0x=0; d. p=0p=0; e. K=α22/2mK=α22/2m

33.

a. Δp2.11×10−34N·sΔp2.11×10−34N·s; b. Δv6.31×10−8mΔv6.31×10−8m; c. Δv/kBT/mα=5.94×10−11Δv/kBT/mα=5.94×10−11

35.

Δτ1.6×10−25sΔτ1.6×10−25s

37.

a. Δf1.59MHzΔf1.59MHz; b. Δω/ω0=3.135×10−9Δω/ω0=3.135×10−9

39.

Carrying out the derivatives yields k2=ω2c2.k2=ω2c2.

41.

Carrying out the derivatives (as above) for the sine function gives a cosine on the right side the equation, so the equality fails. The same occurs for the cosine solution.

43.

E=2k2/2mE=2k2/2m

45.

2k22k2; The particle has definite momentum and therefore definite momentum squared.

47.

9.4 eV, 64%

49.

0.38 nm

51.

1.82 MeV

53.

24.7 nm

55.

6.03Å6.03Å

57.

a.

The wave functions for the n=1 through n=5 states of the electron in an infinite square well are shown. Each function is displaced vertically by its energy, measured in m e V. The n=1 state is the first half wave of the sine function. The n=2 function is the first full wave of the sine function. The n=3 function is the first one and a half waves of the sine function. The n=4 function is the first two waves of the sine function. The n=5 function is the first two and a half waves of the sine function.

;
b. λ53=12.9nm,λ31=25.8nm,λ43=29.4nmλ53=12.9nm,λ31=25.8nm,λ43=29.4nm

59.

proof

61.

6.662×1014Hz6.662×1014Hz

63.

n2.037×1030n2.037×1030

65.

x=0.5mω2x2=ω/4x=0.5mω2x2=ω/4; K=EU=ω/4K=EU=ω/4

67.

proof

69.

A complex function of the form, AeiϕAeiϕ, satisfies Schrӧdinger’s time-independent equation. The operators for kinetic and total energy are linear, so any linear combination of such wave functions is also a valid solution to Schrӧdinger’s equation. Therefore, we conclude that Equation 7.68 satisfies Equation 7.61, and Equation 7.69 satisfies Equation 7.63.

71.

a. 4.21%; b. 0.84%; c. 0.06%

73.

a. 0.13%; b. close to 0%

75.

0.38 nm

Additional Problems

77.

proof

79.

a. 4.0 %; b. 1.4 %; c. 4.0%; d. 1.4%

81.

a. t=mL2/h=2.15×1026yearst=mL2/h=2.15×1026years; b. E1=1.46×10−66J,K=0.4JE1=1.46×10−66J,K=0.4J

83.

proof

85.

1.2 N/m

87.

0

Challenge Problems

89.

19.2µm;11.5µm19.2µm;11.5µm

91.

3.92%

93.

proof

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