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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

8.1

No. The quantum number m=l,l+1,…,0,…,l1,l.m=l,l+1,…,0,…,l1,l. Thus, the magnitude of LzLz is always less than L because <l(l+1)<l(l+1)

8.2

s=3/2<s=3/2<

8.3

frequency quadruples

Conceptual Questions

1.

n (principal quantum number) total energy
ll (orbital angular quantum number) total absolute magnitude of the orbital angular momentum
m (orbital angular projection quantum number) z-component of the orbital angular momentum

3.

The Bohr model describes the electron as a particle that moves around the proton in well-defined orbits. Schrödinger’s model describes the electron as a wave, and knowledge about the position of the electron is restricted to probability statements. The total energy of the electron in the ground state (and all excited states) is the same for both models. However, the orbital angular momentum of the ground state is different for these models. In Bohr’s model, L(ground state)=1L(ground state)=1, and in Schrödinger’s model, L(ground state)=0L(ground state)=0.

5.

a, c, d; The total energy is changed (Zeeman splitting). The work done on the hydrogen atom rotates the atom, so the z-component of angular momentum and polar angle are affected. However, the angular momentum is not affected.

7.

Even in the ground state (l=0l=0), a hydrogen atom has magnetic properties due the intrinsic (internal) electron spin. The magnetic moment of an electron is proportional to its spin.

9.

For all electrons, s=½s=½ and ms=±½.ms=±½. As we will see, not all particles have the same spin quantum number. For example, a photon as a spin 1 (s=1s=1), and a Higgs boson has spin 0 (s=0s=0).

11.

An electron has a magnetic moment associated with its intrinsic (internal) spin. Spin-orbit coupling occurs when this interacts with the magnetic field produced by the orbital angular momentum of the electron.

13.

Elements that belong in the same column in the periodic table of elements have the same fillings of their outer shells, and therefore the same number of valence electrons. For example:
Li: 1s22s11s22s1 (one valence electron in the n=2n=2 shell)
Na: 1s22s2p63s11s22s2p63s1 (one valence electron in the n=2n=2 shell)
Both, Li and Na belong to first column.

15.

Atomic and molecular spectra are said to be “discrete,” because only certain spectral lines are observed. In contrast, spectra from a white light source (consisting of many photon frequencies) are continuous because a continuous “rainbow” of colors is observed.

17.

UV light consists of relatively high frequency (short wavelength) photons. So the energy of the absorbed photon and the energy transition (ΔEΔE) in the atom is relatively large. In comparison, visible light consists of relatively lower-frequency photons. Therefore, the energy transition in the atom and the energy of the emitted photon is relatively small.

19.

For macroscopic systems, the quantum numbers are very large, so the energy difference (ΔEΔE) between adjacent energy levels (orbits) is very small. The energy released in transitions between these closely space energy levels is much too small to be detected.

21.

Laser light relies on the process of stimulated emission. In this process, electrons must be prepared in an excited (upper) metastable state such that the passage of light through the system produces de-excitations and, therefore, additional light.

23.

A Blu-Ray player uses blue laser light to probe the bumps and pits of the disc and a CD player uses red laser light. The relatively short-wavelength blue light is necessary to probe the smaller pits and bumps on a Blu-ray disc; smaller pits and bumps correspond to higher storage densities.

Problems

25.

(r,θ,ϕ)=(6,66°,27°).(r,θ,ϕ)=(6,66°,27°).

27.

±3,±2,±1,0±3,±2,±1,0 are possible

29.

18

31.

F=kQqr2F=kQqr2

33.

(1, 1, 1)

35.

For the orbital angular momentum quantum number, l, the allowed values of:
m=l,l+1,...0,...l1,lm=l,l+1,...0,...l1,l.
With the exception of m=0m=0, the total number is just 2l because the number of states on either side of m=0m=0 is just l. Including m=0m=0, the total number of orbital angular momentum states for the orbital angular momentum quantum number, l, is: 2l+1.2l+1. Later, when we consider electron spin, the total number of angular momentum states will be found to twice this value because each orbital angular momentum states is associated with two states of electron spin: spin up and spin down).

37.

The probability that the 1s electron of a hydrogen atom is found outside of the Bohr radius is a0P(r)dr0.68a0P(r)dr0.68

39.

For n=2n=2, l=0l=0 (1 state), and l=1l=1 (3 states). The total is 4.

41.

The 3p state corresponds to n=3n=3, l=2l=2. Therefore, μ=μB6μ=μB6

43.

The ratio of their masses is 1/207, so the ratio of their magnetic moments is 207. The electron’s magnetic moment is more than 200 times larger than the muon.

45.

a. The 3d state corresponds to n=3n=3, l=2l=2. So,
I=4.43×10−7A.I=4.43×10−7A.
b. The maximum torque occurs when the magnetic moment and external magnetic field vectors are at right angles (sinθ=1)sinθ=1). In this case:
|τ|=μB.|τ|=μB.
τ=5.70×10−26N·m.τ=5.70×10−26N·m.

47.

A 3p electron is in the state n=3n=3 and l=1l=1. The minimum torque magnitude occurs when the magnetic moment and external magnetic field vectors are most parallel (antiparallel). This occurs when m=±1m=±1.The torque magnitude is given by
|τ|=μBsinθ,|τ|=μBsinθ,
Where
μ=(1.31×10−24J/T).μ=(1.31×10−24J/T).
For m=±1,m=±1, we have:
|τ|=2.32×1021N·m.|τ|=2.32×1021N·m.

49.

An infinitesimal work dW done by a magnetic torque ττ to rotate the magnetic moment through an angle dθdθ:
dW=τ(dθ)dW=τ(dθ),
where τ=|μ×B|τ=|μ×B|. Work done is interpreted as a drop in potential energy U, so
dW=dU.dW=dU.
The total energy change is determined by summing over infinitesimal changes in the potential energy:
U=μBcosθU=μBcosθ
U=μ·B.U=μ·B.

51.

Spin up (relative to positive z-axis):
θ=55°.θ=55°.
Spin down (relative to positive z-axis):
θ=cos−1(SzS)=cos−1(1232)=cos−1(−13)=125°.θ=cos−1(SzS)=cos−1(1232)=cos−1(−13)=125°.

53.

The spin projection quantum number is ms=±½ms=±½, so the z-component of the magnetic moment is
μz=±μB.μz=±μB.
The potential energy associated with the interaction between the electron and the external magnetic field is
U=μBB.U=μBB.
The energy difference between these states is ΔE=2μBBΔE=2μBB, so the wavelength of light produced is
λ=8.38×10−5m84μmλ=8.38×10−5m84μm

55.

It is increased by a factor of 2.

57.

a. 32; b.
_2(2+1)0s2(0+1)=21p2(2+1)=62d2(4+1)=103f2(6+1)=14_____________________32_2(2+1)0s2(0+1)=21p2(2+1)=62d2(4+1)=103f2(6+1)=14_____________________32

59.

a. and e. are allowed; the others are not allowed.
b. l=3l=3 not allowed for n=1,l(n1).n=1,l(n1).
c. Cannot have three electrons in s subshell because 3>2(2l+1)=2.3>2(2l+1)=2.
d. Cannot have seven electrons in p subshell (max of 6) 2(2l+1)=2(2+1)=6.2(2l+1)=2(2+1)=6.

61.

[Ar]4s23d6[Ar]4s23d6

63.

a. The minimum value of is l=2l=2 to have nine electrons in it.
b. 3d9.3d9.

65.

[He]2s22p2[He]2s22p2

67.

For He+He+, one electron “orbits” a nucleus with two protons and two neutrons (Z=2Z=2). Ionization energy refers to the energy required to remove the electron from the atom. The energy needed to remove the electron in the ground state of He+He+ ion to infinity is negative the value of the ground state energy, written:
E=−54.4eV.E=−54.4eV.
Thus, the energy to ionize the electron is +54.4eV.+54.4eV.
Similarly, the energy needed to remove an electron in the first excited state of Li2+Li2+ ion to infinity is negative the value of the first excited state energy, written:
E=−30.6eV.E=−30.6eV.
The energy to ionize the electron is 30.6 eV.

69.

The wavelength of the laser is given by:
λ=hcΔE,λ=hcΔE,
where EγEγ is the energy of the photon and ΔEΔE is the magnitude of the energy difference. Solving for the latter, we get:
ΔE=−2.795eV.ΔE=−2.795eV.
The negative sign indicates that the electron lost energy in the transition.

71.

ΔELK(Z1)2(10.2eV)=3.68×103eV.ΔELK(Z1)2(10.2eV)=3.68×103eV.

73.

According to the conservation of the energy, the potential energy of the electron is converted completely into kinetic energy. The initial kinetic energy of the electron is zero (the electron begins at rest). So, the kinetic energy of the electron just before it strikes the target is:
K=eΔV.K=eΔV.
If all of this energy is converted into braking radiation, the frequency of the emitted radiation is a maximum, therefore:
fmax=eΔVh.fmax=eΔVh.
When the emitted frequency is a maximum, then the emitted wavelength is a minimum, so:
λmin=0.1293nm.λmin=0.1293nm.

75.

A muon is 200 times heavier than an electron, but the minimum wavelength does not depend on mass, so the result is unchanged.

77.

4.13×10−11m4.13×10−11m

79.

72.5 keV

81.

The atomic numbers for Cu and Au are Z=29Z=29 and 79, respectively. The X-ray photon frequency for gold is greater than copper by a factor:
(fAufCu)2=(791291)28.(fAufCu)2=(791291)28.
Therefore, the X-ray wavelength of Au is about eight times shorter than for copper.

83.

a. If flesh has the same density as water, then we used 1.34×10231.34×1023 photons. b. 2.52 MW

Additional Problems

85.

The smallest angle corresponds to l=n1l=n1 and m=l=n1m=l=n1. Therefore θ=cos−1(n1n).θ=cos−1(n1n).

87.

a. According to Equation 8.1, when r=0r=0, U(r)=U(r)=, and when r=+,U(r)=0.r=+,U(r)=0. b. The former result suggests that the electron can have an infinite negative potential energy. The quantum model of the hydrogen atom avoids this possibility because the probability density at r=0r=0 is zero.

89.

A formal solution using sums is somewhat complicated. However, the answer easily found by studying the mathematical pattern between the principal quantum number and the total number of orbital angular momentum states.
For n=1n=1, the total number of orbital angular momentum states is 1; for n=2n=2, the total number is 4; and, when n=3n=3, the total number is 9, and so on. The pattern suggests the total number of orbital angular momentum states for the nth shell is n2n2.
(Later, when we consider electron spin, the total number of angular momentum states will be found to be 2n22n2, because each orbital angular momentum states is associated with two states of electron spin; spin up and spin down).

91.

50

93.

The maximum number of orbital angular momentum electron states in the nth shell of an atom is n2n2. Each of these states can be filled by a spin up and spin down electron. So, the maximum number of electron states in the nth shell is 2n22n2.

95.

a., c., and e. are allowed; the others are not allowed. b. l>nl>n is not allowed.
d. 7>2(2l+1)7>2(2l+1)

97.

f=1.8×109Hzf=1.8×109Hz

99.

The atomic numbers for Cu and Ag are Z=29Z=29 and 47, respectively. The X-ray photon frequency for silver is greater than copper by the following factor:
(fAgfCu)2=2.7.(fAgfCu)2=2.7.
Therefore, the X-ray wavelength of Ag is about three times shorter than for copper.

101.

a. 3.24; b. nini is not an integer. c. The wavelength must not be correct. Because ni>2,ni>2, the assumption that the line was from the Balmer series is possible, but the wavelength of the light did not produce an integer value for nini. If the wavelength is correct, then the assumption that the gas is hydrogen is not correct; it might be sodium instead.

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