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Chapter 30

Quantum Physics

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Overview of Chapter 30

• Blackbody Radiation and Planck’s Hypothesis of Quantized Energy • Photons and the Photoelectric Effect • The Mass and Momentum of a Photon • Photon Scattering and the Compton Effect • The de Broglie Hypothesis and Wave-Particle Duality • The Heisenberg Uncertainty Principle • Quantum Tunneling

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30-1 Blackbody Radiation and Planck’s Hypothesis of Quantized Energy

Ideal blackbody absorbs all the light that is incident upon it.

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30-1 Blackbody Radiation and Planck’s Hypothesis

of Quantized Energy

• Ideal blackbody is also an ideal radiator.

• If we measure the intensity of the electromagnetic radiation emitted by an ideal blackbody, we find:

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30-1 Blackbody Radiation and Planck’s Hypothesis of Quantized Energy

• Illustrates a remarkable experimental finding:

• Distribution of energy in blackbody radiation is independent of the material from which the blackbody is constructed

- Depends only on the temperature, T.

• Peak frequency is given by:

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30-1 Blackbody Radiation and Planck’s Hypothesis of Quantized Energy

• Peak frequency increases linearly with the temperature. - Means temperature of a blackbody can be determined by its

color.

• Classical physics calculations were completely unable to produce this temperature dependence

- Called the “ultraviolet catastrophe.”

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30-1 Blackbody Radiation and Planck’s Hypothesis of Quantized Energy

Classical predictions were that the intensity increased rapidly with frequency, hence the ultraviolet catastrophe….

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30-1 Blackbody Radiation and Planck’s Hypothesis of Quantized Energy

• Planck discovered that he could reproduce the experimental curve by assuming that the radiation in a blackbody came in quantized energy packets, depending on the frequency:

The constant h known as Planck’s constant:

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30-1 Blackbody Radiation and Planck’s Hypothesis of Quantized Energy

• Planck’s constant is a very tiny number…

• Means that the quantization of the energy of blackbody radiation is not easily observed in most macroscopic situations.

• It was, however, a most unsatisfactory solution, as it appeared to make no sense.

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30-2 Photons and the Photoelectric EffectEinstein suggested that the quantization of light was real; that light came in small packets, now called photons, of energy:

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30-2 Photons and the Photoelectric EffectTherefore, a more intense beam of light will contain more photons, but the energy of each photon does not change.

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30-2 Photons and the Photoelectric Effect

• Photoelectric effect occurs when a beam of light strikes a metal, and electrons are ejected.

• Each metal has a minimum amount of energy required to eject an electron, called the work function, W0.

• If the electron is given an energy E by the beam of light, its maximum kinetic energy is:

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30-2 Photons and the Photoelectric EffectThis diagram shows the basic layout of a photoelectric effect experiment.

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30-2 Photons and the Photoelectric Effect

Classical predictions: 1. Any beam of light of any color can eject electrons if it is intense

enough. 2. The maximum kinetic energy of an ejected electron should

increase as the intensity increases.

Observations: 1. Light must have a certain minimum frequency in order to eject

electrons. 2. More intensity results in more electrons of the same energy.

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30-2 Photons and the Photoelectric Effect

Explanations: 1. Each photon’s energy is determined by its frequency. If it is

less than the work function, electrons will not be ejected, no matter how intense the beam.

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30-2 Photons and the Photoelectric Effect2. A more intense beam means more photons, and therefore more ejected electrons.

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30-3 The Mass and Momentum of a Photon

Photons have momentum, yet no mass:

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30-4 Photon Scattering and the Compton Effect

The Compton effect occurs when a photon scatters off an atomic electron.

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30-4 Photon Scattering and the Compton Effect

• In order for energy to be conserved, the energy of the scattered photon plus the energy of the electron must equal the energy of the incoming photon.

• Wavelength of the outgoing photon is longer than the wavelength of the incoming one:

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30-5 The de Broglie Hypothesis and Wave-Particle Duality

• In 1923, de Broglie proposed that, as waves can exhibit particle-like behavior, particles should exhibit wave-like behavior as well.

• Proposed that the same relationship between wavelength and momentum should apply to massive particles as well as photons:

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30-5 The de Broglie Hypothesis and Wave-Particle Duality

• Correctness of this assumption has been verified many times over… - One way is by observing interference/diffraction patterns with

particles….

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30-5 The de Broglie Hypothesis and Wave-Particle Duality

Same patterns can be observed using either particles or X-rays.

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30-5 The de Broglie Hypothesis and Wave-Particle Duality

Can perform Young’s two-slit experiment with particles of the appropriate wavelength and find the same diffraction pattern.

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30-5 The de Broglie Hypothesis and Wave-Particle Duality

• Even true if we have a particle beam so weak that only one particle is present at a time!

- Still see the diffraction pattern produced by constructive and destructive interference.

• As the diffraction pattern builds, we cannot predict where any particular particle will land..

- We can predict the final appearance of the pattern…

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30-5 The de Broglie Hypothesis and Wave-Particle Duality

Images show the gradual creation of an electron diffraction pattern.

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30-6 The Heisenberg Uncertainty PrincipleThe uncertainty just mentioned – that we cannot know where any individual electron will hit the screen – is inherent in quantum physics, and is due to the wavelike properties of matter…

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30-6 The Heisenberg Uncertainty Principle

• Electrons diffract through the slit, acquire y-component of momentum that they had not had before.

- Leads to the uncertainty principle:

- “If we know the position of a particle with greater precision, its momentum is more uncertain; if we know the momentum of a particle with greater precision, its position is more uncertain.”

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30-6 The Heisenberg Uncertainty Principle

Mathematically,

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30-6 The Heisenberg Uncertainty Principle

• The uncertainty principle can be cast in terms of energy and time rather than position and momentum:

• Effects of the uncertainty principle are generally not noticeable in macroscopic situations

- Due to the smallness of Planck’s constant, h.

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30-7 Quantum Tunneling

Waves can “tunnel” through narrow gaps of material that they otherwise would not be able to traverse. As the gap widens, the intensity of the transmitted wave decreases exponentially…

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30-7 Quantum Tunneling

• Given their wavelike properties, it is not surprising that particles can tunnel as well.

• Practical application is the scanning tunneling microscope, which can image single atoms using the tunneling of electrons.

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Answer: 3.4 x 1014 Hz

Answer: λ = 880 nm

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Answer: 4.6 x 1032

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Answer: 6.42 x 10-19 J

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Answer: 0.61 µm

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Answer: a) 0.315 nm

Answer: b) 3.94 keV, 3.88 keV

Answer: c) 60 eV…

New Energy Unit 1 eV = 1.6 x 10-19 J

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Answer: 2.0 x 10-36 m

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Answer: 3.4 x 10-34 m

Answer: 57 µm

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Answer: 1.8 x 10-25 J