Quantum Physics

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Chapter 27

• Quantum Physics

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• Quantum Physics I
• Sections 13

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Need for Quantum Physics

• Other problems remained in classical physics
  which relativity did not explain
• Blackbody Radiation
• The electromagnetic radiation emitted by a heated
  object
• Photoelectric Effect
• Emission of electrons by an illuminated metal
• Compton Effect
• A beam of x-rays directed toward a block of
  graphite scattered at a slightly longer
  wavelength
• Spectral Lines
• Emission of sharp spectral lines by gas atoms in
  an electric discharge tube

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Development of Quantum Physics

• Beginning in 1900
• Development of ideas of quantum physics
• Also called wave mechanics
• Highly successful in explaining the behavior of
  atoms, molecules, and nuclei
• Involved a large number of physicists

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Particles vs. Waves

• PARTICLE properties
• individual motion
• position(time) localized
• velocity v ?x / ?t
• mass
• energy, momentum
• dynamics Fma
• interaction collisions
• quantum states
• spin

• WAVE properties
• collective motion
• wavelength (freq) periodic
• velocity v ? f
• dispersion
• energy, momentum
• dynamics wave equation
• interference superposition
• reflection, refraction, trans.
• diffraction Huygens
• standing waves modes
• polarization

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Blackbody Radiation

• An object at any temperature emits
  electromagnetic radiation
• Sometimes called thermal radiation
• Stefans Law describes the total power radiated
• The spectrum of the radiation depends on the
  temperature and properties of the object

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• IR heat lamp
• Red hot
• Night vision

• Silver heat shield
• Space blanket

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Blackbody Radiation Graph

• Experimental data for distribution of energy in
  blackbody radiation
• As the temperature increases, the total amount of
  energy increases
• Shown by the area under the curve
• As the temperature increases, the peak of the
  distribution shifts to shorter wavelengths
• The wavelength of the peak of the blackbody
  distribution was found to follow Weins
  Displacement Law
• ?max T 0.2898 x 10-2 m K
• ?max is the wavelength at which the curves peak
• T is the absolute temperature of the object
  emitting the radiation

Active Figure Blackbody Radiation
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The Ultraviolet Catastrophe

• Classical theory did not match the experimental
  data
• At long wavelengths, the match is good
• At short wavelengths, classical theory predicted
  infinite energy
• At short wavelengths, experiment showed no energy
• This contradiction is called the ultraviolet
  catastrophe

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Max Planck

• 1858 1947
• Introduced a quantum of action now known as
  Plancks constant
• Awarded Nobel Prize in 1918 for discovering the
  quantized nature of energy

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Plancks Resolution

• Planck hypothesized that the blackbody radiation
  was produced by resonators
• Resonators were submicroscopic charged
  oscillators
• The resonators could only have discrete energies
• En n h ƒ
• n is called the quantum number
• ƒ is the frequency of vibration
• h is Plancks constant, h 6.626 x 10-34 J s
• Key Point quantized energy states
• Few high energy resonators populated

Active Figure Planck's Quantized Energy States
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Photoelectric Effect

• When light is incident on certain metallic
  surfaces, electrons are emitted from the surface
• This is called the photoelectric effect
• The emitted electrons are called photoelectrons
• The effect was first discovered by Hertz
• The successful explanation of the effect was
  given by Einstein in 1905
• Received Nobel Prize in 1921 for paper on
  electromagnetic radiation, of which the
  photoelectric effect was a part

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Photoelectric Effect Schematic

• When light strikes E, photoelectrons are emitted
• Electrons collected at C and passing through the
  ammeter are a current in the circuit
• C is maintained at a positive potential by the
  power supply
• The current increases with intensity, until
  reaching a saturation level
• No current flows for voltages less than or equal
  to ?Vs, the stopping potential
• The maximum kinetic energy of the photoelectrons
  is related to the stopping potential KEmax
  eDVs

Active Figure The Photoelectric Effect
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Features Not Explained by Classical Physics/Wave
Theory

• The stopping potential DVs (maximum kinetic
  energy KEmax) is independent of the radiation
  intensity
• Instead, the maximum kinetic energy KEmax of the
  photoelectrons depends on the light frequency
• No electrons are emitted if the incident light
  frequency is below some cutoff frequency that is
  characteristic of the material being illuminated
• Electrons are emitted from the surface almost
  instantaneously, even at very low intensities

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Einsteins Explanation

• A tiny wave packet of light energy, called a
  photon, would be emitted when a
  quantized oscillator jumped from one energy level
  to the next lower one
• Extended Plancks idea of quantization to E.M.
  radiation
• The photons energy would be E hƒ
• Each photon can give all its energy to an
  electron in the metal
• The maximum kinetic energy of the liberated
  photoelectron is KEmax hƒ f
• f is called the work function of the metal it
  is the energy needed by the electron to escape
  the metal

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Explains Classical Problems

• KEmax hƒ f
• The effect is not observed below a certain cutoff
  frequency since the photon energy must be greater
  than or equal to the work function without
  enough energy, electrons are not emitted,
  regardless of the intensity of the light
• The maximum KE depends only on the frequency and
  the work function, not on the intensity
• The maximum KE increases with increasing
  frequency
• The effect is instantaneous since there is a
  one-to-one interaction between the photon and the
  electron

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Verification of Einsteins Theory

• Experimental observations of a linear
  relationship between KEmax and frequency ƒ
  confirm Einsteins theory
• The x-intercept is the cutoff frequency
• KEmax 0 ?

KEmax hƒ f
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Cutoff Wavelength

• The cutoff wavelength is related to the work
  function
• Wavelengths greater than lC incident on a
  material with a work function f dont result in
  the emission of photoelectrons

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Photocells

• Photocells are an application of the
  photoelectric effect
• When light of sufficiently high frequency falls
  on the cell, a current is produced
• Examples
• Streetlights, garage door openers, elevators

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X-Rays

• Electromagnetic radiation with short wavelengths
• Wavelengths less than for ultraviolet
• Wavelengths are typically about 0.1 nm
• X-rays have the ability to penetrate most
  materials with relative ease
• High energy photons which can break chemical
  bonds danger to tissue
• Discovered and named by Roentgen in 1895

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Production by an X-Ray Tube

• X-rays are produced when high-speed electrons are
  suddenly slowed down
• Can be caused by the electron striking a metal
  target
• A current in the filament causes electrons to be
  emitted
• These freed electrons are accelerated toward a
  dense metal target
• The target is held at a higher potential than the
  filament

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X-ray Tube Spectrum

• The x-ray spectrum has two distinct components
• Continuous broad spectrum
• Depends on voltage applied to the tube
• Cutoff wavelength
• Called bremsstrahlung (braking) radiation
• The sharp, intense lines depend on the nature of
  the target material

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Production of X-rays, 2

• An electron passes near a target nucleus
• The electron is deflected from its path by its
  attraction to the nucleus
• This produces an acceleration
• It will emit electromagnetic radiation when it is
  accelerated

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Wavelengths Produced

• If the electron loses all of its energy in the
  collision, the initial energy of the electron is
  completely transformed into a photon
• The wavelength can be found from
• Not all radiation produced is at this wavelength
• Many electrons undergo more than one collision
  before being stopped
• This results in the continuous spectrum produced

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X-ray Applications, Three-Dimensional Conformal
Radiation Therapy (3D-CRT)

• Tumors usually have an irregular shape
• Three-dimensional conformal radiation therapy
  (3D-CRT) uses sophisticated computers and CT
  scans and/or MRI scans to create detailed 3-D
  representations of the tumor and surrounding
  organs
• Radiation beams are then shaped exactly to the
  size and shape of the tumor
• Because the radiation beams are very precisely
  directed, nearby normal tissue receives less
  radiation exposure