ENGR 145: Chemistry of Materials

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Lecture 2 Atomic Theory IWaves, light, and
electrons

• Reading assignment OGN 15.1-15.4
• Learning objectives
• Understand how data on blackbody radiation
  contributed to the development of quantum
  mechanics.
• Understand how the photoelectric effect
  illustrates the particle nature of light, and how
  it allows measurement of the work function of a
  surface.
• Be able to compute the Bohr radius and allowed
  energy levels for electrons in one-electron
  atoms.

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Classical Mechanics vs.Quantum Mechanics

• Classical mechanics energy of a system can be
  continuously varied
• Quantum mechanics energy states are quantized
• Only true if the energy changes are large
  compared to quantum phenomena

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Wave Motion (OGN 15.1)

• Wave Motion
• Amplitude, A
• Wavelength, ? m
• Frequency, ? s-1
• Velocity or speed, v m/s
• v ??

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Light as Waves (OGN 15.1)

• Light electromagnetic radiation
• Speed of light in vacuum c2.9979.108 m/s
• Electric field (E)
• Magnetic field (H)

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Electromagnetic Spectrum

• Visible light is only a small part of the EM
  spectrum

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Wavelength, frequency, and speed
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Evidence for Energy Quantization Blackbody
Radiation (OGN 15.2)

• Stefans law
• IT total energy emitted (all frequencies) per
  second per area
• T absolute temperature K
• 
  (Stefan-Boltzmann constant)
• e emissivity (0 e 1)
• Kirchhoff absorptivity a equals emissivity e
• Black body has e a 1

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Measuring Emissivity
Stefans law explored It seT4 energy per
unit time per unit area P seAT4 power (
energy per unit time) A surface area of
emitter lnP ln(seA) 4lnT
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Measuring Emissivity

• lnP ln(seA) 4lnT
• Put a light bulb in a circuit with a
  variable-voltage power supply, ammeter and
  voltmeter
• Measure current I at different voltages V
• Compute power P IV
• Measure T of filament at each V
• Plot lnP vs lnT
• slope will be 4
• intercept will be ln(seA)
• Solve for e, as everything else is known

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Evidence for Energy Quantization Blackbody
Radiation (OGN 15.2)

• Stefans law
• IT total energy emitted (all frequencies) per
  second per area (area under curve)
• IT(?)d? energy emitted per unit time per area
  in wavelength range ? to ?d?
• Maximum intensity shifts towards shorter
  wavelengths as T?

visible range
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Evidence for Energy Quantization Blackbody
Radiation

• Comments on Fig. 15.6
• Objects can absorb and emit light at wavelengths
  we cannot see.
• A hotter object
• produces more total radiation, and
• the peak in emitted energy shifts to shorter ?
• Astronomers calculate a star's temperature by
  measuring the wavelength at which it emits its
  maximum light

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Evidence for Energy Quantization Blackbody
Radiation (OGN 15.2)

• Wiens displacement law
• If ?1T1 ?2T2 , then the intensity I?1 emitted
  at ?1 was related to the intensity I?2
  emitted at ?2 at any temperature by

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The Ultraviolet Catastrophe and Plancks
Breakthrough (OGN 15.2)
Classical Energy of oscillator can vary
continuously
7000 K
Classical Theory
5000 K
OGN Fig. 15.8
T1646 K
Planck Energy of oscillator is limited to
integer multiples of h?, with h a new fundamental
constant
OGN Fig. 15.9
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Photoelectric Effect (OGN 15.2)

• The experiment
• Metal in vacuum
• Shine light on metal

• The result
• ? lt ?o no electrons emitted regardless of
  intensity
• ? ?o ? metal emits es, more at higher
  intensity

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Photoelectric Effect (OGN 15.2)

• Further results
• ? ?o kinetic energy increases linearly with ?
• with ? h?o, the work function, a property of
  the metal me mass of an e

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Quantization of Energy in Atoms (OGN 15.3)

• Atomic spectra
• Show transitions between allowed energy states
• Are characteristic of the element emitting the
  spectrum

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Photoelectron Spectroscopy (OGN 15.3)

• Measuring chemical composition of a materials
  surface
• Shine EM radiation (e.g. x-rays) on the surface
• Kinetic energy of emitted electrons identifies
  elements
• Amount of electrons indicates proportions of
  elements
• Slight shifts in energies indicate chemical state
  of elements

X-ray photoelectron spectrometer in MSE
Department at Case
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The x-ray used to excite the neon has a
wavelength of 9.89 x 10-11 m. Calculate the
energy of that photon as shown.
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Bohrs Model of the H Atom (1913)

• Assumes that electron moves in orbits of radii
  r around the nucleus of atomic number Z
• Uses classical mechanics KE, PE, angular
  momentum, linear momentum, force balance
• ?o permittivity of free space
• e charge on e a acceleration

• Potential energy betw. e nucleus (Coulombs
  law)
• Total Energy KE PE
• Force balance

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Bohrs Model of the H Atom (contd)

• Bohrs big leap discrete values of the orbital
  angular momenta, mevr nh/2p
• ? discrete energies
• Rydberg
• 1 Ry
• ? discrete radii
• the Bohr radius

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? Atomic Spectra Interpretation by Bohrs Model