AP Physics Chapter 28 Quantum Mechanics and Atomic Physics

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AP Physics Chapter 28Quantum
Mechanics and Atomic Physics
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Chapter 28 Quantum Mechanics and Atomic Physics

• 28.1 Quantization Plancks Hypothesis
• 28.2-5 Omitted

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Homework for Chapter 28

• Read Chapter 28
• HW 28 p. 889 3-6, 9, 12, 15.

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(No Transcript)
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28.1 Matter Waves The De Broglie Hypothesis
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• Photon Momentum
• A photon is a massless particle which carries
  energy.
• Photon energy can be written E hf hc/?
• The momentum of a photon carries is related to
  its wavelength by
• p E hf h
• c c ?
• The energy in electromagnetic waves of
  wavelength ? can be thought of as being carried
  by photon particles, each having a momentum of
  h/?.

On Gold Sheet
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• Louis de Broglie (1892 1987) French
  physicist and Nobel laureate
• De Broglie speculated that if light sometimes
  behaves like a particle, perhaps material
  particles, such as electrons, also have wave
  properties.
• In 1924 de Broglie hypothesized that a moving
  particle has a wave associated with it. The
  wavelength of the particle is related to the
  particles momentum (pmv).
• ? h _h_
• p mv
• These waves associated with moving particles
  were
• called matter waves or, more commonly de Broglie
  waves.
• Question If particles really are associated with
  a wave,
• why then have we never observed wave effects
• such as diffraction or interference for them?

On Gold Sheet
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• Example 28.1 What is the wavelength of the
  matter wave associated with
• a ball of mass 0.50 kg moving with a speed of 25
  m/s?
• an electron moving with a speed of 2.5 x 107 m/s?
• The wavelength of the ball is much shorter than
  that of the electron. That is why matter waves
  are important for small particles like electrons
  since their wavelengths are comparable to the
  sizes of the objects they interact with. It is
  easier to observe interference and diffraction
  for electrons than the ball and all other
  everyday objects.

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• Problem Solving Hint Accelerating an Electron
  Through a Potential Difference, V
• Since p mv and KE ½ mv2, KE p2
• 2m
• By energy conservation, KE UE qV eV
• So, p2 eV or p ? 2meV
• 2m
• For these conditions, the de Broglie wavelength
  is ? h h h2___
• p ? 2meV 2meV
• Substitute in the numbers for h, e, and m ?
  1.50 x 10-9 m
• V
• ? 1.50 nm where V is in volts.
• V

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• Example 28.2 An electron is accelerated by a
  potential difference of 120 V.
• What is the wavelength of the matter wave
  associated with the electron?
• What is the momentum of the electron?
• What is the kinetic energy of the electron?

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• In 1927, two physicists in the US, C.J. Davisson
  and L.H. Germer, used a crystal to diffract a
  beam of electrons, thereby demonstrating a
  wavelike property of particles.

• In order to test de Broglies hypothesis that
  matter behaved like waves, Davisson and Germer
  set up an experiment very similar to what might
  be used to look at the interference pattern from
  x-rays scattering from a crystal surface. The
  basic idea is that the planar nature of crystal
  structure provides scattering surfaces at regular
  intervals, thus waves that scatter from one
  surface can constructively or destructively
  interfere from waves that scatter from the next
  crystal plane deeper into the crystal.

Video http//www.tutorvista.com/content/physics/p
hysics-iv/radiation-and-matter/davisson-and-germer
-experiment.php
Simulation http//phet.colorado.edu/en/simulation
/davisson-germer
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• This simple apparatus send an electron beam with
  an adjustable energy to a crystal surface, and
  then measures the current of electrons detected
  at a particular scattering angle theta. The
  results of an energy scan at a particular angle
  and an angle scan at a fixed energy are shown
  below. Both show a characteristic shape
  indicative of an interference pattern and
  consistent with the planar separation in the
  crystal. This was dramatic proof of the wave
  nature of matter.

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Davisson-Germer Experiment
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• A single crystal of nickel was cut to expose a
  spacing of d 0.215 nm between the lattice
  planes.
• When a beam of electrons of kinetic energy 54.0
  eV was directed onto the crystal face, the
  maximum in the intesity of the scattered
  electrons was observed at an angle of 50.
• According to wave theory, constructive
  interference due to waves reflected from two
  lattice planes a distance of d apart should occur
  at certain angles of scattering ?.
• The theory predicts the first order maximum
  should be observed at an angle given by
• d sin ? ?
• (0.215 nm) sin 50 0.165 nm
• The de Broglie wavelength of the electrons is
• ? 1.50 nm 1.50 nm 0.167 nm
• The wavelengths agree!!

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• Another experiment carried out in the same year
  by G.P.Thomson in Great Britain added further
  proof.
• Thomson passed a beam of energetic electrons
  through a thin metal foil.
• The diffraction pattern of the electrons was the
  same as that of X-rays.
• Particles exhibit wavelike properties..confirmed
  .

electron diffraction pattern
X-ray diffraction pattern
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Check for Understanding

• The momentum of a photon is
• a) zero
• b) equal to c
• c) proportional to its frequency
• d) proportional to its wavelength
• e) given by the de Broglie hypothesis
• Answer c hf pc
• 2. The Davisson-Germer experiment
• a) dealt with X-ray spectra
• b) confirmed blackbody radiation
• c) supplied further evidence for Wiens
  displacement law
• d) demonstrated the wavelike properties of
  electrons
• Answer d

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Check for Understanding
3.
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(No Transcript)
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Homework for Chapter 28

• HW 28 p. 889 3-6, 9, 12, 15.

Formulas for Chapter 28