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The Wave Particle Duality
OR
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Light Waves
Until about 1900, the classical wave theory of
light describedmost observed phenomenon.

• Light wavesCharacterized by
• Amplitude (A)
• Frequency (n)
• Wavelength (l)
• Energy a A2

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And then there was a problem
However, in the early 20th century, several
effects were observed which could not be
understood using the wave theory of light. So
other experiments were done and found it could
behave as both1) The Photo-Electric Effect
(particle) 2) The Compton Effect (particle) 3)
Taylors experiment (wave) 4) DeBroglie
Wavelength (wave)
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Quantized Model of Light (Photons)

• In 1900 Max Planck proposed that light energy
  comes in packets (quanta) spread at random on a
  wave front called PHOTONS.
• He even doubted his idea since
• It went against wave theory by saying that
  electromagnetic waves don't transmit energy
  continuously but in small packets.
• It went against Newtonian physics since objects
  aren't free to vibrate with any energy. The
  energy only has certain discreet values.

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Quantized Model of Light
Energy of a light particle (Photon) h
6.6x10-34 Jsec Plancks constant, after the
scientist Max Planck
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The Electromagnetic Spectrum
Shortest wavelengths (Most energetic photons)
Longest wavelengths (Least energetic photons)
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Photons

• Problems
• Find the energy in electron volts (eV)  for a
  quantum of orange light with frequency 5.00 x
  1014 Hz. (Answer 2.07eV)
• Find the energy in electron volts for a quantum
  of yellow light with a wavelength of 580 nm.
  (Answer 2.14 eV)
•  
• Suggested Textbook Problems
• Page 597 2-6

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Photoelectric Effect
Classical Method
Increase energy by increasing amplitude
electrons emitted ?
No electrons were emitted until the frequency of
the light exceeded a threshold frequency,
at which point electrons were emitted!
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Photoelectric
Electrons are attracted to the (positively
charged) nucleus by theelectrical force In
metals, the outermost electrons are not tightly
bound If given energy electrons can be freed
Classically, we increase the energyof an EM wave
by increasing theintensity (e.g. brightness)
Energy a A2
But this doesnt work ??
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PhotoElectric Effect
An alternate view is that light is acting like a
particle The light particle (photon) must have
enough energy to free the electron Increasing
the Amplitude is just simply increasing the
numberof light particles, but its NOT increasing
the energy of each one! However, if the energy
of these light particle is related to their
frequency, this would explain why higher
frequency light canknock the electrons out of
their atoms, but low frequency light cannot
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Photo-Electric Effect

• See diagram below the energy of thelight
  particle (photon) must overcome the binding
  energy of the electron to the nucleus (Work)
• Ephoton Ek Work.
• Ek Ephoton Work. (Einsteins Photoelectric
  Equation)

Freed electron has Ek
Light particle
Work to free elctron
Metal Surface
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Photo-Electric Problems

• EM radiation of frequency 7.0 X 1014 Hz falls on
  a metal with work function of 0.5eV. 
•     a) Calculate the maximum kinetic energy of
  the emitted photoelectrons and the maximum speed
  of the emitted photoelectrons.
•         (Answer 3.8 x 10 19 J)
•         NOTE Remind students if questions ask
  for speed make sure you convert everything into
  Joules.
•     b) What would be the case if the kinetic
  energy was less than 0.5 eV. (Answer no emission)

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Photo-Electric Problems
2. Calculate the Threshold (minimum) frequency
for a metal with a work function or binding
energy of 1.5 eV. (Answer 3.6 x 1014) 3. A
photoelectric surface has a work function of 1.50
eV.  A red light of wavelength 650 nm is directed
at the surface. Calculate a) The maximum Ek of
the emitted photoelectrons in joules (Answer
6.60 x 10 -20 J) b) The photoelectrons' maximum
speed (Answer  3.81 x 10 5 m/s) c) The cutoff
potential needed to stop the photoelectrons
(Answer 0.412 V)
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Photo-Electric Problems
Suggested Text Questions Pg. 604 10-15
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The Compton Effect
1924 Compton performed the photoelectric exp with
X-rays . Like the photoelectric effect it showed
light behaving as a particle.
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The Compton Effect
Energy and momentum are conserved
Notice There is NO work function since it is
negligible (compared to x-ray energy).
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The Compton Effect
Compton derived the expression for momentum of a
photon.
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Bohrs Complementarity Principle
If light is passing through a medium treat it
like a wave. If light is reacting with matter
treat it as a particle.
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Wave Nature of Matter
DeBroglie thought If light waves can
behave like a particle, might particles act like
waves? DeBroglies wavelength
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Matter Waves (cont)
Ex 1 Compute the wavelength of a 1 kg block
moving at 1000 m/s. l h/mv
6.6x10-34 J s/(1kg)(1000 m/s) 6.6x10-37
m. ? VERY small. therefore wave behavior
of matter cant be seen.
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Electron Microscope

• The electron microscope is a device which uses
  the wave behavior of electrons to make images
  which are otherwise too small using visible
  light!

This image was taken with a Scanning Electron
Microscope (SEM). These devices can resolve
features downto about 1 nm. This is about 100
times better than can be done with visible light
microscopes!
IMPORTANT POINT HERE High energy particles can
be used to reveal the structure of matter !
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High Energy Particles

• High energy particles can provide a way to reveal
  the structure of matter beyond what can be seen
  using an optical microscope.
• The higher the momentum of the particle, the
  smaller thedeBroglie wavelength.
• As wavelength decreases, finer and finer details
  about thestructure of matter are revealed !
• This is done at facilities often referred to as
  atom-smashers or accelerators