Quantum Theory

1
Quantum Theory the History of Light
2
The Beginning of Light

• In the beginning it was dark and cold.
• No sun
• No light
• No earth
• No solar system.
• 4.5 billion years ago, a huge cloud of gas and
  dust was formed.
• This cloud contracted and grew into a central
  molten mass of plasma that became our SUN.
• Through the process of thermonuclear hydrogen
  fusion, the sun began to shine.

3
Is Light a Ray, Wave or Particle?

• The question has been debated many times over the
  years dating back as far as Pythagoras.

4
History of Light

• 582 500 BC Pythagoras theorized that light
  travels in particles where he assumed that every
  visible object emits a steady stream of
  particles, that bombard the eye.
• 427 347 BC Plato suggested that vision was
  produced by rays of light that originate in the
  eye and then strike the object being viewed.
• 384 322 BC Aristotle suggested that light
  travels in waves.
• 320 275 BC Euclid said that light travels in
  rays which came from the eyes in straight lines.
• 300 BC First lenses made by Greeks and Romans
  consisting of glass spheres filled with water.

5
History of Light (cont.)

• 1000 AD al Hathan said that light enters the
  eye from an outside source rather than
  originating from within.
• 1000 AD early 1600s Many inventions occurred
  in the area of optics (glasses and telescopes)
  and an overall general understanding of the
  nature of light (Law of Reflection and Law of
  Refraction).

6
Wave Theory of Light

• Christian Huygens (1629 1695) Light travels in
  wavelets
• Huygen's Wavelets

7
Corpuscle Theory of Light Sir Issac Newton
(1642 1727)

• Newton believed that bodies emitted energy in
  particles or corpuscles that traveled in straight
  lines.
• 1666 Performed an experiment with a prism that
  showed that the suns light is white light
  consisting of all of the colors of the spectrum.

8
Wave Theory of Light Thomas Young (1773
1829)-revisited

• 1801 Through use of the Double-Slit Experiment,
  the wave properties of light were first
  experimentally shown to exist.
• Experiment demonstrated that light undergoes
  interference and diffraction in much the same way
  that water and sound waves do.
• Used source of monochromatic light to eliminate
  the problems with phase differences associated
  with incoherent light.

9
Young Double-Slit Experiment
10
Wave Theory of Light James Clerk Maxwell (1831
1879)

• 1860 James Maxwell hypothesized that electric
  fields changing in time would create magnetic
  fields and vice-versa.
• These fields travel together in space as waves.
• Electromagnetic Wave

11
Max Planck Blackbody Radiation

• All matter, whether cool or hot emits
  electromagnetic waves.
• The light radiated from an incandescent body
  changes with temperature.
• The higher the temperature, the greater the
  intensity and frequency of the light emitted.
• Why does incandescent light come in all
  wavelengths then?
• Incandescent light is produced by vibrating
  atoms, which are systems far more complex than a
  single electron. Thus they are able to emit many
  different energies because f can vary linearly,
  producing a largely continuous energy spectrum.

12
Blackbody Radiation
Plancks theory and experimental evidence show
that as wavelength decreases, the amount of
energy being radiated approaches zero!
Classical theory suggests that as the wavelength
approaches zero, the amount of energy being
radiated should be infinite!
Blackbody Radiation
13
Quantization of Energy

• Energy exists in discrete quantities
• Atoms oscillate at discrete frequencies that
  reflect discrete energy levels.
• Energy is absorbed and emitted in the form of
  photons of radiation.
• E nhf
• Where
• h Plancks Constant (6.626 x 10-34Js)
• f vibrational frequency
• n 0, 1, 2, 3,
• Note Energy is not permitted for values other
  than those which satisfy the equation (You cannot
  have ½ of a photon).
• Each value of n can be thought of as a photon
  where 1 photon would be 1hf and two photons would
  be 2hf and so on.

14
The Photoelectric Effect

• Einstein proposed that light (electromagnetic
  radiation) consists of energy packets (Photons or
  Quanta) where E hf.
• If a photon had a sufficiently high enough
  frequency (or high enough energy) it could cause
  an electron to be ejected by the atom it is
  incident upon.

Photon of light
15
The Photoelectric Effect (cont.)

• The threshold frequency (fo) is the minimum
  frequency of a photon of light required to free
  an electron from an atom.
• At the threshold frequency, the electron will
  have no kinetic energy.
• Light intensity does not affect photoelectron
  emission if the threshold frequency has not been
  achieved.
• In other words, if the frequency is below the
  threshold frequency, it does not matter how
  bright the light is electrons will not be
  ejected.
• The Photoelectric Effect

16
The Photoelectric Effect(cont.)

• The maximum kinetic energy of an emitted electron
  is determined by the relationship of
  conservation of energy where
• KEe hf hfo
• Note this relationship implies that the photon
  has particle properties.
• Also, only one photon can act on one electron at
  any given moment.
• The work function is the minimum amount of energy
  required to remove an electron from an atom such
  that it does not have any kinetic energy.

17
The Photoelectric Effect(cont.)

• What is the relationship between light intensity
  and PE emission?

(a)
(b)
(a) If the threshold frequency is achieved, then
increasing the intensity will emit more
photons. (b) Increasing the intensity has no
affect on the kinetic energy of the emitted
photons.
18
The Photoelectric Effect(cont.)

• What is the relationship between the frequency
  of the photon and PE emission?

Slope h
Threshold Frequency
(a)
(b)
(a) If the threshold frequency is achieved, then
increasing it will NOT emit more
photoelectrons. (b) Increasing the frequency will
impart more kinetic energy to the electron once
fo is achieved.
19
The Photoelectric Effect(cont.)
Cathode
Anode
Photoelectron
E hf - hfo
-
_

Note for an electron to reach the anode, it must
have a sufficient amount of kinetic energy.
20
The Photoelectric Effect(cont.)

• Stopping Potential The minimum electric
  potential required to prevent an electron from
  reaching the anode.
• From electrostatics
• V Ed
• Where
• E electric field intensity (V/m)
• d distance between two plates
• W KE
• -qVo ½mev2
• Where
• Vo stopping potential
• q charge of an electron
• me mass of an electron
• v speed of electron

21
Applications of the Photoelectric Effect

• Photocells Used to operate switches and relays,
  alarms, door openers and boilers.
• CCD (Charged Coupled Devices) Low light
  imagery.
• Solar Cells
• Research in quantum physics.

22
Quantum Energy Units

• The units for energy is Joules.
• Joules is very large for atomic systems.
• Use smaller unit instead Electron Volt.
• One electron volt is equal to the energy of an
  electron accelerated across a potential
  difference of one volt.
• qe 1.6 x 10-19 C
• 1 eV (1.60 x 10-19 C)(1 V) 1.60 x 10-19 C?V
• 1 eV 1.60 x 10-19 J

23
Wave-Particle Duality of Light

• Einsteins theory suggests that although a photon
  of light has no mass, it does possess kinetic
  energy.
• Einstein further predicted that a photon of light
  should also have momentum as follows.
• p hf/c h/?
• The fact that a photon can have momentum again
  implies that it has particle properties.

Momentum, p mass x velocity
24
Wave-Particle Duality of Light
The Compton Effect (1922)
Incident Photon X-ray
-
Conservation of Energy Momentum The energy and
momentum gained by the electron equals the energy
and momentum lost by the photon.
hf/c hf /c mve
25
Particles vs. Waves (Light)

• Wave Theory
• Explained through polarization.
• Explained through reflection.
• Explained through diffraction interference.
• Explained through refraction.
• Particle Theory
• Explained through photoelectric emission.
• Explained through the Compton effect.
• Explained through reflection.
• Explained through refraction.

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Wavelike Behavior of Particles

• The photoelectric effect and Compton scattering
  showed that electromagnetic radiation has
  particle properties.
• Could a particle behave like a wave?
• The answer is yes!
• p mv h/?
• ? h/mv
• Where
• ? de Broglie wavelength

27
Wavelike Behavior of Particles

• Proof of the wavelike behavior of particles was
  made by diffracting electrons off a thin crystal
  lattice.
• The particles showed similar interference
  patterns to light when passed through a
  diffraction grating.

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Particles vs. Waves
Particles Waves
Mass Frequency
Size Wavelength
Kinetic Energy Amplitude
Momentum

• Physicists have demonstrated that light has both
  wavelike and particle characteristics that need
  to be considered when explaining its behavior.
• Similarly, particles such as electrons
  exhibit wavelike behavior.

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Key Ideas

• Objects that are hot enough will emit light
  because of the charge particles inside their
  atoms.
• The spectrum of light produced by an incandescent
  body is dependent on its temperature.
• Planck suggested that the spectrum of an
  incandescent body can only be comprised of
  certain energy levels (E nhf).
• The photoelectric effect is the emissions of
  electrons from metals when exposed to EM
  radiation of a minimum frequency (fo).

30
Key Ideas

• The minimum energy required to free an electron
  from the atom is the work function (E hfo).
• Light comes in discrete packets of energy called
  photons.
• Photons of light have momentum (p h/?) - even
  though they are massless.
• Energy and momentum are conserved in
  photon-electron collisions.
• Particles have wavelike attributes similar to
  light.