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Wave - Particle Duality

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					Quantum Theory & the
      History of Light
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.
Is Light a Ray, Wave or
Particle?
   The question has been debated many times over the
    years dating back as far as Pythagoras.
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.
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 1600’s: 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).
Wave Theory of Light
   Christian Huygens (1629 – 1695): Light travels
    in wavelets
   Huygen's Wavelets
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 sun’s light is white light consisting of all of the colors of the
    spectrum.
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.
Young Double-Slit Experiment
     Huygen’s Wavelets




         www.src.wits.ac.za
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




                                             www.hyperphysics.com
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.
     Blackbody Radiation
Planck’s theory and
experimental
evidence show that
as wavelength
decreases, the
amount of energy       Classical theory suggests
being radiated         that as the wavelength
approaches zero!       approaches zero, the
                       amount of energy being
                       radiated should be
                       infinite!




 Blackbody Radiation
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 = Planck’s Constant (6.626 x 10-34J•s)
                          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….
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
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
The Photoelectric Effect(cont.)
   The maximum kinetic energy of an emitted electron is
    determined by the relationship of conservation of
    energy where:                            Work Function

                      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.
The Photoelectric Effect(cont.)
What is the relationship between light intensity and
PE emission?




      Intensity                     Intensity

       (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.
The Photoelectric Effect(cont.)
What is the relationship between the frequency of
the photon and PE emission?

                                               Slope = h



      Frequency                    Frequency
                  Threshold
       (a)        Frequency         (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.
The Photoelectric Effect(cont.)
    Cathode
                                          E
                        Photoelectron         Anode
                    -     E = hf - hfo

                        Photon
                    E = hf = hc/              _
                                          E
      +

 Note: for an electron to reach the anode, it must have
 a sufficient amount of kinetic energy.
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
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.
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
                                        This is
    1 eV = 1.60 x   10-19   J           Important!!
Wave-Particle Duality of Light
   Einstein’s 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/λ

   The fact that a photon can have momentum
    again implies that it has particle properties.
        *Momentum,   p = mass x velocity
Wave-Particle Duality of Light
The Compton Effect (1922):                 E = ½ mve2
                                           p = mve
                                            -
                          Collision


Incident Photon = X-ray               -

              Momentum
              p = hf/c
              E = hf
Conservation of Energy & Momentum:
The energy and momentum gained by the       E = hf ’
electron equals the energy and momentum     p = hf ’/c
lost by the photon.
                     hf/c – hf ‘/c = mve
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.
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/λ
                λ = h/mv
                Where:
                      λ = de Broglie wavelength
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.
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.
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).
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.

				
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