First step toward the Quantum, Light in a Box. Take a box, in thermal equilibrium at a certain temperature, hot enough so that we can observe the light coming out of a little hole. Think oven.

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• First step toward the Quantum, Light in a Box.
  Take a box, in thermal equilibrium at a certain
  temperature, hot enough so that we can observe
  the light coming out of a little hole. Think
  oven.
• Along x, p waves, p1,2,3
• Along y, q waves, q1,2,3...
• Along z, r waves, r1,2,3
• these are the normal modes of Maxwell wave
  equation. All have same average thermal energy
  for given temperature.

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• Thermal equilibrium has quite a long history
  thermodynamics and statistical theory of gases
  etc. Hard to escape that each degree of freedom
  must have the same average energy.
• We look at the inside of the box through the
  little hole as we heat the oven,
• dull red, cherry red, bright red, yellow,
  white-hot, bluish, etc.
• but p, q, and r go up to infinity, more shorter
  and shorter wavelengths, or wavenumbers kx ky kz
  each go to infinity.
• The number of ks increases like the volume of a
  sphere, so they crowd to big values, predict most
  light is very blue.

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• We said very blue violet comes after blue in
  the spectrum, so the prediction that the spectrum
  is crowded toward the short wavelengths was
  called the ultraviolet catastrophe
• Of course, there cant be a catastrophe
  something must save us! Once again, it is
  Maxwell vs. some other sacred belief. Last time
  it was Maxwell vs. Newton. Newton lost. Now it
  is Maxwell vs. equipartition.

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• Planck thought this was a weird condition. It
  was soon seen (by Einstein) that this explains
  lots of other things too. The specific heat of a
  gas of hydrogen molecules, H2 is rather strange
  ( amount of energy to increase temperature by
  one degree)
• explained by needing kT at least enough to equal
  the energy of translation, rotation, vibration of
  the molecule

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• Photoelectric effect photons are
  real!---Einsteins first home-run. (Photon is
  a term to describe the quantum of light.) The
  experiment, in a vacuum illuminated by a selected
  wavelength of light illuminating a clean metal
  surface

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• What would we expect? We are kicking electrons
  out of the metal. They didnt just fall out, so
  they must be bound. Model binding by a spring,
  which we have to break to get the electron out.
  The electric field of the light wiggles the
  electron, pumping in energy until we break the
  spring. Expect
• there is a threshold in light intensity to get
  electrons and the kinetic energy goes up with
  light intensity
• any wavelength will do, low frequencies more
  effective
• it takes a long time (seconds to hours) to free
  the electrons

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• What is seen
• electrons come instantly when light is turned on
• there is no threshold in light intensity, and
  kinetic energy of the electrons independent of
  light intensity
• there is a threshold in the frequency of the
  light to get any electrons, only the short
  wavelengths are effective, depending on the
  choice of metal (its work function W)
• Big, big discrepancy. Einstein saw all would
  become clear if the quantum of light was really a
  particle, the photon, with energy
• E?hf

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• Typical experiment results

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• The Einstein theory
• It gives us everything we need, with precision
  agreement with the black body Planck fit.

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• Quick revisit of how we know that light is a wave
  (after all, Newton had decided that light was
  particles moving with c) Thomas Young (1801)
  was skillful enough to see interference from two
  slits
• a recent improvement is a fast switch that can
  send light from one slit to a detector,
• after it has gone through the slit

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• Compton said, lets use a wave-type device to
  choose light (waves) of a given wave length and
  then scatter them from an electron, a billiard
  ball-type experiment, and then make another
  wave-type measurement to see if we can predict
  their new wavelength, if they still have one

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• For the electron, the lightest particle around to
  scatter from,
• Compare to 500 nm for light, so not much effect
  for visible light. We need light of wavelength,
  say 0.02 nm, to get a big effect. Light of this
  wavelength we call X-rays discovered by
  Roentgen in 1895. They can be nicely diffracted
  by the planes of atoms in a crystal, and that is
  how Compton supplied the wave-type measurement
  before and after scattering.

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• For just now, we can summarize the wave-particle
  puzzle by saying that when we do a wave-type
  experiment, light behaves like a wave. When we
  do a particle-type experiment, light behaves like
  a particle. When the two are combined, as in the
  Compton scattering experiment, the behavior of
  the light switches back and forth according to
  the demands made on it by the actual apparatus
  used. The key new point here is the fact that
  the measuring apparatus seems to affect the
  physical system, instead of just recording some
  pure reality.

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• A look at atoms, with the quantum in mind.
• Surely there is charge in atoms, and the nature
  of the electron was clarified by J.J. Thompson,
  measured e/m and Milliken, measured e electrons
  are light.
• Excited atoms give off definite frequencies of
  light, so something is ringing like a bell. It
  will be the light parts that are moving, the
  electrons. What is the structure? Plum Pudding
  model

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• Breakthrough! Rutherford calculated the small
  deflection an alpha particle (Helium nucleus from
  a radioactive element) passing through a very
  thin foil of a heavy element (gold)
• The angles are expected to be small, because the
  positive charge is spread out so the field is
  relatively small, and while the negative charge
  is assumed to be concentrated on the electrons,
  the mass of the electron is 8000 times smaller
  than that of the Helium, so it cant push the
  alpha around much at all. Rutherford designed
  an experiment to look at these small angles.

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• In Rutherfords words It was as incredible as if
  you fired a 15-inch shell at a piece of tissue
  paper and it came back and hit you.
• He could calculate that the only way this could
  happen was if all the positive charge of the atom
  was concentrated in a clump no more than 1/10,000
  the diameter of the atom. He called this the
  nucleus, and started to study it.
• Meanwhile, this leaves us with puzzles about the
  structure of the atoms. What keeps the electrons
  from falling in to all that positive charge?
  Planetary motion you would think, but moving
  electrons radiate about 1 of their energy per
  turn. (Maxwell)

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• Bohr saw that the quantum concept could be the
  answer, and he knew too, that he didnt know
  enough to make a true model, so he tried
  something provisional, rather a new style. His
  propositions
• 1. Use Newtons Laws to calculate dynamics
• 2. Electrons can only exist is certain special
  orbits called stationary states.
• 3. The angular momentum L of the electrons
  moving around the nucleus is quantized in units
  of h/2? defined as the symbol ? pronounced h
  bar, or L n? .
• 4. When the atom makes a transition, between two
  states different by ??E, ??E?f the famous
  quantum jumps.

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• The calculation is simple

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• The energy of the atom is the sum of the kinetic
  energy and the potential energy