Physics II

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Physics II

• Crucial Experiments

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Synopsis
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Resumé/Prospectus

• We have spent some time carefully establishing
  the atomic structure of matter and the structure
  of the atom itself.
• Not only do we deal with matter constantly we
  also deal with electromagnetic energy
• We now try to learn what e-m radiation is like

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The Big Differences

• As we delve into this study the big difference
  between our new perspective and that of our
  previous studies will be that not only does
  matter come in discrete lumps, but so does light,
  energy, momentum, angular momentum
• Matter and e-m share another feature they can
  exhibit both particle-like and wave-like
  properties

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Old Quantum Theory

• Blackbody Radiation (1900)
• Photoelectric Effect (1905)
• Compton Effect (1923)
• Bohr Atom (1913)

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Thermal Radiation

• Thermal Radiation
• Based on knowledge that all bodies at non-zero
  temperatures radiate and absorb e-m radiation
• Radiate at all wavelengths is the supposition
• But at different wavelengths intensities vary
• In ordinary materials nature of surface matters

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Kirchhoffs Contribution

• Hypothesized that the intensity distribution
  function of radiation depended only on
  temperature and wavelength (not on the material
  but only on the radiation.)
• Important detail
• Detecting devices cannot measure intensity at a
  single frequency but rather in a narrow box or
  channel of frequencies
• I? f(?,T) (J/m2)/(m.s) or (W/m2) / m

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Absorption/emission

• Emission coefficient
• ?? (W/m2)/m
• Energy emitted per unit time in tiny channel
• Absorption coefficient
• ?? (unitless)
• Fraction of e-m energy absorbed per unit time in
  tiny channel

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Kirchhoffs radiation law

• Clearly, at equilibrium, in an enclosure,the
  whole of radiation absorbed must equal that
  emitted else temperature would rise or fall.
• Kirchhoff tightened this to hold for each narrow
  channel
• Energy radiated by walls in channel energy
  absorbed in that channel
• ??I? ??
• hypothetical radiation with unit absorption
  coefficient at all frequencies is called
  blackbody radiation and also cavity radiation

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Cavity radiation photo

• Note brighter area at hole (near center)

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Kirchhoff and spectra

• Hot gases emit a discrete spectra characteristic
  of that material
• Cool gases viewed against white light produce a
  characteristic absorption spectrum
• Frequencies of emission and absorption spectra
  coincide for like elements
• Hot solids emit continuous radiation
• Atomic interactions in solid blur the
  characteristic frequencies
• Cavity radiation independent of material

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Other features of cavity radiation

• Stefan-Boltzmann Law
• Power per unit area emitted is proportional to
  the fourth power of the absolute temperature
• P/A ?T4
• Derivation uses fact that radiation exerts
  pressure
• Wien displacement law
• The wavelength of the radiation with peak
  intensity is inversely proportional to the
  absolute temperature
• ?pT constant
• Uses Doppler shift produced by a moving mirror

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Planck Curves

• Max Planck (1900)
• Considered a metallic cavity enclosure containing
  radiation in equilibrium with the radiating
  oscillators that compose the wall
• Tried to curve-fit the experimental curves of
  the spectral distribution emerging from the
  cavity
• The physics of the time predicted very different
  curves

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Classical predictions

• While the experimental curves were near zero at
  very low and very high frequencies, (high and low
  wavelengths) classical physics predicted
  divergences at short wavelengths (high
  frequencies)
• The Ultraviolet Catastrophe

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Plancks way out

• Here is a good reference. It is at
• http//spiff.rit.edu/classes/phys314/lectures/plan
  ck/planck.html
• The basic idea was that the interaction of the
  radiation and oscillators of walls was quantized,
  the size of the quantum depending on the
  frequency of the light
• Discontinuity appeared in the interaction

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Planck Curve simulators

• http//www.usask.ca/chemistry/courses/243/links/BB
  R/BBR.html
• http//csep10.phys.utk.edu/guidry/java/blackbody/b
  lackbody.html

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Einstein went further

• In the work for which he received the 1921 Nobel
  prize, Einstein, in 1905, explained the odd
  results of the photoelectric effect experiments
  by generalizing Plancks notion to suggest that
  light (e-m radiation) itself was made up of
  quantized particles (localized lumps) of energy,
  later called photons by G.N. Lewis
• http//hyperphysics.phy-astr.gsu.edu/hbase/mod1.ht
  mlc5

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Photoeffect Java Applets

• http//www.walter-fendt.de/ph11e/photoeffect.htm

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The resulting arithmetic

• Conservation of energy as photon strikes a single
  electron in the metal (and photon disappears) and
  electrons are emitted to form a measurable
  current.
• hf KEmax ?
• KEmax eVS
• h 6.626 0693(11) x 10-34 J s
• h 4.135 667 43(35) x 10-15 eV s

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Compton Effect

• The photoelectric effect uses visible and
  ultraviolet light to impinge on electrons bound
  with the same order of magnitude energy
• Arthur Holly Compton (inventor of the speed bump)
  used X-rays
• X-rays have much higher energy than electrons in
  the target
• Electrons are free

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The main idea

• Compton (and Debye) independently derived the
  equation for the difference in wavelengths
  between the incident X-ray and the secondary
  scattered X-ray by assuming a collision between
  BB like entities -- X-Ray photon and electron.
• Used ideas of special relativity to do so.
• Conservation of energy
• Conservation of momentum

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Java Applets

• http//www.walter-fendt.de/ph11e/photoeffect.htm
• http//www.launc.tased.edu.au/online/sciences/phys
  ics/compton.html

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Experimental Arrangement

• Schematic representation of experiment

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Compton effect data

• Compton Scattering

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Compton wavelength

• ?C h/(mc)
• Some values (CODATA 2002)
• ?C 2.426 310 238(16) x 10-12 m (electron)
• ?C 1.319 590 9067(88) x 10-15 m (neutron)
• ?C 1.321 409 8555(88) x 10-15 m (proton)
• ?C 0.697 72(11) x 10-15 m (tau)