Properties of Light

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Atomic Structure
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X-ray Spectrum
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Atomic Structure

• Atoms have electrons in energy levels of
  increasing energy
• outer electrons are removed more easily than the
  inner electrons
• consider an electron of kinetic energy K passing
  close to an atom
• a collision in which the electron loses kinetic
  energy which appears as the energy hf of a photon
  which radiates away from the atom
• x-rays are emitted ( bremsstrahlung)
• there is a minimum wavelength. Why?

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X-ray spectrum

• If electron loses all its energy, eVaccel
  hfmax hc/?min
• ?min is independent of the material and depends
  only on KE of electrons
• note that if h0, then ?min hc/eVaccel
  would be zero!
• the peaks at larger ? depend on the material
• arise when the incident electron knocks out an
  inner electron
• this leaves a hole in an inner shell which is
  filled by an outer electron with the emission of
  an x-ray photon

Note K? K? lines
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M shell gt n3
L shell gt n2
K shell gt n1
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Moseley Plot

• Moseley (1913) measured characteristic x-rays of
  as many elements as he could find at the time
• he found that he could order the elements by
  atomic number Z rather than by atomic weight
  (i.e. increasing number of electrons)
• for the K? he plotted the square root of
  frequency vs position in periodic table and found
  a straight line
• data could be fit to

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Bohr Theory

• Characteristic x-ray spectrum identifies elements
• depends on Z which determines the chemical
  properties
• K-shell electrons are close to nucleus
• visible spectrum involves transitions of outer
  electrons
• Bohr theory works for hydrogen but not
  multi-electron atoms
• however it works well for the Moseley plot
• consider an L-electron (n2 level) about to make
  a transition to the K-shell which now only has
  one electron left
• L electron sees a net charge of Ze (-e)
  (Z-1)e
• more precise calculations find (Z-b)e where b1
• Bohr theory for a transition ?E between n2 and
  n1 levels

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Bohr Theory

• Replace Z by (Z-b) (Z-1)

• Agrees fairly well with the experimental data for
  K-lines
• does not work well for L-lines
• need quantum mechanical treatment
• does not work well at higher values of Z

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Properties of Light

• Sunlight is composed of many wavelengths

Continuous visible spectrum
Line spectra from H, He, Ba, Hg
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Photon-Atom Interactions
Energy of photon too small f f
Scattered photon has f lt f
hf just matches ?E
Atom excited to higher level and makes several
transitions
Electron escapes and photon absorbed
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Photon-Atom Interactions
Much higher energy and a photon is emitted
Atom in excited state and hf matches ?E
Outgoing photon is in phase with incident photon
and in same direction gt more photons!
Light from different atoms is coherent
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Incoherent and not monochromatic
Incoherent and monochromatic
Coherent and monochromatic
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Lasers

• Light amplification by stimulated emission of
  radiation
• produces a beam of coherent photons by stimulated
  emission

laser
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Ruby Laser
Normally all atoms are in the ground state E1
For the laser to work, we need more atoms in an
excited state --gt called population
inversion
Optical pumping is used to excite electrons to
higher levels which then relax to the state E2
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Particle picture
Wave picture
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lasers