Hydrogen Balmer Spectrum

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Hydrogen Balmer Spectrum
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Hydrogen Balmer Spectrum
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Splitting of Energy Levels

• Splitting of energy levels results mainly from
  the relativistic and magnetic interaction related
  to angular momentum in the atom.
• The single electron of a hydrogen atom can have
  both orbital and spin angular momentum, and
  various possible combinations of these quantities
  generally have different energies. As a result
  the Bohr energy levels are split into components
  called the fine structure of the levels. A
  subtle effect called the Lamb shift displaces
  certain of the fine-structure components,
  creating additional splittings. Finally, the
  interaction of the electrons magnetic moment
  with that of the nucleus gives rise to a
  hyperfine structure. The fine structure and the
  Lamb shifts are shown here at a larger scale than
  the Bohr levels, and the hyperfine splittings of
  the second and third Bohr levels are shown at
  still greater magnification.

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Background Spin-Orbit Coupling
Nucleus
Electron
Spin
http//www.aacg.bham.ac.uk/magnetic_materials/orig
in_of_magnetism.htm
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Background Fine Structure

• Electron sees multiple B fields
• Zeeman splitting occurs
• Emission can now come from two degenerate
  statesfine structure splitting

Zeeman splitting in hydrogen

• From proton viewpointhyperfine structure
• For hydrogen, split emission results in Balmer
  alpha lines

http//hyperphysics.phy-astr.gsu.edu/hbase/hframe.
html
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Background Fine Structure Constant

• Introduction of the fine structure constant (?)
• Arnold Sommerfield, 1916
• Predicting spectra (Balmer lines in hydrogen)
• Expanding Bohr model
• Relativity
• Elliptical orbits
• Dirac theory used to ? formulate Hamiltonian

http//hyperphysics.phy-astr.gsu.edu/hbase/hframe.
html
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Background The Theory

• The H-atom Hamiltonian

http//www.newscientist.com/article.ns?iddn6092
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Beating Doppler Broadening
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Flame Test
Ca, Sr, Ba
Na, K, Li
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Sodium
Barium
Strontium
Calcium
Iron
Magnesium
Lithium
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Color Figure 23. Four chemoluminescent Cyalume"
light sticks, 15-cm long, made American Cyanamid
Company.