The Sodium Doublet
The magnitude of the spin-orbit interaction has the form mzB = mBSzLz. In the case of the sodium doublet, the difference in energy for the 3p3/2 and 3p1/2 comes from a change of 1 unit in the spin orientation with the orbital part presumed to be the same. The change in energy is of the form DE = mBgB = 0.0021 eV where mB is the Bohr magneton and g is the electron spin g-factor with value very close to 2. This gives an estimate of the internal magnetic field needed to produce the observed splitting: mBgB = (5.79 x 10-5 eV/T)2B = 0.0021 eV B = 18 Tesla This is a very large magnetic field by laboratory standards. Large magnets with dimensions over a meter, used for NMR and ESR experiments, have magnetic fields on the order of a Tesla.
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Index Other spectra References Thornton & Rex Sec 9.2 Serway, Moses, Moyer Sec 8.3 | ||||
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The Sodium Zeeman EffectThe sodium spectrum is dominated by the bright doublet known as the Sodium D-lines at 588.9950 and 589.5924 nanometers. From the energy level diagram it can be seen that these lines are emitted in a transition from the 3p to the 3s levels.
The size of the magnetic energy contribution depends upon a geometrical factor called the Lande' g-factor. The values for the relevant quantum numbers and the associated values for the Lande' g-factor are shown in the table below.
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Sodium Zeeman Effect: Early ObservationsThe splitting of the sodium doublet in the presence of an external magnetic field was observed by Pieter Zeeman in 1896, and the effect was subsequently named the Zeeman effect. It is remarkable that so much detailed spectroscopy was done long before the Bohr theory, and perhaps even more remarkable that Zeeman's first study of the sodium Zeeman splitting was done the year before J. J.Thomson's discovery of the electron in 1897. After Thomson's work, Zeeman and Lorentz did further study of the influence of magnetic fields on the spectral emissions from atoms. By analysis of the splitting of the sodium doublet, they were able to demonstrate that the charge to mass ratio of the charge responsible for the splitting was the same as Thomson's electron. This was the first direct demonstration that electrons were involved in the production of the spectral line emissions. |
Index Reference Leighton Ch 2 | ||
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