Fine structure

As the fine structure splitting of individual spectral lines into several closely spaced lines is called within the line spectra of atoms. This means that there are energy levels of the respective atom, which are very close together, because each spectral line can be associated with a distance of energy levels.

However, the magnitude of this split is finer as compared to the other levels of about 10,000 times less, because the corrections will with, the atomic number, and α is the fine structure constant. Thus, the change in the wavelengths for the Hα, Hβ and hv - line of the Balmer series for the hydrogen atom only 0.14 Å, 0.08 Å and 0.07 Å ( for comparison is: the wavelength of the Hα line is at 6562.8 Å). This also explains the relatively late discovery of the fine structure by Willis Eugene Lamb, for which he was awarded the 1955 Nobel Prize in Physics.

Origin

The lifting of the degeneracy of the energy levels is a consequence of the Dirac equation of relativistic quantum mechanics. To account for these effects, one adds correction terms to the non-relativistic Hamiltonian of the system and the rest energy of the electron. The Hamiltonian is then, to first order:

The correction terms for the non- relativistic Schrödinger or Pauli equation are:

  • - The relativistic correction to the kinetic energy
  • - The spin -orbit coupling
  • - The Darwin term as a correction to the potential energy

The energy shift, known as a fine structure, then in accordance with

In addition to the fine structure can be observed even finer structures in the spectra: the hyperfine structure, but which is not a relativistic effect, but an interaction between the electron and nuclear spin.

In the hydrogen atom

In the hydrogen atom can be summarized relativistic effects, spin -orbit coupling and Darwin term to the following formula for the correction of the energy levels:

With

  • The energy levels of the hydrogen atom without fine structure the Rydberg energy
  • The atomic number
  • The principal quantum number

This formula gives for each possible and a lowering of the energy.

Swell

  • Atomic physics
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