Sommerfield model

As a final note, closer inspection of the emission lines from Na shows that most emission lines are not, in fact, single lines, but are closely spaced doublets or triplets - for example, the strong yellow line discussed above at 589.3 nm is composed of two separate lines at 589.0 and 589.6 nm. This is termed fine structure, and is not predictable from the Bohr model of the atom. It is addressed in the Bohr-Sommerfield model, and is the result of a quantum mechanical interaction, known as spin-orbit coupling, further discussion of which is not necessary for this volume. 

The DOS at 0 K is shown in Figure 11.18 using the free electron model. However, the Drude-Lorentz model employs the classical equipartition of energy and does not take into account the fact that quantum mechanics places restrictions on the placement of the electrons (as a result of the Pauli exclusion principle). A revised theory, known as the Sommerfield model, allows for this modification. At temperatures above 0 K, the fraction, f(E), of allowed energy levels with energy E follows the... 

German physicist Arnold Sommerfield (1868-1951) modifies Bohr s model of the atom specifying elliptical orbits for the electrons introduces azimuthal and magnetic quantum numbers in addition to the principal quantum number. 

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