abstract-eckert – Niels Bohr Archive

Michael Eckert, Deutsches Museum, Germany
Extending Bohr: Sommerfeld's early atomic theory, 1913-1916

Arnold Sommerfeld's response to Bohr's atomic model is reviewed from the perspective of Sommerfeld's personal research agenda. He admired Bohr's derivation of the Rydberg formula for hydrogen but was otherwise critical about the model. In 1913, Sommerfeld attempted to explain the recently discovered Paschen-Back-effect by generalizing Lorentz's classical theory of the Zeeman effect. The discovery of the splitting of spectral lines in an electric field (Stark effect) entered his agenda as another challenge. In both cases the classical approaches finally failed, so that Sommerfeld resorted to Bohr's model as an alternative. He extended Bohr's model by quantizing both the azimutal and radial motion of the electron around the nucleus. In the non-relativistic case he recovered Bohr's Rydberg formula (now with a sum of two quantum numbers instead of a single one as in Bohr's model); in the relativistic case he obtained what became known as the fine-structure-formula. Although the development  from the Bohr- to the Bohr-Sommerfeld-theory has been the subject of detailed historical accounts, the dynamics of this process appears in a new light when described mainly from the perspective of Sommerfeld's private and professional correspondence.