Fundamental series

The fundamental series is a set of spectral lines in a set caused by transition between d and f orbitals in atoms.

Originally the series was discovered in the infrared by Fowler and independently by Arno Bergmann.[1] This resulted in the name Bergmann series used for such a set of lines in a spectrum. However the name was changed as Bergmann also discovered other series of lines. And other discoverers also established other such series. They became known as the fundamental series.[2] Bergmann observed lithium at 5347 cm⁻¹, sodium at 5416 cm⁻¹ potassium at 6592 cm⁻¹.[2] Bergmann observed that the lines in the series in the caesium spectrum were double. His discovery was announced in Contributions to the Knowledge of the Infra-Red Emission Spectra of the Alkalies, Jena 1907.[3] Carl Runge called this series the "new series". He predicted that the lines of potassium and rubidium would be in pairs.[3] He expressed the frequencies of the series lines by a formula and predicted a connection of the series limit to the other known series. In 1909 W. M. Hicks produced approximate formulas for the various series and noticed that this series had a simpler formula than the others and thus called it the "fundamental series" and used the letter F.[1][4]

The formula that more resembled the hydrogen spectrum calculations was because of a smaller quantum defect. There is no physical basis to call this fundamental.[5] The fundamental series was described as badly-named.[6] It is the last spectroscopic series to have a special designation.[6] The next series involving transitions between F and G subshells is known as the FG series.[6]

Frequencies of the lines in the series are given by this formula:

${\displaystyle \nu ={\frac {R}{\left[3+d\right]^{2}}}-{\frac {R}{\left[m+f\right]^{2}}}{\text{, with }}m=4,5,6,...,}$

R is the Rydberg correction, ${\displaystyle T_{BS}={\frac {R}{\left[3+d\right]^{2}}}}$ is the series limit, represented by 3D, and ${\displaystyle {\frac {R}{\left[m+f\right]^{2}}}}$ is represented by mF. A shortened formula is then given by ${\displaystyle \nu =3D-mF}$ with values of m being integers from 4 upwards.[7] The two numbers separated by the "−" are called terms, that represent the energy level of an atom.

The limit of the fundamental series is the same as the 3D level.[5]

The terms can have different designations, mF for single line systems, mΦ for doublets and mf for triplets.[8]

Lines in the fundamental series are split into compound doublets, due to the D and F subshells having different spin possibilities. The splitting of the D subshell is very small and that of the F subshell even less so, so the fine structure in the fundamental series is harder to resolve than that in the sharp or diffuse series.[7]