Fundamental series

{{Short description|Series of lines in atomic spectra}}

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.{{cite journal|last1=Saunders|first1=F. A.|title=Review of Recent Work on the Series Spectra of Helium and of Hydrogen|journal=Astrophysical Journal|date=August 1919|bibcode=1919ApJ....50..151S|volume=50|page=151|doi = 10.1086/142490 |doi-access=free}} 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.{{cite book|last1=Brand|first1=J. C. D.|title=Lines of Light|date=24 Nov 1995|publisher=CRC Press|page=135|url=https://books.google.com/books?id=sKx0IBC22p4C&pg=PA135|isbn=9782884491631}} Bergmann observed lithium at 5347 cm⁻¹, sodium at 5416 cm⁻¹ potassium at 6592 cm⁻¹. 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.{{cite journal|last1=Runge|first1=Carl|title=The Spectra of the Alkalies|journal=Astrophysical Journal|date=December 1907|volume=27|pages=158–160|bibcode=1908ApJ....27..158R|doi = 10.1086/141538 }} Carl Runge called this series the "new series". He predicted that the lines of potassium and rubidium would be in pairs. 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.{{cite journal|last1=Hicks|first1=W. M.|title=A Critical Study of Spectral Series.-Part I. The Alkalies H and He|journal=Philosophical Transactions of the Royal Society of London A|date=9 December 1909|volume=210|issue=459–470|pages=57–111|jstor=90988|doi=10.1098/rsta.1911.0003|doi-access=free}}

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.{{cite book|last1=Candler|first1=A. C.|title=Atomic Spectra and the Vector Model: Volume 1|date=1937|publisher=Cambridge University Press|location=Cambridge, UK|isbn=9781001286228|page=22|url=https://books.google.com/books?id=SWw3AAAAIAAJ&pg=PA22|accessdate=28 August 2015}} The fundamental series was described as badly-named.{{cite journal|last1=Fowler|first1=A.|title=Spectra and atoms|journal=Journal of the Chemical Society (Resumed)|date=23 February 1928|pages=764–780|doi=10.1039/JR9280000764|s2cid=37856069 |url=http://pubs.rsc.org/en/content/articlelanding/1928/jr/jr9280000764|url-access=subscription}} {{subscription required}} It is the last spectroscopic series to have a special designation. The next series involving transitions between F and G subshells is known as the FG series.

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

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

R is the Rydberg constant, $T\_\{BS\}=\backslash frac\{R\}\{\backslash left[\; 3+d\backslash right]^2\}$ is the series limit, represented by 3D, and $\backslash frac\{R\}\{\backslash left[\; m+f\backslash right]^2\}$ is represented by mF. A shortened formula is then given by $\backslash nu=3D-mF$ with values of m being integers from 4 upwards. 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.

The terms can have different designations, mF for single line systems, mΦ for doublets and mf for triplets.{{cite journal|last1=Saunders|first1=F. A.|title=Some Recent Discoveries in Spectrum Series|journal=Astrophysical Journal|date=1915|volume=41|page=323|bibcode=1915ApJ....41..323S|doi = 10.1086/142175 }}

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.{{cite book|last1=Herzberg|first1=Gerhard|title=Atomic Spectra and Atomic Structure|publisher=Courier Corporation|url=https://archive.org/details/in.ernet.dli.2015.202294|page=[https://archive.org/details/in.ernet.dli.2015.202294/page/n74 56]|isbn=9780486601151|date=January 1944}}