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The Pickering series (also known as the Pickering–Fowler series) consists of three lines of singly ionised
helium Helium (from ) is a chemical element; it has chemical symbol, symbol He and atomic number 2. It is a colorless, odorless, non-toxic, inert gas, inert, monatomic gas and the first in the noble gas group in the periodic table. Its boiling point is ...
found, usually in absorption, in the spectra of hot stars like
Wolf–Rayet star Wolf–Rayet stars, often abbreviated as WR stars, are a rare heterogeneous set of stars with unusual spectroscopy, spectra showing prominent broad emission lines of ionised helium and highly ionised nitrogen or carbon. The spectra indicate very ...
s. The name comes from Edward Charles Pickering and Alfred Fowler. The lines are produced by transitions from a higher energy level of an electron to a level with principal quantum number ''n'' = 4. The lines have wavelengths: *10124 Å (''n'' = 5 to ''n'' = 4) (infrared) *6560 Å (''n'' = 6 to ''n'' = 4) *5412 Å (''n'' = 7 to ''n'' = 4) *4859 Å (''n'' = 8 to ''n'' = 4) *4541 Å (''n'' = 9 to ''n'' = 4) *4339 Å (''n'' = 10 to ''n'' = 4) *3645.56 Å (''n'' = ∞ to ''n'' = 4, theoretical limit, ultraviolet) The transitions from the even-n states overlap with
hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
lines and are therefore masked in typical absorption stellar spectra. However, they are seen in emission in the spectra of Wolf-Rayet stars, as these stars have little or no hydrogen. In 1896, Pickering published observations of previously unknown lines in the spectra of the star Zeta Puppis. Pickering attributed the observation to a new form of hydrogen with half-integer transition levels. Fowler managed to produce similar lines from a hydrogen–helium mixture in 1912, and supported Pickering's conclusion as to their origin.
Niels Bohr Niels Henrik David Bohr (, ; ; 7 October 1885 – 18 November 1962) was a Danish theoretical physicist who made foundational contributions to understanding atomic structure and old quantum theory, quantum theory, for which he received the No ...
, however, included an analysis of the series in his 'trilogy' on atomic structure and concluded that Pickering and Fowler were wrong and that the spectral lines arise instead from singly ionised
helium Helium (from ) is a chemical element; it has chemical symbol, symbol He and atomic number 2. It is a colorless, odorless, non-toxic, inert gas, inert, monatomic gas and the first in the noble gas group in the periodic table. Its boiling point is ...
, He+. Fowler was initially skeptical but was ultimately convinced that Bohr was correct, and by 1915 "spectroscopists had transferred he Pickering seriesdefinitively rom hydrogento helium." Bohr's theoretical work on the Pickering series had demonstrated the need for "a re-examination of problems that seemed already to have been solved within classical theories" and provided important confirmation for his atomic theory.


Wavelength formula

The energy differences between levels in the Bohr model, and hence the wavelengths of emitted or absorbed photons, is given by the Rydberg formula: \frac = Z^2 R_M \left( \frac - \frac \right) where For helium, Z=2, the Pickering-Fowler series is for n_1=4 and the reduced mass for _2^4\text^ is \mu=\frac thus \frac=\frac\approx 0.99986396 , which is usually approximated as 1 (in fact, although this number changes for each isotope of helium, it is approximately constant). A more accurate description may be used with the Bohr–Sommerfeld model of the atom. The theoretical limit for the wavelength in the Pickering-Fowler is given by: \lambda_\infty^\text = \frac, which is approximatedly 364.556 nm, which is the same limit as in the Balmer series ( hydrogen spectral series for n_2=2). Notice how the transitions in the Pickering-Fowler series for n=6,8,10 (6560Å ,4859Å and 4339Å respectively), are nearly identical to the transitions in the Balmer series for n=3,4,5 (6563Å ,4861Å and 4340Å respectively). The fact that the Pickering-Fowler series has entries inbetween those values, led scientist to believe it was due to hydrogen with half transitions ("half-hydrogen"). However, Niels Bohr showed, using his model, it was due to the singly ionised helium _2\text^{+}, a hydrogen-like atom. This also shows the predictability of Bohr model.


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PROTO-HYDROGEN
Astronomical spectroscopy Helium