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Pickering series

The transitions from the even-n states overlap with hydrogen 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.^[3] Pickering attributed the observation to a new form of hydrogen with half-integer transition levels.^[4][5] Fowler managed to produce similar lines from a hydrogen–helium mixture in 1912, and supported Pickering's conclusion as to their origin.^[6] Niels Bohr, however, included an analysis of the series in his 'trilogy'^[7][8]onatomic structure^[9] and concluded that Pickering and Fowler were wrong and that the spectral lines arise instead from singly ionised helium, He⁺.^[10] Fowler was initially skeptical^[11] but was ultimately convinced^[12] that Bohr was correct,^[7] and by 1915 "spectroscopists had transferred [the Pickering series] definitively [from hydrogen] to helium."^[1][13] 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.^[1]

Wavelength formula[edit]

The energy differences between levels in the Bohr model, and hence the wavelengths of emitted or absorbed photons, is given by the Rydberg formula:^[14]

${\displaystyle n_{1}}$ is the principal quantum number of the lower energy level,

${\displaystyle n_{2}}$ is the principal quantum number of the upper energy level, and

${\displaystyle R_{M}}$ is the Rydberg constant for a nucleus of mass ${\displaystyle M}$. It follows ${\displaystyle R_{M}={\frac {\mu }{m_{e}}}R_{\infty }}$ with ${\displaystyle \mu }$ the reduced mass of the nucleus and ${\displaystyle R_{\infty }={\frac {m_{e}{q_{e}}^{4}}{64\pi ^{3}{\varepsilon _{0}}^{2}\hbar ^{3}c}}}$isRydberg constant.

For helium, ${\displaystyle Z=2}$, the Pickering-Fowler series is for ${\displaystyle n_{1}=4}$ and the reduced mass for ${\displaystyle {}_{2}^{4}{\text{He}}^{+}}$is${\displaystyle \mu ={\frac {1}{{\frac {1}{m_{e}}}+{\frac {1}{2m_{p}+2m_{n}}}}}}$ thus ${\displaystyle {\frac {\mu }{m_{e}}}={\frac {1}{1+{\frac {m_{e}}{2m_{p}+2m_{n}}}}}\approx 0.99986396}$, which is usually approximated as ${\displaystyle 1}$ (in fact, although this number changes for each isotope of helium, it is approximately constant). A more accurate description may be used with the Sommerfeld model of the atom.

The theoretical limit for the wavelength in the Pickering-Fowler is given by: ${\displaystyle \lambda _{\infty }^{\text{PF}}={\frac {4}{R_{\infty }}}}$, which is approximatedly 364.556 nm, which is the same limit as in the Balmer series (hydrogen spectral series for ${\displaystyle n_{2}=2}$). 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 ${\displaystyle {}_{2}{\text{He}}^{+}}$, a hydrogen-like atom. This also shows the predictability of Bohr model.

See also[edit]

• Hydrogen spectral series
• Rydberg formula
• Bohr model
• Sommerfeld model

References[edit]

External links[edit]

• PROTO-HYDROGEN