Pickering series

The Pickering series is a spectral series of simply ionized helium (He ⁺ or He II) in the light of the star ζ-Puppis ( Zeta -Puppis , Naos ) discovered in 1896 by the American astronomer Edward Charles Pickering .

Description and explanation

Comparison of the spectral lines

Balmer	Pickering
656.3 nm	656.0 nm
-	541.2 nm
486.1 nm	485.9 nm
-	454.2 nm
434.0 nm	433.9 nm
-	420.0 nm
410.2 nm	410.0 nm

In the Pickering series, every second line roughly corresponds to the Balmer series for hydrogen . The additional wavelengths can also be calculated approximately well with Balmer's equation if half values ​​are used in addition to the natural numbers . Pickering therefore initially suspected a special state of hydrogen, but this could not be confirmed. Niels Bohr found out that the series corresponds to the wavelengths of the emission spectrum of He ⁺ .

Assuming Bohr's model of the atom , which is now outdated, but sufficiently accurate for this purpose, the movement of the nucleus explains why the corresponding lines of the Pickering series and the Balmer series do not exactly match: the nucleus and the electron orbit the common center of mass, which results in a slight change in the Rydberg constant R _∞ .

formula

Wavelengths and numbers

The wave numbers or wavelengths of the Pickering series can be calculated using the following formula: ${\displaystyle {\tilde {\nu }}}$ ${\displaystyle \lambda }$

${\displaystyle {\begin{aligned}{\tilde {\nu }}={\frac {1}{\lambda }}&=R_{\infty }\cdot \left({\frac {1}{2^{2}}}-{\frac {1}{k^{2}}}\right)\\&=4\cdot R_{\infty }\cdot \left({\frac {1}{4^{2}}}-{\frac {1}{n^{2}}}\right),\end{aligned}}}$

in which

• ${\displaystyle R_{\infty }=1{,}0973731534\cdot 10^{7}\,{\mathrm {m^{-1}} }}$is the Rydberg constant and
• ${\displaystyle k={\frac {n}{2}}}$with , so the term in brackets is always greater than zero. If is even, becomes integer, and you get exactly the same terms as in the Balmer series. ${\displaystyle n\in \mathbb {N} _{>4}}$ ${\displaystyle n=5,6,7,\dots ,}$ ${\displaystyle n}$ ${\displaystyle k}$

If you take the core movement into account, the formula changes slightly:

${\displaystyle {\begin{aligned}{\tilde {\nu }}={\frac {1}{\lambda }}&=4\cdot {\frac {R_{\infty }}{1+{\frac {m_{\mathrm {e} }}{M_{\mathrm {He} }}}}}\cdot \left({\frac {1}{4^{2}}}-{\frac {1}{n^{2}}}\right)\\&=4\cdot R_{\mathrm {He} }\cdot \left({\frac {1}{4^{2}}}-{\frac {1}{n^{2}}}\right)\end{aligned}}}$

With

• the electron mass ${\displaystyle m_{\mathrm {e} }}$
• the nuclear mass of helium. ${\displaystyle M_{\mathrm {He} }}$

With the Balmer series, the core mass of hydrogen would have to be used at this point . ${\displaystyle M_{\mathrm {He} }}$ ${\displaystyle M_{\mathrm {H} }}$

Energy of photons

The energy of a photon can be calculated by , where the speed of light in vacuum, and the Planck's constant is. ${\displaystyle E}$ ${\displaystyle E=h\cdot c\cdot {\tilde {\nu }}=h\cdot {\frac {c}{\lambda }}}$ ${\displaystyle c}$ ${\displaystyle h}$

For the Pickering series this results in:

${\displaystyle {\begin{aligned}E&=h\cdot c\cdot 4\cdot R_{\infty }\cdot \left({\frac {1}{4^{2}}}-{\frac {1}{n^{2}}}\right)\\&=4\cdot \mathrm {Ry} \cdot \left({\frac {1}{4^{2}}}-{\frac {1}{n^{2}}}\right)\\&\approx 54{,}4\,\mathrm {eV} \cdot \left({\frac {1}{4^{2}}}-{\frac {1}{n^{2}}}\right).\end{aligned}}}$

In the formula is the Rydberg energy or the ionization energy of hydrogen. ${\displaystyle \mathrm {Ry} =E_{\mathrm {R} }=h\cdot c\cdot R_{\infty }}$

Web links

• Pickering series at student level ( LEIFI )

literature

• Edward Charles Pickering: Stars having peculiar spectra. New variable stars in Crux and Cygnus. Astronomische Nachrichten, Issue 142, pp. 87/88, 1896 ( online October 31, 2010)

• Edward Charles Pickering: The Spectrum of ζ Puppis. The Astrophysical Journal , Volume 5, 1897 ( online October 31, 2010)

• HH Plaskett: The Pickering Series and Bohr's Atom. Journal of the Royal Astronomical Society of Canada , Volume 16, pp. 137-149, 1922 ( online October 31, 2010)

Individual evidence

1. ^ HH Plaskett: The Pickering Series and Bohr's Atom. Journal of the Royal Astronomical Society of Canada, Volume 16, pp. 147, 1922 ( online October 31, 2010).