Note
Date: June 21, 2012
Brief History of Rydberg Constant by Dan Petru Danescu, e-mail: [email protected]
Keywords: Rydberg constant, Bohr theory, double helix of magnetic field, fundamental physical constants.
Contents: 1. Title page 2. Timeline. 4. References. 5. Sheet 1 « From electrostatics interaction to the Bohr theory » 6. Sheet 2 «An interpretation of Rydberg’s constant ». .
Timeline
• 1666 : Isaac Newton [1] demonstrated that sunlight was composed of continuous series of colors. Newton introduced the word « spectrum » to describe this phenomenon.
• 1752 : T. Melville of University of Glasgow, Scotland, was the first to observe discrete spectral lines [2].
• 1853-1855 : A.J. Angstrom and others developed the phenomenon of discrete emission lines (flame emission spectroscopy), [3].
• 1885 : Analyzing the spectral lines of hydrogen J.J. Balmer [4] established the following empirical relationship
m 2 = KB . (1) m 2 n 2
−8 for n = 2, KB ( Balmer’s constant) = 3645.6×10 cm, and m = 3, 4, 5, 6, and so forth.
• J.R. Rydberg in 1890 [5], modified the Balmer formula to include all spectral series of lines for the hydrogen atom,
1 1 1 = R∞ . (2) λ n 2 m2
This relation is known in scientific literature as the Rydberg formula. The « Rydberg constant » ( R∞ ) describes the inverse wavelengths or frequencies of light (R∞c) in various series of related spectral lines, such as those emitted by hydrogen atoms. The value of this constant is based on the assumption that the nucleus of the hydrogen atom emitting light is very massive compared with a single orbiting electron. Symbol ∞, attached Rydberg constant, means just that.
• N. Bohr in 1913 [6] deduced theoretically constant R∞ based on its atomic model. -10 17 -27 Using constants e = 4.7×10 esu, e/me = 5.31×10 esu/g, h = 6.5× 10 erg.s, result
2 4 2π mee 15 (R∞c=) = 3.1×10 Hz. (3) h3 and
15 10 5 -1 R∞= 3.1×10 / 3×10 =1.03×10 cm (4)
2
• A. Sommerfeld in 1919-1922 [7] calculated constant with high accuracy,
m -1 R∞ = RH ( 1+ ) =1.09737.11 ± 0.06 cm (5) mH
-1 (RH = 109677.691 ± 0.06 cm and mH/m = 1847).
• R.T. Birge in 1929 [8] calculated constant value,
-1 R∞ =109737.42±0.06 cm (6)
• 2008 : CODATA recommanded the following values of the Rydberg constants [9],
-1 R∞ = 10 973 731.568 539(55) m ; (7)
15 R∞c = 3.289 841 960 364(17)×10 Hz ; (8)
R∞hc = 13.605 692 53(30) eV ; (9)
-18 R∞hc = 2.179 872 171(96)×10 J . (10)
•In the period 2010-2011 D.P. Danescu proposed a new interpretation of Bohr's theory [10], [11]. Considering quantification as a property of double helix of magnetic field (Sheets 1 and 2) wavelength that occurs is even Rydberg constant inverse.
3
References
[1] Isaac Newton, (1672), “New Theory about Light and Colors”, Philosophical Transactions of the Royal Society, No. 80, pp. 3075-3087. [2] T. Melville, (1752), Lecture entitled “Observations on light and colours” to the Medical Society of Edinburg. [3] A.J. Angstrom, (1855) «Optiska undersokningar » Philosophical Magazine, 9, 327- 342. [4]. J. J. Balmer, (1885), "Notiz uber die Spectrallinien des Wasserstoffs", Annalen der Physik 261 (5): 80–87. [5] J. R. Rydberg, (1890), « Research on the Structure of the Emission Spectra of the Chemical Elements » Kongl. Svenska Vetenskaps Akademians Handlin-gar, Vol. 23, (Stockholm), No. 11. [6] N. Bohr, (1913), « On the Constitution of Atoms and Molecules », Philosophical Magazine 26, 1-24. [7] A. Sommerfeld, (1919), « Atombau und Spektrallinien », Friedrich Vieweg und Sohn, Braunschweig. [8] R.T. Birge (1929), « Probable Values of the General Physical Constants », Phys. Rev. Supp., Vol.1, No.1. [9] P. J. Mohr, B. N. Taylor, and D. B. Newell, (2008), Rev. Mod. Phys. 80(2), 633-730. [10] D.P. Danescu, (2010), « From the Bohr Theory to Modern Atomic Quantum Theory and the Double Helix of Magnetic Field », General Science Journal, Internet. [11] D.P. Danescu, (2011), « About the Atom Vector Model » , General Science Journal, Internet.
4 Sheet 1 From electrostatics interaction to the Bohr’s theory
5
Sheet 2 An interpretation of Rydberg’s constant
6