Classical Harmonic overtones observed in Zinc emission line spectra
Following on from the theoretical proposals outlined in the following paper: ‘Hydrogen spectral series as Harmonic overtones of a single fundamental wavelength’, it can be shown that the observed data from NIST also matches closely to spectral lines for zinc predicted using the same proposed harmonic relationship seen between the various observed Hydrogen emission lines in the Balmer and Paschen Hydrogen spectral series as outlined in the above paper.
(The following are some of the stronger observed zinc emission lines from NIST 2086,2138,2350,2542,2550,2561,2608,2770,2800,3075,3282,3302,3345,3515,3779,3965,4292,4680,4722,4810,6362 Angstroms.)
Introduction
In the above cited paper it is shown that all observed hydrogen spectral lines in the optical spectrum and their respective sets of Lyman, Balmer ,Paschen etc are based on one single fundamental wavelength f. That wavelength for Hydrogen being the Lyman Alpha line. And further that each alpha line from each spectral set within the Hydrogen series has a specific mathematical harmonic relationship with not only the B,C,D,E lines within each set, but also with all other lines from all the other sets observed within the Hydrogen spectral series.
At the end of the above paper it also suggests that as one progresses up through the elements in the periodic table each successively heavier element should therefore have successively more fundamental wavelengths to account for not just its increase atomic number but also the increased complexity of emission spectra lines seen for successively heavier elements. Ie. If Hydrogen has only one fundamental wavelength in optical , Helium will have 2, Lithium 3, etc.
From this theoretical assumption it follows that Zinc must also have multiple fundamental wavelengths. And that two of the strongest observed spectral zinc lines at 4680 and 6362 angstroms can be shown to be alpha spectral lines generated by one or more of Zincs proposed fundamental wavelengths. And that each will also have a matching set of B,C,D,E and limit lines in the Zinc emission spectra. And indeed it can be shown here that the many of the stronger observed optical lines in Zinc do match the mathematical relationship seen also in Hydrogen and specifically in the analysis here with the Hydrogen Paschen and Balmer series. The following calculations show that using this theoretical assumption one can get a reasonably close match between these two Zinc “alpha” lines mentioned above and other stronger observed emission lines seen in the Zinc optical spectra. Confirming that the harmonic relationship between A,B,C,D, E and limit lines for the well known Balmer and Paschen series in Hydrogen series can be also observed between various lines in the Zinc optical emission spectra. The analysis below matches the two Zinc alpha lines of 4680 and 6362 with two separate fundamental wavelengths of 885 and 232 angstroms. And that these two lines are from a Balmer or Paschen like series for zinc. With each of the two fundamental wavelengths generating either a Paschen or Balmer like series for zinc as described below.
Methods
As outlined in table 1 of the above cited paper there is a clear fundamental harmonic relationship between any Alpha line in any of the spectral line sets for hydrogen with the other B,C,D,E and associated limit lines from each respective set.
For instance, if one refers to table 1 in the above cited paper, the Hydrogen Balmer Alpha line at 6563 Angstroms is 1.8 times the Balmer limit line of 3646. And further to this the Hydrogen Balmer B,C,D,E lines are each respectively 1.33,1.19,1.125, and 1.088 times the Hydrogen Balmer limit.
Applying the above formula of the observed relationship between the Hydrogen Balmer and Paschen alpha lines and their respective sets to the strongest lines seen in zinc at 6362 and 4680 gives the following results. Indicating that many of the lines observed in the Zinc optical emission spectra and recorded at NIST, are part of spectral sets that have the same harmonic relationships as the Balmer and Paschen sets have in Hydrogen. Using this same harmonic relationship are the calculations for ‘Balmer and Paschen like’ predicted line sets for zinc:
Paaschen A 4680, B 3258, C 2778, D 2559, E 2350, limit 2088
Balmer A 6362, B 4700, C 4205, D 3976, E 3817, limit 3543.
If one then refers to the observed spectral line data from NIST (and noted above at the beginning of this page) one can see there is a good match between calculated Zinc spectral lines using the proposed fundamental frequency relationship first noted for Hydrogen in the above paper and the observed confirmed strong line data for Zinc from NIST.
Paschen: (Where f is 308 angstroms)
Calculated: 4680, 3258, 2778, 2559, 2350, 2088 (limit)
Observed: 4680, 3282, 2800, 2561, 2350, 2087
Balmer: (Where f is 1178 angstroms)
Calculated: 6362, 4700, 4205, 3976, 3817, 3543(limit)
Observed: 6362, 4700, 4292, 3965, 3779, 3515
*Please note the “observed” line cited above for the predicted ‘Balmer-like’ series for Zinc at 4700 is actually a series of observed spectral lines in Zinc observed between 4680 and 4722 Angstroms in NIST.
Based on the theoretical model proposed in the cited paper in table 1, when applied to the Zinc spectra these calculations also suggest that at least two of Zincs proposed fundamental frequencies f can be calculated as follows. (In that each of zincs fundamental wavelengths is always equivalent to a Lyman alpha line):
Ballmer limit/4 * 1.33 = f frequency 1178 Angstroms (~NIST 1108)
Paschen limit/9 * 1.33 = f frequency 308 Angstroms
