Classical Harmonic overtones observed in Zinc emission line spectra

 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 1178 and 308 angstroms. And that these two lines are from a Balmer or Paschen like series respectively for zinc. With each of these two fundamental wavelengths generating either a Paschen or Balmer like series for zinc and matched to strong emission lines in the zinc spectra 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 

Stern Gerlach experiment 1922

In the original 1922 Stern Gerlach experiment the single horizontally propagating incident beam was split into two ‘up’ or ‘down’ diverging beams. An observation not consistent with predictions of the time which were that the path deflection angles in a classical model should be deflected up or down in only an even range of angles. Here it is proposed that net translational forces on a dipole in an inhomogeneous field can correctly model the observed split paths for a classical model. In that the dipoles will initially experience a range of very small path deflections via the up or down net translational forces on them as they enter the apparatus. A deflection force dependent upon the specific angle of the N-S axis of polarity of each incident dipole relative to the applied external N-S field in the apparatus. This separation of the beam into 2 paths, one up and one down is effectively a classical version of the “space quantisation” often referred to in QT. After entering the field, the dipoles will then have been sorted into two up and down paths as well as each path having a range of these very small different angled path deflections from the horizontal incident path. They will then all each experience an additional amount of net translational forces applied equally on all aligned dipoles as they propagate through the 3.2 cm length of the external field. Separating the 2 up and down sets into two distinct paths.

Introduction

Spin is a theoretical construct that seems to be preventing Quantum theorists from finding simpler solutions to experiments based on classical models only. Here it is proposed that if atoms are treated as magnetic dipoles subject to inhomogeneous magnetic fields, then the Stern Gerlach experiment can be explained sufficiently by a classical model.

We know in the experiment that the incident beam must consist of all angles of dipole polarisations. And so it follows that statistically this must be a 50/50 split. That is half must have their N pole facing up from any angle between horizontal to perpendicular to the beam path. And the other half must have the same range of angles between 0-90 degrees but all with their N pole facing down. And we know separately from experimental observations that a dipole will be repelled if its N pole faces towards the N pole of an external field. Or attracted if its S pole faces the external field’s N Pole. Implying that in a classical model, as it is also expected to do in QT, half of the dipoles will be initially deflected upwards in a range of angles by the external field. And half deflected downwards. Separately there is also a statistical preference for a greater number of dipoles with their N-S dipoles fields facing parallel to the direction of motion of the dipole in a beam.

In accordance with well accepted classical models of net force on dipoles in inhomogeneous fields each atom in the incident beam will experience a path deflection upon entering an inhomogeneous magnetic field depending on each incident atom’s dipole field angle relative to the external field. This path deflection is proportional to the net translational force imposed on the dipole by the inhomogeneous external field of the S -G apparatus. As illustrated in Fig 1, a dipole whose field angle is closest to perpendicular to the inhomogeneous field will receive the least net force. And a dipole oriented with its field parallel to the external field will receive the greatest net up or down force. It is at this moment of entry into the external magnetic field of the apparatus that this range of positive or negative deflections on the dipole paths are effected. And once inside the field, all dipole fields are now aligned N-S with the external field. From which point on a net translational force is then applied equally to all the now aligned dipoles as they pass through the 3.2 cm length of the inhomogeneous magnetic field part of the apparatus. A net up or down translational force which pulls the two “quantised” north south beams of dipoles farther and farther apart in curved paths. With each dipole receiving the same amount of net force up or down as all of the other dipoles. Illustrated in Fig 1 as the curved paths showing the effect of the constant up or down net translational forces on the moving dipoles. This net force eventually separates the beam into 2 North and south paths at the image plane. As is observed in the original S-G experiment. This initial up down range of path splitting of the deflected beams atoms based on incident dipole angles is essentially what is usually referred to as space quantisation in QT.

Separately, it is worth pointing out here that currently no published experiments showing the multiple beam paths predicted for other elements in a S-G apparatus and predicted by Quantum theory has ever been successfully completed. All available reference show that all single element S-G style tests always gave only the same double humped split paths in the image plane as the silver atoms did in the original experiment. Casting serious doubts over the validity of Quantum theory and its failed ‘space quantisation’ multi path predictions for atomic elements other than silver.

Quantisation into Positive or negative paths in a classical model

It is important here to explain in more detail how the beam splitting can be explained classically. In that the even spread of angles of dipole fields in the experiment, as predicted by a Classical model in 1922, can still be made consistent with the observed split paths at the image plane without invoking space quantisation. The answer lies in the fact that after the dipoles have upon entry aligned themselves with the external field, the net translational force up or down on a dipole will be constant for all dipoles travelling in the horizontal beam equally as they pass through the rest of the 3.2 cm of external N-S field. Which means that all angles of paths with up (down) directions will now be pulled up (down) additionally by the same amount of force away from their original horizontal path. Take for example a dipole whose path angle away from the horizontal after entering the field will have been deflected upwards by a very small path deviation of an angle of only 0.00000001 degrees. If one calculates what path deflection that would give after travelling 3.2 cm it would not be measurable. This is also close enough to be statistically considered as zero dipoles in the beam at this angle for the purposes of modelling the experiment. But after it travels through the 3.2 cm of the beam this aligned dipole will also have been subjected to a total additional amount of net up translational force from the external field. And that total would have deflected the dipole up by an additional angle to its path to become measurable. That amount in the Stern Gerlach experiment was observed to be between a 0.1mm to 0.2mm path shift from the original horizontal path. Effectively creating the atom free empty middle band in the image plane in a classical model.

Stage 2 and 3 deflection paths modelled classically

To make stages 2 and 3 also consistent with a classical model one can then assume that after stage 1 as outlined above, all the silver atoms polarities have field directions that match the inhomogeneous field of stage 1. When travelling through the stage 2 inhomogeneous field, which is also in the same magnetic field orientation as stage 1, no splitting of the beam will occur in stage 2. As the beam of silver atoms polarities are now lined up with both the stage 1 and 2 external fields. The beam will only be deflected up towards the stronger N pole of the external field due to net translational forces on each dipole in the beam. And proceed as a single deflected beam to stage 3. In stage 3 the dipole alignment process resets and starts over again to repeat the same splitting process as seen in stage 1. Because the beam entering stage 3 has all its atoms polarities in the beam now aligned at right angles to the applied inhomogeneous field in stage 3. And therefore, all dipoles will have to have their polarities rotated and deflected up or down so as to be re-aligned again to the stage 3 external field. Unfortunately, this purely classical effect seen in stages 2 and 3 is also often misinterpreted in QT as space quantisation.

Summary and conclusion

Upon entry into the inhomogeneous field of the apparatus the incident dipoles experience an initial deflection proportional to the angle between the specific dipole field angle and the direction of the inhomogeneous external field. This sorts the incoming beam into two sets of paths. One up and one down. Each path has a range of deflection angles from the original beam path. Deflections which are still much too small to be measurable at the image plane in Stern Gerlach. It is important to note that at this point all the atoms have also had their dipole field angles re-aligned with the North South external field by rotational force.

What is remarkable is that Quantum theorists then and now have been unable to understand the basics of net translational magnetic effects on dipoles. In that they don’t seem to realise that net force initially separates the dipoles into either up or down paths upon their entry into the external field with a range of net forces proportional to the incident dipole angles. At which point the now aligned dipoles in each set all experience the same total of net translational force from the external field as they continue on through the 3.2 cm path in the apparatus. And it is this net force which further separates the up or down sets to become observable as two separate beams at the other end of the apparatus field. 

Reference

1. The Stern-Gerlach Experiment Translation of: “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld” 2023 Martin Bauer