A Physical Model for Atoms and Nuclei

Foundations of Science February 2002 Reprint/Internet Article Page 1 http://CommonSenseScience.org

A Physical Model for Atoms and NucleiPart 1 Joseph Lucas and Charles W. Lucas, Jr.

Abstract. A physical geometrical packing model for the structure of the atom is developed based on the physical toroidal ring model of elementary particles proposed by Bergman.[1] From the physical characteristics of real electrons from experiments by Compton [2,3,4] this work derives, using combinatorial geometry, the number of electrons that will pack into the various physical shells about the nucleus in agreement with the observed structure of the Periodic Table of the Elements. The constraints used in the combinatorial geometry derivation are based upon Josephs simple but fundamental ring dipole magnet experiments and spherical symmetry. From a magnetic basis the model explains the physical origin of the valence electrons for chemical binding and the reason why the periodic table has only seven periods. The same geometrical packing model is extended to describe the physical geometrical packing of protons and neutrons in the physical shells of the nucleus. It accurately predicts the nuclear magic numbers indicative of nuclear shell structure as well as suggesting the physical origin of the nuclide spin and the liquid-drop features of nuclides.

Introduction Quantum Mechanics and Relativity Theory form the foundation upon which modern physics rests. Yet some philosophers and scientists object to these very successful theories, because they involve assumptions known to be false and because they are mathematics theories that fail to give a physical understanding of the processes occurring. Both Quantum Mechanics and Relativity Theory are based on the assumption of point-like particles. However, electron scattering experiments, for which Robert Hofstadter [5] received the Nobel Prize in 1961, have shown that neutrons, protons, and other elementary particles have a measurable finite size, an internal charge distribution (indicative of internal structure), and elastically deform in interactions (See Figure 1). The size and shape of the electron was measured by Compton [2, 3, 4] and refined more Most of this paper first appeared IN GALILEAN ELECTRODYNAMICS, Volume 7, Number 1, January/February 1996, and is reprinted by permission.

Figure 1. Charge Density of Proton and Neutron


completely by Bostick [6, 7], his last graduate student. The finite size, internal particle structure, and elastic deformation of shape are ignored by both Quantum Mechanics and Relativity Theory. In modern relativistic quantum theories of the atom and nucleus, it is postulated that the charged electrons and protons move in their respective shell orbits with specific angular momentum about the center of the nucleus without continuously radiating electromagnetic energy. These postulates violate both Amperes and Faradays laws of electrodynamics from which Larmors formula for total power P radiation from a moving charge is derived, i.e.,

( )132 2

3

2

dtdv

ceP =

Larmors formula agrees with all the macroscopic experiments with accelerating charges. It requires all accelerated charged particles to emit radiation continuously while being accelerated. However, radiation from the orbiting electrons and protons in the atom postulated by quantum theory is not observed and violates energy conservation. Quantum models of the atom are unable to show that the forces in the atom are in dynamical equilibrium for S states with zero angular momentum. Normally some angular momentum is needed to give rise to a centrifugal force to balance the electrical Coulomb force attracting the negatively charged electron toward the positively charged nucleus. Otherwise, the Coulomb force causes the electron to fall into the nucleus and annihilate itself with a proton. For S states, quantum mechanics postulates that the negative electron vibrates back and forth through the nucleus without interacting with the positively charged protons. This postulate violates electrodynamics laws without any physical justification. In quantum mechanics the self-field of finite-size elementary particles and their changes due to deformation are ignored. These are real physical and experimentally measurable effects. Quantum theories lead to a 100 percent random basis for events of the physical universe. This is in disagreement with common sense experience and the notion that all effects are produced by some cause. Despite the shortcomings of Quantum Mechanics and Relativity Theory, they have persisted as pillars of modern physics. Their status is due in part to the fact that they yield mathematical formulas that accurately predict many phenomena. Also, no better alternative theories have yet been identified and accepted. This situation has been changed by three events. The first event occurred in 1915 when Ewald and Oseen [8, 9] discovered the extinction effect in electrodynamics. Experimentally they found that when light passes through any media, even the best man-made vacuum, it is absorbed by atoms and re-emitted in such a way that it moves with the


speed of light plus the velocity of the atoms on which it was absorbed. In 1963 Fox [10, 11, and 12] realized that this experimental evidence allowed the famous Michelson-Morley modified Fizeau experiment of 1886 to be explained by classical electrodynamics using the Galilean transformation instead of relativity theory. Basically the extinction effect invalidated the second postulate of Relativity Theory that the speed of light was c in all reference frames. The second event occurred in 1978 when Barnes [13] published his remarkable proof from electrodynamics showing that all the known results predicted by Special Theory of Relativity (STR), i.e. the change in mass of elementary particles with velocity, the change in electromagnetic fields of elementary particles with velocity, and the change in decay half-life with velocity could be predicted exactly from classical electrodynamics of finite-size elastically deformable elementary particles. Once this proof was published, scientists began to realize that Relativity Theory cannot be applied to real physical finite-size elastically deformable elementary particles without always obtaining a bad result. This is due to the fact that electrodynamics is sufficient by itself without help from another theory. The third event occurred in 1990 when Bergman [1] called attention to a successful physical model for the electron, proton, and other elementary particles based on a spinning toroidal ring of continuous charge. This model depicts the electron and the proton as thin rings of charge circulating at the speed of light. The continuous charge in the ring is repulsive to itself due to the Coulomb interaction. This force is exactly balanced by the magnetic pinch effect due to the current in the ring. The balance of electric coulomb and magnetic Lorentz forces determines R, the radius of the ring (See Figure 2). The half-thickness of the ring r is extremely small. Bergman speculates that the electric and magnetic forces on the ring must in general be unequal with the electrical repulsive forces predominating at small radii and the magnetic pinch effect predominating at large radii. Bergman suggests that there are special values of the radius for which the electric and magnetic forces are equal, but no explicit proof of this has been given. Furthermore, Bergman notes that the dynamic radius of an electron closely bound to a proton in a neutron would be significantly smaller than the radius of an electron weakly bound to a distant proton in the hydrogen atom due to the elasticity of the toroidal ring model. Three features of the spinning charged ring model of electrons and protons are especially important to the structure of the atom. The dominating characteristics provided by the ring model are first, the physical size of each particle; second, the magnetic dipole exhibited by each particle; and third, the property that a charged spinning ring, which is surrounded by static electric and magnetic fields, does not radiate continuously.

Figure 2 Spinning Ring Model of Elementary Particles


Plancks constant h, the fundamental constant of quantum mechanics, is derived by Bergman [1] to be

( )28ln2

2

=rR

ceh

o The value of h is determined from the ring structure by the balance of electric and magnetic forces. Since Bergmans model is a physical model, it allows one to predict from first principles Plancks constant h, spin, magnetic moment, mass, and other physical properties of elementary particles. According to the rules of logic employed in science, whenever one theory is able to predict the value of the fundamental constant of another theory and give a physical explanation of it, that theory is automatically superior. Thus Bergmans physical model of elementary particles is superior to and more fundamental than all quantum models. Due to the objections mentioned above to the theories of Quantum Mechanics and Relativity plus the three events also described above, it seemed appropriate that new work be undertaken to develop a new theory of the atom and nucleus based on real physical electrons, protons, and neutrons that have finite size, ring charge structure, and are elastically deformable. The New Model of the Atom The scattering experiments performed by Rutherford showed that the atom consists of a tiny massive nucleus with containing protons and neutrons with the less massive electrons on the outer surface. Amperes law and Faradays law require that the electrons radiate electromagnetic energy continuously if they move in an orbit about the nucleus. Since continuous radiation of the proper frequency for the electron to be orbiting the nucleus is not observed, it is logical to assume from classical electrodynamics that the electrons do not orbit the nucleus. If electrons in the atom do not orbit the nucleus, but rather come to some stable equilibrium distance from it due to the balance of electric and magnetic forces, then it should be possible to predict the way the electrons pack themselves in layers or shells about the nucleus. Finding the structure of the atom should be a problem of geometry. There is a field of geometry, called Combinatorial Geometry that concerns itself with relations among members of finite systems of geometric figures subject to various conditions and constraints. Two of the important topics addressed by Combinatorial

Figure 3 Classic Problem in

Combinatorial Geometry


Geometry are packing and covering. An example of packing is the number of equal sized disks in a plane about a central disk. It is easily seen that six equal circular disks may be placed around another disk of the same size, subject to the constraints that the central disk is touched by all the others and that no two disks overlap (see Figure 3). In the three dimensional case it is possible to place twelve balls (solid spheres) around a given ball, subject to the constraints that all the balls touch the central ball and no two balls overlap. Now in the case of the atom, consisting of a central nucleus with finite size electrons packed about it in layers or shells, one can also use Combinatorial Geometry. In this case, there are additional constraints. The balls or electron rings have a magnetic moment and an electrical attraction to the nucleus or central shell. From observation and general symmetry principles, one assumes that each layer or shell of the atom must be constructed in such a way that the total magnetic moment in each shell sums to zero and the cancellation of the magnetic moments is perfectly spherical, i.e. all great circles that pass through the arrangement of electrons must have the same number of electrons and no magnetic moment. In order to learn more about the magnetic constraints, ceramic ring magnets of 9/8 inch diameter, 1/4 inch thickness, and a 5/16 inch center hole were obtained from Radio Shack for performing key experiments. The north pole of each magnet was painted white. The magnets were then hung by string in a circular ring to determine the equilibrium arrangement. Only a circular ring with an even number of magnets was found to come to equilibrium in a circular arrangement. When the arrangement of magnets with an even number of magnets came to equilibrium, the magnets were oriented such that they precisely alternated the north-south orientation as one proceeded around the ring (see Figure 4). Spherical symmetry implies that no matter which great circles of electrons are packed in a shell, the same precise pattern of alternation of magnetic orientation should exist. This constraint along with the one requiring an even number of magnets in each great circle is sufficient to determine the sizes of each of the packing shells of electrons about the nucleus. Using the method of enumeration, i.e. examining each possible shell size one by one, one finds that the successive shells that satisfy the packing constraints are described by Table 1.

Shell Size Total Electrons

#1 1 great circle of 2 electrons 2 #2 2 great circles of 4 electrons 8 #3 3 great circles of 6 electrons 18 #4 4 great circles of 8 electrons 32 #5 5 great circles of 10 electrons 50

Figure 4 Equilibrium Position of Ring

Magnets in a Circle

Table 1 Shell Sizes that Satisfy

Packing Constraints


An illustration of shell #2 is provided by Figure 5, which shows a filled shell of eight electrons consisting of two groups of four rings each. The principle magnetic flux line for each group is also shown. The spinning charged ring electrons shown in Figure 5 are all located on two great circles (which are not shown). A larger shell of 18 electrons, shell #3 of Table 1, is illustrated by Figure 6. In this arrangement, three groups of six electrons form the filled shell. All the ring electrons are located on three great circles. In order to study the relative magnetic binding strengths of each of these great circle shell sizes, an apparatus was constructed consisting of a wooden board with circular arrangements of 2, 4, 6, 8, 10,... wooden pegs spaced such that ring magnets could be mounted on the pegs while comfortably touching one another in a

circular pattern. One of the pegs was removed from each great circle of magnets, and the force to remove the associated ring magnet was measured. In order to eliminate the effect of friction, the board was held on edge, and the weight on the magnet needed to pull it away from the great circle was measured (including its own weight). Figure 7 illustrates the experimental apparatus. The results of these magnet experiments are shown in Graph 1. The graph shows the relative binding strengths of the various great circle configurations of ring magnets. Note that great circles of four ring magnets are most tightly bound. This suggests that in atoms, the shells of

two great circles of four electrons will be strongly bound, giving rise to valence like effects observed in chemical bonding. Also note that great circle arrangements of ten or more ring magnets show no more inclination to bind in a circular shape than an odd number of ring magnets. From this result, one does not expect shells of 50 electrons or more to be found to exist in the atomic electron shells. Thus the atom should have only 4 electron shell sizes, i.e. 2, 8, 18 and 32 electrons.

Figure 5 Filled Shell of 8 Electrons

Figure 6 Fixed Shell of 18 Electrons

Graph 1 Binding Force per Magnet by Ring Size (Experiment with Board and Magnets)


Additional magnet experiments were performed to obtain a crude measure of the relative binding strength of whole shells. This was done by using two layers of ring magnets for shell size #2, three layers of ring magnets for shell size #3, etc., and measuring the force necessary to remove one stack of ring magnets. The results are shown in Graph 2. The magnet experiments suggest that shells of 18 electrons are most tightly bound and that shells of 32 electrons are slightly less bound than shells of eight.

Additional ring magnet experiments were done to determine how many shells with the same number of electrons might be stable when packed about the nucleus. This is done by forming a great circle of magnets for each shell and arranging them in a concentric manner on a very smooth flat surface. The configuration of two rings is found to be stable when the outer ring has the opposite magnetic orientation of the inner ring next to it. When three or more concentric rings of the same number of magnets are constructed, the configuration is found to be unstable with rings rearranging to form other sizes. Thus the ring magnets like to be oriented in pairs in all directions. This causes two concentric rings of the identical number of magnets to be stable. From an analysis of the electrical forces of attraction or each electron shell with the nucleus and the total binding strength for each shell, the order of the shells is determined by the configuration with minimum energy. For example, the electrical attraction of each magnetic shell with the positively charged nucleus increases with shell size. As a result, a larger shell can displace a smaller shell with fewer charges, provided that the

MagnetsSouth Pole Up

MagnetsNorth Pole Up

Wood Pegs

String

WeightsWeights Weights Weights Weights

PlasticWeight

Container

Wood Board

Figure 7. Experimental Apparatus

Graph 2 Binding Force per Magnet by Shell Size (Experiments with Board and Magnets)


space it occupies is large enough to hold the larger shell. This constraint allows larger shells to displace the second shell of a pair of smaller shells. Taking this into account and noting that the first shell size is paired with the nucleus itself, one obtains the following shell structure for the atom:

Total electrons

Shell electrons

Nucleus at center

K shell

L shell

M shell

N shell

O shell

P shell

Q shell

2 2 N 2 10 8 U 2 8 18 8 C 2 8 8 36 18 L 2 8 18 8 54 18 E 2 8 18 18 8 86 32 U 2 8 18 32 18 8

118 32 S 2 8 18 32 32 18 8

Note the arrows indicating the opposite orientation of the magnetic moments of the electrons in one shell with those of another. The structure shown in Table 2 is identical with that given in the Periodic Table of the Elements. Table 3 shows in detail how the fourth shell displaces the third shell. Conclusions The geometrical packing model presented for the atom is very successful in describing some atomic data. The approach taken here is more fundamental and straightforward than the methods used by quantum mechanics and the special theory of relativity. The new model does not incorporate the philosophically objectionable assumptions of quantum mechanics. It replaces features of quantum models that are known to be inconsistent or in violation of proven laws. Unlike the quantum models, the geometrical packing model is not simply mathematical, but it is a physical model with boundaries, sizes, and structures. In this sense the model satisfies a major goal of physics which is, after all, to describe matter of the physical universe. Although the framework of a new theory of matter has been presented, the basic approach needs to be extended to give successful descriptions of black body radiation, the photoelectric effect, and the energy levels of the atom before it can fully displace the quantum models. (Please note that this work has been successfully completed and published [14]. It will be featured in a future issue.)

Table 2 Distribution of Electrons in Packing Shells


References 1. Bergman, D. L., and Wesley, J. P., Spinning Charged Ring Model of

Electron Yielding Anomalous Magnetic Moment, Galilean Electrodynamics, Vol. 1, no. 5, pp. 63-67 (Sept/Oct 1990).

2. Compton, Arthur H., American Physical Society address December 1917, Physical Review Series II, p. 330 (1918).

3. Compton, Arthur H., Physical Review Series II, Vol. XIV No. 1, pp. 20-43 (1919).

4. Compton, Arthur H., Physical Review Series II, Vol. XIV No. 3, pp. 247-259 (1919).

5. Hofstadter, R., Reviews of Modern Physics, Vol. 28, p. 213 (1956). 6. Bostick, Winston H., Physics of Fluids, Vol. 9, p.2079 (1966). 7. Bostick, Winston H., Mass, Charge, and Current: The Essence and

Morphology, Physics Essays, Vol. 4, No. 1, pp. 45-49 (1991).

Electron Shells

Atomic Atomic 1st 2nd 3rd 4th

Symbol Number Shell Shell Shell Shell

Ar 18 2 8 8 K 19 2 8 8 1 Ca 20 2 8 8 2 Sc 21 2 8 9 2 Ti 22 2 8 10 2 V 23 2 8 11 2 Cr 24 2 8 13 1 Mn 25 2 8 13 2 Fe 26 2 8 14 2 Co 27 2 8 15 2 Ni 28 2 8 16 2 Cu 29 2 8 18 1 Zn 30 2 8 18 2 Ga 31 2 8 18 3 Ge 32 2 8 18 4 As 33 2 8 18 5 Se 34 2 8 18 6 Br 35 2 8 18 7 Kr 36 2 8 18 8

Table 3 Step by Step Buildup of the Fourth Shell


8. Ewald-Oseen, Annealed der Physic (1915). 9. Born and Wolf, Principles of Optics 6th Edition, pp. 71, 101-104 (1955). 10. Fox, J. G., American Journal of Physics, Vol. 30, p. 297 (1962). 11. Fox, J. G., American Journal of Physics, Vol. 33, p. 1 (1965). 12. Fox, J. G., J. Optical Society of America, Vol. 57, p. 967 (1967). 13. Barnes, T. G., Alternatives to Einsteins Special Theory of Relativity,

Physics of the Future, Institute for Creation Research, El Cajon, CA, pp. 88-94 (1983).

14. Lucas, Jr., Charles W. and Lucas, Joseph C., A New foundation for Modern Science, Proceedings of the Fourth International Conference on Creationism (Creation Science Fellowship, Inc., Pittsburgh, PA ) pp. 379-394 (1988).

A Physical Model for Atoms and NucleiPart 2Joseph Lucas and Charles W. Lucas, Jr.

Abstract. A physical Geometrical Packing Model for thestructure of the atom is developed based on the physicaltoroidal ring model of elementary particles proposed byBergman [1]. From the physical characteristics of realelectrons from experiments by Compton [2, 3, 4] this workderives, using combinatorial geometry, the number of electronsthat will pack into the various physical shells about the nucleusin agreement with the observed structure of the Periodic Tableof the Elements.

The constraints used in the combinatorial geometry derivationare based upon Josephs simple but fundamental ring dipolemagnet experiments and spherical symmetry. From amagnetic basis the model explains the physical origin of thevalence electrons for chemical binding and the reason why theperiodic table has only seven periods.

The same Geometrical Packing Model is extended to describethe physical geometrical packing of protons and neutrons in thephysical shells of the nucleus. It accurately predicts the nuclearmagic numbers indicative of nuclear shell structure as well assuggesting the physical origin of the nuclide spin and the liquid-drop features of nuclides.

New Model of the Nucleus

In the first part of this paper a new model of the atom, based on ring electrons, waspresented in terms of physical geometrical packing under the constraints of sphericalsymmetry and some experimental results for ring dipole magnets. Due to the success ofthis model over competing models, such as the Quantum Model, it seems only natural toattempt to apply it to the packing of nucleons in the nucleus. Bergmans SpinningCharged Ring Model for elementary particles indicates that the structure of the proton isalso a toroid like that of the electron, except that it has a much smaller radius in freespace and the charge is of opposite sign.

According to traditional physics, the nucleus contains two types of particles: protons andneutrons. Outside of the free nucleus, the neutron is unstable and decays into an electronand a proton with a half-life of about 13 minutes. According to Bergmans model, theneutron is not a legitimate elementary particle; rather it is really a bound combination ofan electron and proton. Thus, in extending the physical packing model to the nucleus, itwill be necessary to take into account the Z protons per nuclide, plus the N neutrons

Most of this paper first appeared IN GALILEAN ELECTRODYNAMICS, Volume 7, Number 1,January/February 1996, and is revised and reprinted by permission.

which consist of N protonsand N electrons. One shouldnote that the elastic ringelectrons have a muchsmaller equilibrium sizewhen intimately bound witha proton in a neutronconfiguration, than whenloosely bound to a proton ina hydrogen molecularconfiguration.

One might expect that thenumber of protons in eachtype of nuclear packingshell should be exactly thesame as for electrons in theatomic case. Conversely,one might expect somedifference due to the presence of two types of particles in the nucleus and the fact thatthere is no central charge binding all the nucleons to the center of the nucleus.

If one looks at the nuclear magicnumbers 2, 8, 20, 28, 50, 82, 126 (thesums of complete shell sizes) whichrepresent the size of the variousnuclear shells as seen in many typesof periodic nuclear data, one soonrealizes that something is differentabout the nucleus. The packingappears, at first, to be quite differentfrom the atomic magic numbers of 2,10, 18, 36, 54, 86, 118the totalnumber of electrons when interioratomic shells are filled. (This is onereason why modern science has atheory for the nucleus that is differentand separate from atomic theory.)

An examination of the experimentally measured nuclear density shapes in Graph 3 givesan important clue as to what is happening. From Graph 3, one sees that the density ofnuclides at the center decreases with increasing size or mass of the nucleus. In the atomiccase, the electron density at a particular radius always increases with more massive atomsuntil the shell at that radius is filled. After that the density stays constant at that radiuswith more massive atoms. The nuclear density data seems to indicate that the proton andneutron shells do not remain in a stable configuration once they are filled and additional

Graph 3Nuclear Density for Various Nuclides [6]

Graph 2

nucleons are added to make heavier nuclides. Rather, at some point, the balance ofelectric and magnetic forces in the nucleus is such that the smaller interior shellsrearrange into larger shells that are more strongly bound. Thus, the average nucleardensity near the center of the nucleus drops, because the small innermost shells aremissing.

This observation has been confirmed by a ring magnet experiment in which the strengthof binding of the shell was measured versus shell size (see Graph 2). Using the notionthat smaller shells may come apart and rearrange themselves into larger more stable shellconfigurations, the nuclear magic shell numbers can be explained in terms of thecombinatorial geometry packing shells as shown in Table 4.

Table 4. Nuclear Shells____________Combinatorial Geometry Shells__________

From Table 4 one sees that the notion of shells rearranging into larger more stable shells,due to the lack of an attracting nuclear center, seems capable of explaining the magicnumber shell-like features of the nuclides. But what about the nuclides in between themagic number shells?

The nuclides between the magic number nuclides have a number of physical propertieswhich the physical Geometrical Packing Model should explain. One of these propertiesis the spin or magnetic moment of the nuclides. Magic number nuclides have no spin ormagnetic moment, because they consist of only completed (full) shells which arespherically symmetric. Nuclides with an even number of neutrons and protons also haveno net spin.

In the nuclear shell model for which Maria Goeppert Mayer received the Nobel Prize in1963, [7, 8, 9, 10] the odd unpaired nucleons in shells give rise to the net spin andmagnetic moment of the nucleus. The spin of a nucleon is a combination of its intrinsicspin plus its orbital angular momentum (from assumed orbiting motion). The QuantumNuclear Shell Model is a planetary type model in that the nucleons move in orbits aboutthe center of the nucleus and possess orbital angular momentum about the center of thenucleus. The orbital model fails to predict correct spins for nuclides in 114 out of 339cases in the 44 page version of Table 5 (see the first page of Table 5 at the end of thisarticle.)

Total Number of Nucleons 2 2 8 8 18 18 32 32 50 502 28 820 2 1828 2 8 1850 18 3282 32 50126 8 18 18 32 50

In the physical Geometrical Packing Model, the nucleons do not normally orbit about thecenter of the nucleus. Amperes Law and Faradays Law in electrodynamics require thatcharged nucleons radiate energy continuously if they orbit the nucleus. This radiationwould cause the nucleus to collapse and never be stable. In the Geometrical PackingModel the balance of electric and magnetic forces on the finite-size charged electronsand proton rings in the nucleus causes them to come to a balanced equilibrium positionsome distance from the center of the nucleus without having to orbit the center of thenucleus. The spin of a nuclide is assumed to be due to the odd, unpaired nucleons in thepartially filled shells. Using the rule that odd numbers of neutrons and/or protons in ashell link together like ring dipole magnets in a line to form the nuclear spin or magneticmoment by merely adding their intrinsic nucleon spins or moments together allows thespin of all known nuclides (stable or unstable) to be predicted (see the first page of Table5 at the end of this article).

In order to complete the shell structure for all the nuclides that have been observed, thebalance of electric and magnetic forces in the shells must be taken into account. Themathematics for handling large numbers of toroidal rings spatially distributed andallowed to deform is very complicated, so this was done systematically in a crude waythrough a series of assumed rules obtained by an analysis of nuclide data as follows:

Rule 1. Inside the nucleus, neutrons polarize into electrons and protons whichparticipate in the formation of packing shells.

Rule 2. Neutrons cause protons to be more tightly bound in packing shells byforming a triplet of shells, i.e. p-e-p, with an electron shell in the middlebinding the proton shells by Coulomb attraction.

Rule 3. Due to the binding effect of theneutrons, shells of 50 protons are nowbound, whereas atomic shells of 50electrons are not.

Rule 4. Most stable nuclides have protons onlyin the outermost shells.

Rule 5. The balance of electric and magneticforces in the nucleus causes theinnermost shells of nucleons to breakup to form larger, more stable shells.

Rule 6. The balance of electric and magneticforces in the nucleus causes thenucleons to rearrange to form aminimum number of shells.

Rule 7. When there are an odd number ofneutrons and/or protons in a shell, the magnetic fields or spins of the odd

Figure 8Arrangement of O16 Nucleus

nucleons add.

Rule 8. The number of neutrons and protons in a partially filled shell cannot differby more than 25 percent.

Rule 9. The number of neutrons and protons in a shell cannot exceed the shellsmaximum number for each.

Rule 10. When the number of neutrons and protons must differ by two or more in ashell, the difference occurs in the most weakly bound shells first.

Rule 11. When one shell can be partially filled, or a second more strongly boundshell completely filled and the first shell partially filled, the latter occurs.

Rule 12. Two shells will combine to form a larger shell when they can populate atleast 75 percent of the shell.

Table 5 shows how these very reasonable rules work out for some of the observed stable

and unstable nuclides. (The entire 44 page table is available from the authors.) Figure 8illustrates the arrangement of electrons and protons in the nucleus of the oxygen O16atom. One filled shell of eight electrons is surrounded by two shells of protons, forminga proton-electron triplet. The eight large rings represent electrons, and the sixteen smallrings represent protons, although no attempt has been made to show the ring diameters inscale. The electron could be the same size as the proton in the nucleus due to its

Graph 4Number of nuclear shell model failures to predict nuclide spin by nucleon number

elasticity.

Note that the Geometrical Packing Model approach is more successful than the QuantumNuclear Shell Model. The full 44 page version of Table 5 reveals that quantum modelsare unable to predict the correct spin for two-thirds of the odd N and/or Z nuclides,indicating serious deficiencies in the Quantum Nuclear Shell Model. Graph 4 shows thefailures of the Quantum Nuclear Shell Model by N and Z. Note that the quantum modelis best close to magic number shells.

Liquid Drop Properties of the Nucleus

There are some nuclear properties, such as thebinding energy per nucleon and certain nuclearproperties such as spontaneous nuclear fission,that the Quantum Nuclear Shell Model has beenunable to adequately describe. However, thesethings can be satisfactorily described by theLiquid Drop Model of the nucleus. TheQuantum Nuclear Shell Model and the LiquidDrop Model are incompatible in that the surfaceof the nucleus in shell models should not act likea liquid surface. In the Geometrical PackingModel, however, there is a physical basis for theLiquid Drop Model. This can be seen fromFigures 9, 10, 11 and 12. For these figures, thestructure of the spherical shells has beensymbolically represented by a slice cross sectionthrough the center of the nucleus such that each spherical shell shows up as a circle orring. Each proton shell is shown explicitly. Each neutron shell is depicted as an electronshell plus a proton shell, i.e. the neutrons polarize in such a way that the neutron shellappears to be an electron shell plus a proton shell.

Note that in each of Figures 9, 10, 11 and 12that in the innermost part of the nucleus,electron and proton shells alternate as oneproceeds from the center of the nucleusoutward. This alternating sandwich effectkeeps them tightly bound together. However, atthree shells in from the outermost shell, thereare always two proton shells in a row for thelarger nuclides. This causes the last threealternating sandwich of bound shells to berepulsed by the inner nucleus. Thus, they areonly weakly bound to the inner nucleus.

Figure 9

Figure 10Shell Structure of CA-40

This weak binding allows the outermost tripletof shells to have liquid-like properties andforms the proper justification for a LiquidDrop Model of the nucleus. Such an effectdoes not exist in quantum shell models of thenucleus, because they are based on a centralforce potential instead of allowing a dynamicrearrangement of shells to minimize thebinding energy of the nucleus.

Another quantity the physical GeometricalPacking Model should be able to predict is themass of each nuclide (stable or unstable) or anequivalent quantity known as the bindingenergy W per nucleon A, i.e., W /A. TheLiquid Drop Model of the nucleus has beenthe most successful of all previous nuclear models in predicting the binding energy pernucleon using the semi-empirical mass formula with each term determined by least-square fitting to the nuclide data. However, the semi-empirical mass formula of theLiquid Drop Model that is used in the least-square fitting is ill-conditioned, making theresults obtained from least-square fitting afunction of the initial guess for each of theparameters in the formula. This is indicative ofa formula whose terms do not uniquely describethe binding of the nucleons. One set of initialguesses for the parameters in the semi-empirical mass formula leads to a good fit ofthe light nuclei. Another set of initial guessesleads to a good fit of the heavy nuclei.However, no set of initial guesses for the least-square analysis leads to a good fit of both lightand heavy nuclei.

In the Geometrical Packing Model, a somewhatdifferent formula is used for the binding energyper nucleon (W/A). The terms represent similareffects, but the terms are dependent on thephysical shell structures as shown below andare not ill-conditioned.

W/A = K1 K2 (# Neutrons ++++ # Protons in outermost shell) / A K3 Z (Z 1) A4/3 K4 (# paired Neutrons # paired Protons)2 / A

Figure 11Shell Structure of Sn-118

Figure 12Shell Structure of Pb-208

K5 (# unpaired Protons ++++ # unpaired Neutrons) / AThe first term, K1, represents a constant energy density for nuclear binding. From theassumption of constant energy density within the nucleus, the Geometrical PackingModel has the same first term as the semi-empirical mass formula with all the other termsbeing of opposite sign and corrections to this assumption.

The second term takes into account the effect of the surface in reducing the bindingenergy. In the Geometrical Packing Model, the exact count of the number of neutronsand protons in the outermost shell is used, instead of an approximation to that number.

The third term corrects for the effect of Coulomb repulsion of protons on the bindingenergy. This is the same as in the Liquid Drop Model.

The fourth term represents the magnetic tendency to have equal numbers of proton andneutron magnets paired in the nucleus as a whole. This term is proportional to the actualdifference between the number of paired neutrons and protons, instead of anapproximation to that number employed by the Liquid Drop Model.

The last term takesinto account theodd number ofneutron and/orprotons in a shellthat are not pairedup. These valueswere taken fromthe completeversion of Table 5.

Graph 5 shows anexcellent least-square fit of theformula to allknown stable andunstable nuclidebinding energies.The GeometricalPacking Model is able to predict the binding energy per nucleon to four significantfigures for the average nuclide. This is better than the Liquid Drop Model which canonly fit well either the light stable nuclei or the heavy stable nuclei [11]. The GeometricalPacking Model can fit both light and heavy stable nuclei simultaneously as well as theunstable nuclei with one set of parameters.

Graph 5Nuclear Binding Energy per Nucleon

SummaryA simple physical Geometrical Packing Model hasbeen presented to describe the packing of electronsabout the nucleus in layers or shells as well as thepacking of neutrons and protons in the nucleusitself. An example of this packing scheme is shownin Figure 13 for the Ne20 atom. The arrangement ofelectrons for the neon atom was determined byhanging ten ring dipole magnets by strings in thesymmetrical pattern of the appropriate shells. Of allthe possible configurations the one thatexperimentally achieves stability is shown in Figure13. This configuration minimizes the sum ofmagnetic moments for each shell and achievessymmetry by locating the electrons of each shell ona great circle.

The packing model is completely electromagnetic inorigin. It is based upon the 1917 experiments ofCompton [2, 3, 4] in which he showed that the sizeand shape of the electron could be determined by analysis of hard X-ray and gamma rayscattering to be thin flexible rings of charge. One of Comptons last graduate students,Winston Bostick, proposed in 1966 [12, 13] that the closed string or fiber of charge thatmakes up the electron has the configuration of a helical spring that is connected end-to-end to form a deformable ring or toroid. The size and structure of the neutron and protonis based upon the electron scattering experiments of Nobel Laureate Robert Hofstadter[14]. The shape and structure of the packing shells comes from our ring magnetexperiments and the work of David Bergman [1].

This new Geometrical Packing Model for the atom does not incorporate the objectionableassumptions of Quantum Mechanics for the atom that (1) electrons move in orbits aboutthe nucleus with definite angular momentum, (2) electrons are point-like particles with nosize or structure, and (3) electron orbits with no angular momentum are in stablemechanical equilibrium with the nucleus with no known physical basis. The firstassumption violates Amperes Law and Faradays Law in electrodynamics which requirethat electrons in orbit about the nucleus must radiate energy continuously. The secondassumption is false, because it disagrees with the experiments of Compton, Bostick, andHofstadter and it requires an infinite density concentration of energy. The thirdassumption violates mechanical conditions for stability.

The new physical packing model successfully predicts all the known properties of thePeriodic Table of the Elements, including the reason why there are only seven periodsdue to the geometrical properties of the nucleons magnetic fields. The quantum modelscannot show why there are only seven periods.

Figure 13Approximate Arrangement of Ne20 Atom

The new packing model explains the physical origin of the structure of nuclear shells inagreement with the observed charge density of nuclides. The Quantum Nuclear ShellModel l, which is based upon a central force potential, cannot explain the observeddecrease of central nuclide density with increasing number of nucleons.

The new model explains the physical origin of nuclear spin in agreement with practicallyall observed nuclei, whether stable or unstable (of the 339 nuclei listed in the full versionof Table 5, even Hg-204 was correctly predictedalthough the reported datum was inerror). Quantum Nuclear Shell Models cannot do this with so few assumptions.

The Geometrical Packing Model gives a physical basis for why the outer surface of thenucleus has liquid-like properties. Thus, the Liquid Drop Model of the nucleus isphysically compatible with the Geometrical Packing Model, but not with any quantumshell model of the nucleus based upon a central force potential.

The Geometrical Packing Model is capable of improving upon the Liquid Drop Model ofthe nucleus in that it gives rise to a better defined semi-empirical mass formula that is notill-conditioned for least-square fitting. This allows the least-square fitting process toproduce a better fit to the nuclear binding energy per nucleon over the entire range ofnuclides.

Conclusions

The Geometrical Packing Model presented for the atom and nucleus is very successful indescribing some atomic and nuclear data. The approach taken is more fundamental andstraightforward than the methods used by Quantum Mechanics. The new model does notincorporate any of the objectionable assumptions of Quantum Mechanics and replacesthose features of the quantum models that are known to be inconsistent or in violation ofproven laws. Unlike the quantum models, the Geometrical Packing Model for ringparticles is not simply mathematical, but it is a physical model with boundaries, sizes anddetailed structure. Thus it satisfies one of the major goals of physics which is tophysically describe the matter of the physical universe.

Although the framework of a new theory of matter has been presented, the basicapproach needs to be extended to give successful descriptions of blackbody radiation, thephotoelectric effect, and the energy levels of the atom giving rise to absorption andemission spectra before it can more fully qualify to displace the quantum models[15].Also, the Geometrical Packing Model needs to be extended to develop a new,comprehensive theory of elementary particles that can displace the Standard Model ofElementary Particles, the Supersymmetric String Model, and Quantum Mechanics on allsize scales. This work is currently under way and promises to be just as successful as theGeometrical Packing Model.

References

1. Bergman, D. L. and Wesley, J. P., Spinning Charged Ring Model of ElectronYielding Anomalous Magnetic Moment, Galilean Electrodynamics, Vol. 1, No. 5,pp. 63-67 (Sept/Oct 1990).

2. Compton, Arthur H., American Physical Society address December 1917, PhysicalReview Series II, p. 330 (1918).

3. Compton, Arthur H., Physical Review Series II, Vol. XIV, No. 1, pp. 20-43 (1919).

4. Compton, Arthur H., Physical Review Series II, Vol. XIV, No. 3, pp. 247-259(1919).

5. Lucas, J., and Lucas, Jr., C. W., A Physical Model for Atoms and NucleiPart 1,Foundations of Science, Vol. 5, No. 1 (May 2002).

6. Eisberg, R. M., Fundamentals of Modern Physics, John Wiley & Sons, Inc., NewYork & London, p. 571 (1961); Hofstadter, R. Annual Review of Nuclear Science,Vol. 7, Annual Reviews, Stanford (1957).

7. Mayer, M. G., Physical Review, Vol. 74, p. 235 (1948).

8. Mayer, M. G., Physical Review, Vol. 75, p. 1969 (1949).

9. Mayer, M. G., Physical Review, Vol. 78, pp.

10. Mayer, M. G., and Jensen, J. H. D., Elementary Theory of Nuclear Shell Structure,John Wiley & Sons, New York (1955).

11. Howard, Robert A., Nuclear Physics, Wadsworth Publishing Co., Belmont, CA(1963) pp. 304-313.

12. Bostick, Winston H., Physics of Fluids, Vol. 9, p. 2079 (1966).

13. Bostick, Winston H., Mass, Charge and Current: The Essence and Morphology,Physics Essays, Vol. 4, No. 1, pp. 45-49 (1991).

14. Hofstadter, R., Reviews of Modern Physics, Vol. 28, p. 213 (1956).

15. Please note that this work has already been successfully completed in the authors1994-1995 science fair project A New Classical Basis for Quantum Physics whichwas awarded a Grand Prize at the 1995 International Science and Engineering Fair inHamilton, Ontario, Canada.

16. Lide, D. R., editor, CRC Handbook of Chemistry and Physics, 73rd Edition, CRCPress, Ann Arbor (1993).

TABLE 5TABLE OF NUCLIDE DATA [16]

ATOMIC A Z P1 N1 P2 N2 P3 N3 P4 N4 P5 N5 P6 N6 P7 N7 P8 N8 ACTUAL RING SHELL HALF- ABUNDANCESYMBOL MEASURED MODEL MODEL LIFE

SPIN SPIN SPIN

n 1 0 0 1 1/2 1/2 1/2 13. m 0.000H 1 1 1 1/2 1/2 1/2 99.985H 2 1 1 1 1 1,0 1,0 0.015H 3 1 1 2 1/2 1/2 1/2 12.26 y 0.000H 4 1 1 3 2 2,1 2,1 0.000He 3 2 2 1 1/2 1/2 1/2 0.000He 4 2 2 2 0 0 0 100.000He 5 2 2 3 3/2 3/2 3/2 0.000He 6 2 2 4 0 0 0 0.000He 10 2 2 8 0 0 0 0.000He 7 2 2 2 3 (3/2) 3/2 3/2 0.000He 8 2 2 6 0 0 0 0.000He 9 2 2 1 6 (1/2) 1/2 5/2 0.000Li 4 3 1 3 2 2,1 2,1 0.000Li 5 3 2 3 3/2 3/2 3/2 0.000Li 6 3 2 2 1 1 1 1,0 3,0 7.500Li 7 3 3 4 3/2 3/2 3/2 0.000Li 8 3 2 2 1 3 2 2,1 3,0 0.000Li 9 3 2 3 4 3/2 3/2 3/2 0.000Li 10 3 2 3 5 ? 4,1 4,1 0.000Li 11 3 3 8 3/2 3/2 3/2 0.000Be 6 4 2 2 2 0 0 0 0.000Be 7 4 2 2 3 3/2 3/2 3/2 0.000Be 8 4 2 2 2 2 0 0 0 0.000Be 9 4 2 2 2 3 3/2 3/2 3/2 100.000Be 10 4 2 2 2 4 0 0 0 0.000Be 11 4 1 4 6 1/2 1/2 1/2 13.7 s 0.000Be 12 4 2 4 6 0 0 0 0.000Be 13 4 4 4 5 (5/2) 5/2 5/2 0.000Be 13 4 1 4 8 (1/2) 1/2 1/2 0.000Be 14 4 2 2 2 2 6 0 0 0 0.000B 7 5 2 2 3 (3/2) 3/2 1/2 0.000B 8 5 2 2 3 1 2 2,1 2,1 0.000B 9 5 2 2 3 2 3/2 3/2 3/2 0.000B 10 5 2 2 3 3 3 3,0 3,0 18.700B 11 5 2 2 3 4 3/2 3/2 3/2 81.300B 12 5 1 1 4 6 1 1,0 2,1 0.000B 13 5 2 2 2 3 4 3/2 3/2 3/2 0.000B 14 5 1 3 4 6 2 2,1 4,1 0.000B 15 5 2 2 3 8 ? 3/2 3/2 0.000B 16 5 2 3 3 8 0 3,0 4,1 0.000B 17 5 2 3 4 8 (3/2) 3/2 3/2 0.000B 18 5 2 3 5 8 ? 4,1 4,1 0.000B 19 5 2 2 3 4 8 ? 3/2 3/2 0.000C 8 6 2 4 2 0 0 0 0.000C 9 6 2 4 3 (3/2) 3/2 3/2 0.000C 10 6 2 4 4 0 0 0 0.000

Notes for Table 5:

1. The complete 44 page table is available from the authors for $3.00 postage and handling in U.S.2. Z is the number of protons per nuclide. N is the number of neutrons per nuclide. A = Z + N is the nuclides atomic number.3. P1, P2, etc., give the number of protons in that nuclear shell.4. N1, N2, etc., give the number of neutrons in that nuclear shell. (Each neutron shell consists of one proton and one electron shell.)5. Actual Measured Spin is the experimentally measured nuclide spin. A parenthesis around the spin value means that the spin is

inferred but not actually measured.6. Half-life gives time in seconds (s), minutes (m), hours (h), days (d) or years (y).7. Abundance gives the relative abundance of the nuclide for the element.

A Physical Model for Atoms and NucleiPart 3Joseph Lucas and Charles W. Lucas, Jr.

29045 Livingston DriveMechanicsville, MD 20659 USA

Extension of New Model of the Atom. The Geometrical Packing Model presented for theatom and nucleus in parts 1 [6,7] and 2 [7,8] based on the Toroidal Particle Model werevery successful in describing some atomic and nuclear data. The physical approach(based on experiment) taken in these papers is more fundamental and straightforward thanthe mathematical methods (based on unproven postulates) used by Quantum Mechanics.The new model does not incorporate any of the objectionable assumptions and postulatesof Quantum Mechanics and replaces those features of the Quantum Models that areknown to be inconsistent or in violation of proven laws. Unlike the Quantum Models, theGeometrical Packing Model for ring particles is not simply mathematical, but it is a phys-ical model with boundaries, sizes and detailed structure that can be verified experimen-tally. Thus it satisfies one of the major goals of physics which is to physically describethe matter of the physical universe.

Although the framework of a new theory of matter has been presented, the basic approachneeds to be extended to give successful descriptions of blackbody radiation, the photo-electric effect, and the energy levels of the atom giving rise to absorption and emissionspectra before it can more fully qualify to displace the Quantum Models. (Please note thatthis work was initially completed in Josephs 1994-1995 science fair project A NewClassical Basis for Quantum Physics which was awarded a Grand Prize, sponsored byNASA, at the 1995 International Science and Engineering Fair in Hamilton, Ontario,Canada.) The purpose of this third article in the series is to extend the application of theRing Model to the emission spectra of atoms.

Abstract. A physical Geometrical Packing Model for the structure of the atom isdeveloped based on the physical toroidal Ring Model of elementary particles pro-posed by Bergman [1]. From the physical characteristics of real electrons fromexperiments by Compton [2,3,4] this work derives, using combinatorial geometry,the number of electrons that will pack into the various physical shells about thenucleus in agreement with the observed structure of the Periodic Table of theElements. The constraints used in the combinatorial geometry derivation arebased upon simple but fundamental ring dipole magnet experiments and spheri-cal symmetry. From a magnetic basis the model explains the physical origin ofthe valence electrons for chemical binding and the reason why the Periodic Tablehas only seven periods. The Toroidal Model is extended in this article to describethe emission spectra of hydrogen and other atoms. Use is made of some of theauthors standing wave experiments in large toroidal springs. The resulting modelaccurately predicts the same emission spectral lines as the Quantum Modelincluding the fine structure and hyperfine structure. Moreover it goes beyond theDirac Quantum Model of the atom to predict 64 new lines or transitions in theextreme ultraviolet emission spectra of hydrogen that have been confirmed by theExtreme Ultraviolet Physics Laboratory at Berkeley from its NASA rocket experi-ment data [5].

History of Modern Atomic Data and Theory. When experimenters of the past examinedthe emitted spectra from hot solids and gases, they discovered that solids emit a continu-ous spectrum of electromagnetic radiation while monoatomic gases emit radiation con-centrated at a number of discrete wavelengths. Each of these wavelength components iscalled a line, because thespectroscopes used torecord the spectra on filmemployed slits with a prismto separate the wavelengthsof light or different coloredimages of the slit (seeFigure 1). These spectro-scopes were only able tomeasure those wavelengthsnear the range of visiblelight.

Experimenters observed patterns in the spectroscopic lines of monoatomic gases likehydrogen (see Figure 2). In these patterns or series of lines the spacing between adjacentlines of the spectrum continuously decreased with decreasing wavelength of the lines untilit converged at some limit.A number of these serieswere found for hydrogengas. About 1890 Rydberg[9, pp. 110-113] found anempirical formula, calledthe Rydberg Formula, thatdescribed these series ofwavelengths as shown inTable 1.

In 1913, Bohr developedhis Quantum Model, called the Bohr Model, to describe the atom and predict the atomicline series described so well by Rydbergs empirical formula. Bohrs model was based onthe following postulates [9, p. 114]:

1. An electron in an atom moves in a circular orbit about the nucleus under theinfluence of the Coulomb attraction between the electron and the nucleus,and obeying the laws of classical mechanics.

2. But, instead of the infinity of orbits which would be possible in classicalmechanics, it is only possible for an electron to move in an orbit for which itsangular momentum L is an integral multiple of Plancks constant h dividedby 2, i.e. L = nh/2.

Figure 1Apparatus for Atomic Spectroscopy

[9, pp. 110-113]

Figure 2Balmer Line Series for Hydrogen

[9, pp. 110-113]

3. Despite the fact that it is constantly accelerating, an electron moving in suchan allowed orbit does not radiate electromagnetic energy. Thus its total ener-gy remains constant.

4. Electromagnetic energy is emitted if an electron, initially moving in an orbitof total energy Ei, discontinuously changes its motion so that it moves in anorbit of total energy Ef. The frequency of the emitted radiation is equal tothe quantity (Ei Ef) divided by Plancks constant h, i.e. = (Ei - Ef)/h.

Bohrs postulates were very radical. They assumed that some electromagnetic laws, suchas Coulombs force law held on the microscopic scale, but not Amperes law or Faradayslaw. Thus the laws of physics were assumed to be different on the microscopic scale thanon the macroscopic scale. Also, Bohr neglected the finite size of the electron.

The justification for Bohrs postulates was that they led to a model that produced a math-ematical equation that predicted the atomic emission line spectra of one-electron atoms.Logically, however, this type of justification is incomplete. One must also justify each ofthe assumptions or postulates individually. This was never done.

The success of the Bohr theory was very striking, but the Bohr postulates were somewhatmysterious. Also there was the question of the relation between Bohrs quantization ofthe angular momentum of an electron moving in a circular orbit and Plancks quantizationof the total energy of an entity, such as an electron, executing simple harmonic motionsince both incorporated Plancks constant h.

In 1916 Wilson and Sommerfeld [9, pp. 128-131] postulated a set of rules for the quanti-zation of any physical system for which the coordinates are periodic functions of time asfollows:

For any physical system in which the coordinates are periodic functionsof time, there exists a quantum condition of each coordinate. These quan-tum conditions are where q is one of the coordinates, pq is the momentum

Table 1. Hydrogen Spectral Line Series

WavelengthName Range () Rydberg Formula

Lyman Ultraviolet k = 1/ = RH [1/(1)2 - 1/(n)2] n = 2,3,4,...Balmer Visible k = 1/ = RH [1/(2)2 - 1/(n)2] n = 3,4,5,...Paschen Infrared k = 1/ = RH [1/(3)2 - 1/(n)2] n = 4,5,6,...Brackett Infrared k = 1/ = RH [1/(4)2 - 1/(n)2] n = 5,6,7,...Pfund Infrared k = 1/ = RH [1/(5)2 - 1/(n)2] n = 6,7,8,...where RH = 109677.576 ! .012 cm

-1is the Rydberg constant.

associated with that coordinate, nq is the quantum number which takeson integral values, and % means that the integration is taken over oneperiod of the coordinate q.

The application of the Wilson-Sommerfeld quantization rule to the coordinate where q= and pq = L = mr2d/dt yields

or

The application of the Wilson-Sommerfeld quantization rule to a particle of mass m exe-cuting simple harmonic motion with frequency yields

Sommerfeld used the Wilson-Sommerfeld quantization rules to evaluate the size andshape of the allowed elliptical orbits as well as the total energy of the electron moving insuch an orbit. Describing the motion in terms of the polar coordinates r and , he obtainedthe quantum conditions

By requiring a condition for mechanical stability, i.e. the centripetal force is equal to theelectrical Coulomb force, a third equation is obtained. Solving them simultaneously heobtained

( )= 19dqphn qq

( )20220

LdLdLLddqphn qq =====

( )212

hnnhL ==

( )22..20 nhEeiExmdxpnh ====

( )23,...3,2,12 === nhnLhndL( ) ,...3,2,12/1 === rrrr nhnbaLhndrp

( ) ( )24,...3,2,12222

=+== rnnnZehna

,...3,2,1,02

,...3,2,1 2242

==== rnhneZEn

nnab

where n is called the principal quantum num-ber, and n is called the azimuthal quantumnumber. The second equation above gives theshape of the orbit, i.e. the ratio of the semi-major to the semi-minor axes b/a. It is deter-mined by the ratio of n to n. For n = n theorbits are circles of radius a. Figure 3 shows toscale the possible orbits corresponding to thefirst three values of the principal quantum num-ber. Note that for each value of the principalquantum number n, there are n differentallowed orbits. One of these, the circular orbit,is the orbit described by the original Bohr the-ory. The others are elliptical.

The third equation above indicates that all ofthe different possible orbits for a given n havethe same total energy of the electron. The several orbits characterized by a common valueof n are said to be degenerate. Sommerfeld removed this degeneracy by treating theproblem using relativistic mechanics. In this approach the size of the relativistic correc-tion depends on the average velocity of the electron which, in turn, depends on the ellip-ticity of the orbit. Sommerfelds derivation showed that the total energy of an electron inan orbit characterized by the quantum numbers n and n is given by

where = 2 e2/hc l 1/137 is called the fine structure constant.Experimentally, it is observed that transitions only take place between orbitals for which

This condition for orbital transitions is called a selection rule. It states that the changein angular momentum of the electron orbital must be one unit of angular momentum foremission and absorption of electromagnetic radiation. Conservation of angular momen-tum implies that electromagnetic radiation carries one unit of angular momentum.

This version of quantum theory had a number of notable shortcomings [9, pp. 136-137]:

1. The theory only treats systems which have periodic motion, but thereare many systems which are not periodic.

2. Although the theory allows one to calculate the energies of the allowed

Figure 3Standing Wave of Bohr Orbits

( ) ( )254311

2/2

22

22

42

+=

nnnZ

hneZE

( )261= fi nn

states of a system and the frequency of the quanta emitted or absorbedwhen the system makes a transition between allowed states, the theorydoes not reveal how to calculate the rate at which transitions take place.

3. The theory is only really applicable to one-electron atoms. The alkalielements (Li, Na, K, Rb, Cs) can be treated approximately, but onlybecause they are similar to a one-electron atom.

In 1924 de Broglie [9, pp. 139-141] introduced the idea that particles such as electrons,alpha particles, billiard balls, etc. display properties characteristic of waves. De Brogliepostulated that the wavelength and the frequency of the waves associated with a par-ticle of momentum p and total relativistic energy E are given by the equations

The requirement that the waves associated with a particle undergoing any sort of period-ic motion be a set of standing waves is equivalent to the requirement that the motion ofthe particle satisfy the Wilson-Sommerfeld quantization rules. The time independent fea-tures of the standing waves associated with an electron in one of its allowed states in anatom was used to explain why the motion described by the standing wave does not causethe electron to emit electromagnetic radiation. (Note that the fundamental standingwave in the charge density of charge fibers of the toroidal ring is exactly the deBroglie wavelength. The so-called particle-wave duality is only a mystery for point-like particles.)

The de Broglie postulate says that the motion of a particle is governed by the propagationof its associated waves, but it does not tell the way in which these waves propagate. Tohandle the case of a particle moving under the influence of forces, we need an equationthat tells how the waves propagate under these more general circumstances.

In 1925 Schrdinger [9, pp. 165-170] developed a propagation equation for matter waves,called the Schrdinger equation. It was patterned after the wave equation for strings. Hedenoted the waves by the mathematical wave function (x,t). Instead of using relativis-tic kinematics,

Schrdinger used the classical definition of total energy.

The three requirements that Schrdinger felt his equation must satisfy were:

1. It must be consistent with de Broglies postulate and conservation ofenergy

2. The equation must be linear in the wave function (x,t) in order to pre-

( )27hEph ==

( )28where2 22 ooo mmcmVmPE =++=

( )292

2

Vm

PE +=

dict the interference phenomena as observed in the Davisson-Germerexperiments

3. The potential energy may be a general function of x and t.

On the basis of these assumptions, Schrdinger postulated the full non-relativistic waveequation to be

The Schrdinger wave equation contains the imaginary number i. As a consequence itssolutions are complex (real and imaginary) functions of x and t, i.e. not real functions ofx and t. Thus the wave function cannot represent the real amplitude of the matter wavethat can be physically measured. The question of what is waving and in what medium cannot be answered!! The original wave equations for strings does not contain imaginaryterms, and the real wave function describes the amplitude of the matter wave in the string.

A relationship between the wavefunction (x,t) and the probability of finding the particleat coordinate x was suggested by Born [10] in 1926 in the form of the following postulate:

If, at the instant t, a measurement is made to locate the particle associ-ated with the wave function(x,t), then the probability P(x,t)dx that theparticle will be found at a coordinate between x and x+dx issuch that probability is conserved, i.e.

One problem that the Schrdinger matter wave model has that the Bohr model did nothave is that it predicts the existence of l = 0 orS states. Here the electron has no angularmomentum about the nucleus and no mecha-nism due to orbital motion to keep theCoulomb force from pulling the electron intothe nucleus. Thus the Schrdinger matterwave model denies the Coulomb force for S-wave electrons, but not for l > 0 electrons.This is a serious inconsistency in logic. Therelativistic version of the Schrdinger matterwave equation, called the Dirac Matter WaveEquation, also has this problem.

( ) ( ) ( ) ( )31,,, dxtxtxdxtxP =

( ) ( ) ( ) ( ) ( )30,,,,22

2

2

2

ttxihtxtxVtx

xm

h

=+

( ) ( ) ( )321,, = dxtxtx

Figure 4Mechanical Model of a Toroidal

Elementary Particle

New Experiments on Standing Waves ina Ring. In order to learn more aboutstanding waves in mechanical rings, alarge metal spring 1.5 in diameter and12 long (Slinky from James Industries,Inc. Beaver Street ExtensionHollidaysburg, PA 16648) was obtainedwith the two ends fastened together toform a ring. The ring was suspended by100 thin strings 19 long to form a ringwith a diameter of 48 (see Figure 4).When the ring was perturbed by ametronome pendulum at various frequen-cies to form standing waves, the very low-energy standing waves had = n(2R)and the high-energy standing waves had = (2R)/n where R = 48 and n = 1, 2, 3, ...and is the wavelength of the standing wave (see Figure 5).

New Classical Derivation of One Electron Atomic Energy Levels. The requirements thatthe new classical approach to the energy levels of the atom must satisfy are as follows:

1. Must be based on the proven laws of physics instead of arbitrary postulates.

2. Must maintain the fundamental laws of physics to be the same on all sizescales.

3. Must conserve energy and momentum.

4. Must be consistent with de Broglies postulate.

5. Must have stable equilibrium states in agreement with observation.

6. Must be consistent with the Wilson-Sommerfeld quantization rules for stand-ing waves or stationary states.

7. Must give rise to a real wave equation describing the current density in theelectron ring.

For a one-electron atom the equilibrium configurationis shown in Figure 6.

Assuming that the mass m of the electron ring is asso-ciated with the charge of the ring, the condition for themechanical stability of the electron ring is fromNewtons laws and electrodynamics

Figure 5. Experimental Standing Waves in Toroidal Spring

Figure 6One-Electron ring( )3322

2

Rmv

RZe =

where v is the velocity of the charge in the ring, R is the radius of the ring, and e is thetotal charge of the ring.

Now the requirement that the waves associated with a particle undergoing any sort of peri-odic motion be a set of standing waves is equivalent to the requirement that the motion ofthe particle satisfy the Wilson-Sommerfeld quantization rules. The angular momentum inthe plane of the ring for a free electron is given by Bergman[1,11]

where 2R = o and me = mm = m /2.

For the atom there are standing waves with two or more wavelengths around the circum-ference of the ring. In this case

Also it is possible to have standing waves where the standing wave has a wavelengthequal to multiple times the circumference of the ring. In this case

Thus the most general case is

Equation (33) may be written

So

Now consider the total energy of an atomic electron. If we define the potential energy tobe zero when the electron is infinitely distant from the nucleus, then the potential energyV at any finite distance r can be obtained by integrating the energy imparted to the elec-tron by the Coulomb force acting from infinity to R, i.e.

The potential energy is negative, because the Coulomb force is attractive.

( )342

8log8 2

2 h=

===rR

ceemcRvRmL e

oe

( )35,...3,2,12 == nnR o

( )36,...3/1,2/1,12 == nnR o

( )37,...3,2,1,21,31...2 hnLnwherenR o ===

( ) ( )382 22222mR

nmRLmRvZe h===

( ) ( )39,...3,2,1,21,31...2222

== nmZe

nR h

( )40222

RZedr

rZeV

R

==

The kinetic energy T of the electron can be evaluated from equation (33) to be

The total energy E of the electron is then

From equation (39)

From = c and E = h = hc/.

Note that the condition for standing waves in the ring leads to a quantization of the totalenergy of the electron bound to a nucleus of charge Ze.

EXPERIMENTAL CONFIRMATION OF NEW MODEL OF ATOM

When Rydberg analyzed the hydrogen emission spectrum to obtain his empirical formulain 1890, the line spectrum data was only available from the near ultraviolet, the visibleand the infrared spectrum. This situation continued through the time that Bohr (1913)developed his model of the atom and Schrdinger (1925) and Dirac (1925) developedtheir wave equations.

Then in 1991 Labov and Bowyer [5] at the University of California at Berkeley devised away to measure the extreme ultraviolet spectrum from 80-650 Angstrom (). They put agrazing incidence spectrometer on a sounding rocket to get above the earths atmosphere.Flying in the shadow of the earth and pointing away from the sun toward a dark area ofthe universe, the spectrometer measured the spectrum from 80 to 650 . Presumably thispart of the universe consists primarily of hydrogen and helium gas. The spectrumobtained is shown in Figure 7. There are a large number of spectral lines or peaks.

The Quantum Theory of the Atom does not predict that there are any spectral lines fromhydrogen or helium to be observed in this range. The new classical model of the atompredicts 64 spectral lines and peaks for hydrogen in this range as shown in Table 2 (at theend of this paper). All of the transition lines of Table 2 are found in the spectral data of

( )4122

22

RZemvT ==

( )4222

222

TR

ZeR

ZeRZeVTE ==+=+=

( )4312 22

42

=n

emZEh

( )4411 22 nZRhcEk H==

13

4

cm1096814

==hc

mR eH

Labov and Bowyer [5]. Furthermore the predicted transitional data accounts for most ofthe principal peaks of the observed spectrum as shown in Figure 7.

Multi-Electron Atoms. The procedures above only apply to one-electron atoms, especial-ly hydrogen. In order to treat atoms with more than one electron, it is useful to review theresults of Amperes experiments for the forces between current loops [12].

1. The effect of a current is reversed when the direction of the current isreversed.

2. The effect of a current flowing in a circuit twisted into small sinuosities isthe same as if the circuit were smoothed out.

3. The force exerted by a closed circuit on an element of another circuit isat right angles to the latter.

4. The force between two elements of circuits is unaffected when all lineardimensions are increased proportionately and the current strengthsremain unaltered.

The important point to note is that the forces between plain wire loops and wire loops withsmall sinuosities is the same. Figure 8 shows the neon atom consisting of two complete

Figure 7 [5]Extreme Ultraviolet Spectrum for Helium and Hydrogen

Numbered peaks correspond to hydrogenspectral lines predicted by new ClassicalTheory of the Atom but not QuantumMechanics (numbers are keyed to Table 2).

electron shells with the magnetic flux loops for each shelldrawn and the great circles on which they reside.According to Amperes experimental law each magneticflux loop may be replaced by a circular wire. The threeresulting parallel circular loops may be replaced by onecircular loop with the nucleus at the center. The effectiveradius may be different from that of the free electron.Thus for closed shell atoms, the atom acts effectively asif it had a single electron ring about the nucleus, just likethe Bohr model for a one-electron atom like hydrogen.

For the rest of the atoms the situation is not as neat. If thelast outermost electron shell has a number of electronsdivisible by four, the symmetry may reduce to an equiv-alent ring as above.

For atoms with an odd number of electrons other than 1 and all other cases, the symme-try may not reduce to a single loop. Some sort of computer modeling program may beneeded in order to get precise values for the energy levels and absorption and emissionspectra. (Note that the Quantum Models have problems with these atoms also.)

Fine Structure and Hyperfine Structure in Atomic Spectra. In the past classical mod-els of the atom, nucleus and elementary particles were unable to describe certain phenom-ena such as the atomic spectra fine structure due to electron spin-orbit coupling (quantuminterpretation) and the atomic spectra hyperfine structure due to nuclear-spin electron-spin coupling, because there was no classical quantity known as the spin of the electronor nucleon. In particular the electron was usually modeled as a sphere with a magneticmoment due to the rotation of charge but no additional quantity called spin. This situa-tion has been rectified by the refinement of the Bergmans [1] Toroidal Model and theBosticks [13,14] Charge Fiber Model of the electron and other elementary particles byLucas [15] into a full fledged Classical Electrodynamic Model of Elementary Particles.

According to the Lucas Model all elementary particles are composed of multiple inter-twined primary charge fibers. These primary charge fibers may be complex and consistof multiple intertwined secondary charge fibers. The secondary charge fibers may also becomplex and consist of multiple tertiary charge fibers.

In this model the electron is the simplest of all elementary particles. It consists of threesimple intertwined primary charge fibers in a toroidal shape. The figures 9, 10, 11,12, 13below[16] show the n = 1 fundamental or ground state of the electron, the n = 2 first excit-ed state or harmonic of the fundamental, the n = 3 second excited state or harmonic of thefundamental. Also shown are the n = 1/2 and n = 1/3 sub-harmonics of the fundamental.These latter states are characteristic of continuous rods or springs not discontinuous par-ticles. No parallel exists for these latter n = 1/2, 1/3, etc. states in the quantum orbits ofthe point electron about the nucleus of the atom.

Figure 8. Neon Atom.(Redrawn here to showsymmetrical placement ofinner shell of two electrons.)

The rotation of the three charge fibers aboutthe thickness of the toroidal ring producesthe spin s of the electron. The number of theharmonic in the ring gives the orbital quan-tum number l. The total angular momentumquantum number j = l + s is merely the totalangular momentum of the charge fibers inthe electron. The fine structure is due to thespin-orbit coupling or the interaction ofthe spin angular momentum about the cross section of the toroid with the angular momen-tum about the circumference of the toroid. The hyperfine structure is due to the interac-tion of the sum of the toroidal neutron and proton spins in the nucleus with the spin of thetoroidal electron.

The absorption and emission of light by the atomic electrons is explained by a combina-tion of macroscopic string theory and macroscopic antenna theory. A stretched string ina musical instrument is caused to change its vibration mode from the fundamental to thefirst harmonic by plucking it or hitting it at the appropriate place to transfer additionalenergy to the vibration. For the vibrating string this additional energy added to the stringis dissipated as heat and the string returns to the fundamental vibration. From macroscop-ic radio antenna theory the wavelength of the radiation emitted is a function of the phys-ical length of the antenna. In this manner one gets radiation as harmonics of the funda-mental length of the antenna and as sub-harmonics of the fundamental length. Thus this

Electron n = 1

Figure 9Electron Fundamental or Ground State

Figure 10Electron 1st Harmonic or Excited State

Figure 11Electron 2nd Harmonic or Excited State

Figure 12Electron 1st Subharmonic

Figure 13Electron 2nd Subharmonic

Electron n = 3Electron n = 2

Electron n = 1/2 Electron n = 1/3

Charge Fiber Model for Elementary Particles and the electron in particular gives a physi-cal explanation of absorption and emission on finite size electrons in an atom that is supe-rior to the non-physical explanation of Quantum Mechanics that has no analogy in themacroscopic world.

Summary. A new foundation for modern science based upon classical electrodynamicsthat has been expanded to allow particles to have finite size in the shape of a ring of chargecomposed of charge fibers is presented. This version of electrodynamics satisfies the rulesof logic that undergird the scientific method. It is able to describe the emission spectra ofatoms in a logically superior way compared to the politically correct relativistic QuantumElectrodynamics Theory as developed by Planck, Einstein, and Dirac. It is logically supe-rior for the following reasons:

1. A simpler approachonly electrodynamics, no Quantum or Relativity theory needed

2. Describes more dataespecially the extreme ultraviolet emission spec-trum of hydrogen

3. No obviously false assumptions or postulates like the point-particle assumption

4. Uses fewer postulates

5. Allows the laws of mechanics to hold on all size scales as always expected

6. Allows the laws of electrodynamics to hold on all size scales as always expected

7. Describes the physical mechanism for absorption and emission of electro-magnetic energy in terms of the harmonic and sub-harmonics of the fundamental vibration/rotation of charge fibers analogous to the way that macroscopic antennas work

8. Eliminates the random chance statistical basis of Quantum Mechanics in favor of a logical cause-and-effect basis

9. Allows absolute reference frames for all physical phenomena

10. Describes the emission and absorption spectra of multi-electron atoms

This approach, based on logic, leads to an electrodynamic description of the physical uni-verse based upon the logical laws of cause and effect. It is compatible with the Biblicalview of the universe created and sustained by God via electromagnetic means [17].

References.1. Bergman, D. L. And Wesley, J. P., Spinning Charged Ring Model of Electron

Yielding Anomalous Magnetic Moment, Galilean Electrodynamics, Vol. 1, No. 5,pp. 63-67 (Sept/Oct 1990).

2. Compton, Arthur H., American Physical Society address December 1917, PhysicalReview Series II, p. 330 (1918).

3. Compton, Arthur H., Physical Review Series II, Vol. XIV, No. 1, pp. 20-43 (1919).4. Compton, Arthur H., Physical Review Series II, Vol. XIV, No. 3, pp. 247-259 (1919).5. Labov, Simon E. and Stuart Bowyer, Spectral Observations of the Extreme

Ultraviolet of Background, The Astrophysical Journal, vol. 371, p. 810 (1990).6. Lucas, Joseph and Charles W. Lucas, Jr.,A Physical Model for Atoms and

NucleiPart 1, Foundations of Science, vol. 5, no. 1, pp. 1-7 (2002).7. Lucas, Joseph, A Physical Model for Atoms and Nuclei, Galilean Electrodynamics,

vol. 7, pp. 3-12(1996).8. Lucas, Joseph, and Charles W. Lucas, Jr., A Physical Model for Atoms and

NucleiPart 2, Foundations of Science, vol. 5, No. 2, pp. 1-8 (2002).9. Eisberg, Robert Martin, Fundamentals of Modern Physics (John Wiley and Sons,

Inc., New York, 1961).10. Born, Max, The Mechanics of the Atom, Bell, p. 95 (1927).11. Bergman, David L., Spinning Charged Ring Model of Elementary Particles,

Galilean Electrodynamics, vol. 2, p. 30 (1991).12. Ampere, Mem. De lAcad. VI, p. 175 (1825).13. Bostick, Winston H., Physics of Fluids, Vol. 9, p. 2079 (1966).14. Bostick, Winston H., Mass, Charge and Current: The Essence and Morphology,

Physics Essays, Vol. 4, No. 1, pp. 45-49 (1991).15. Lucas, Jr., Charles W., A Classical Electromagnetic Theory of Elementary Particles,

to be published in the proceedings of the second Physics as a Science Workshopheld at Lanzarote in the Canary Islands June 30 through July 6, 2002 in the Journal ofNew Energy.

16. These diagrams of the electron were initially drawn by Clayton Harrison, 2728 EastFranklin Avenue, Minneapolis, Minnesota 55406, with email [email protected],and then redrawn by David L. Bergman, Common Sense Science, P.O. Box 767306,Roswell, Georgia 30076, in terms of a single fiber. Future work will relate multiplesplit fibers to the unstable elementary particles.

17. Lucas, Jr., Charles W., A Physical Scientific Mechanism by Which God CreatedAccording to the Scriptures and Science, Proceedings of the Second InternationalConference on Creationism, Vol. 1, pp. 127-136. The conference was held July 30 toAugust 4, 1990 in Pittsburgh, PA and was published by Creation Science Fellowship,Inc., 362 Ashland Avenue, Pittsburgh, PA 15228.

TABLE 2 [5]

PREDICTED SPECTRAL LINES IN THE RANGE 80-650

PEAK RING MODEL PREDICTED OBSERVED# TRANSITION ORDER WAVELENGTH WAVELENGTH

() ()1 k = 1/ = RH [1/(1/6)2 - 1/(1/5)2] 1st 82.9 85 ! 5

-1/C Compton He Scattered 96.5 96 ! 52nd 165.8 165 ! 53rd 248.7 246 ! 54th 331.6 332 ! 55th 414.4 415 ! 56th 497.3 498 ! 57th 580.2 580 ! 5

2 k = 1/ = RH [1/(1/5)2 - 1/(1/4)2] 1st 101.3 101 ! 5-1/C Compton He

Scattered 122.5 122 ! 52nd 202.6 202 ! 53rd 303.9 303 ! 54th 405.2 405 ! 55th 506.5 506 ! 56th 607.8 608 ! 5

3 k = 1/ = RH [1/(1/3)2 - 1/(4)2] 1st 102.0 103 ! 5-1/C Compton He


4 k = 1/ = RH [1/(1/3)2 - 1/(3)2] 1st 102.6 103 ! 5 -1/C Compton He


5 k = 1/ = RH [1/(1/3)2 - 1/(2)2] 1st 104.2 103 5 -1/C Compton He



Scattered 141.6 140 ! 52nd 227.9 228 ! 53rd 341.9 342 ! 54th 455.9 458 ! 55th 569.9 570 ! 5


Scattered 167.7 168 ! 52nd 260.5 260 ! 53rd 390.8 390 ! 54th 521.0 520 ! 55th 651.3 645 ! 8


Scattered 265.1 265 ! 52nd 364.7 367 ! 53rd 547.1 547 ! 5


Scattered 384.7 385 ! 52nd 464.0 465 ! 5


Scattered 391.3 390 ! 52nd 468.8 470 ! 5


Scattered 416.2 415 ! 52nd 486.3 486 ! 5


Scattered 633.8 634 ! 52nd 607.8 603 ! 5

13 k = 1/C = Helium Resonance Scattered 584.6 584 ! 5

Foundations of Science August, 2003 Reprint/Internet Article Page 1 http://CommonSenseScience.org

A Physical Model for Atoms and Nuclei Part 4 Blackbody Radiation and the Photoelectric Effect

Charles W. Lucas, Jr. 29045 Livingston Drive

Mechanicsville, MD 20659 [email protected]

Abstract. A physical geometrical packing model for the structure of the atom was developed previously [1-8] based on the physical toroidal ring model of elementary particles proposed by Bergman [9]. From the physical characteristics of real electrons experimentally determined by Compton [10-12] this work derived, using combinatorial geometry, the number of electrons that pack into the various physical shells about the nucleus in agreement with the observed structure of the Periodic Table of the Elements. The constraints used in the combinatorial geometry derivation were based upon simple but fundamental ring dipole magnet experiments and spherical symmetry. From a magnetic basis the model explained the physical origin of the valence electrons for chemical binding and the reason why the Periodic Table has only seven periods. The toroidal model was then extended to describe the emission spectra of hydrogen and other atoms. Use was made of some of the authors standing-wave experiments with large toroidal springs. The resulting model accurately predicted the same emission spectral lines as the Quantum Model including the fine structure and hyperfine structure. Moreover it went beyond the Dirac and Bohr quantum models of the atom to predict 64 new lines or transitions in the extreme ultraviolet emission spectra of hydrogen that have been confirmed by the Extreme Ultraviolet Physics Lab at Berkeley from its NASA rocket experiment data [13]. In this work blackbody radiation and the photoelectric effect are explained in terms of the Ring Model and electromagnetic waves. Here the emphasis is on the atom consisting of finite-size electrons acting as contain-ers with quantized internal standing-wave-type structures for absorbing and emitting electromagnetic waves in contrast to the notion of quantized packaging of electromagnetic energy into particles called photons. Classical Explanation of Quantum Phenomena. Historically the Theory of Quantum Physics was invented to explain three phenomena, i.e. blackbody radiation, the photoelectric effect, and the structure and energy levels of the atom. In the first part of this research based on Bergmans physical model of elementary

Figure 1. Absorption and Emission of Radiation

by Ring-Electrons. Top (absorption) Energy is absorbed from the incoming lightwave by the electron (magnetic induction). Redistri-bution of charge is shown with electron in a state of excited energy. The actual distribution of charge is more complicated than the drawing shows. Bottom (emission) Electron releases energy by radiation of a new wave and another redistribution of charge (emission in accordance with electric induction).

Absorption

Emission

Foundations of Science August, 2003 Reprint/Internet Article Page 2 http://CommonSenseScience.org

particles [9], the structure of both the atom and the nucleus was predicted using combinatorial geometry and electrodynamics [1-8]. In this part the research is extended to explain the remaining phenomena that were foundational to Quantum Theory. One outcome of this work is the conclusion that quantum effects are not due to the Quantum Electrodynamics Theory of point-particles with a quantum of electromagnetic energy called a photon, but rather to the internal structure of finite-size electro-dynamic particles. This possibility has always been recognized, but not seriously considered because it was not known how to explain some key experimental data such as the Photoelectric Effect and Blackbody Radiation. Blackbody Radiation [8]. In 1901 Max Planck [14] was able to find a mathematical expression that fit the blackbody radiation data. His attempts to work backwards to find the correct physical theory resulted in the birth of Quantum Physics. However, this theory was never fully satisfactory. It was based on the notion that point-charges undergoing simple harmonic motion in the blackbody were absorbing and emitting radiation. This picture led to oscillations of point-electron charges that were too big to remain in the lattice of the solid. Also, the empirical laws of electrodynamics were violated by Plancks theory. Both Ampres Law and Faradays Law require continuous emission and absorption of radiation for simple harmonic motion of point-electron charges. Finally, the Quantum Theory of blackbody radiation was not compatible with optical reflection, refraction, and diffrac

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A Physical Model for Atoms and Nuclei