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The Atom {© 14/11/2017}

This paper, which was released by Keith Dixon-Roche (one of CalQlata's Contributors) on the 14th of November 2017 explains the atom using Newton's and Coulomb's laws and without the need for a unification theory.
His description fully complies with Rydberg's Atom

Note: All the input data in these calculations has been provided by CalQlata's Constants page.
All calculations are the sole copyright priority of Keith Dixon-Roche © 2017
Keith Dixon-Roche is also responsible for all the other web pages on this site related to atomic theory
A 'pdf' version of this paper can be found at: The Atom - The Paper

This paper should be read in conjunction with the following:
Laws of Motion
Planetary Spin
Rydberg Atom
Planck Atom
Newton Atom

The Atom (a summary)

This page is a summary of the above paper.

The levels of accuracy on this page have been set to assist CalQlata in its effort to ensure that the calculations are not aproximations.
To this end, Calqlata has confirmed all constants used in these calculations via original formulas and indisputable data where possible.

Conclusions

The calculations included in this paper have clearly shown that Newton's laws of motion and Coulomb's laws for electrostatic force, can be used to fully explain the behaviour of protons, neutrons and electrons within a classical atom without additional assistance. It is therefore the author's opinion that there is no need for a unification theory.

Moreover, the atom is not nearly as complicated as has been claimed. It comprises only three sub-atomic particles;  electrons following evenly spaced circular orbits around a nucleus of protons and neutrons.

The beryllium atom

Fig 1. Typical Atomic Model

A very simple system!

Exactly as shown in Fig 1

There is no such thing as mass as we know it. Mass is a partial energy state that varies with kinetic energy.

Henri Poincaré's relativistic relationship; E = m.v²
should be; E = m.v² + J.ω²

Every part of every atom (from Z = 1 to Z = 92) has been fully analysed and explained using Newton's and Coulomb's laws during the generation of this paper.

The Body System

Any atom.

Methodology

Devise a simple mathematical procedure using Newton's and Coulomb's laws conjointly that will work from atomic and shell numbers, through a description of the properties and behaviour of every electron, proton and neutron in any atom in such a way that perfect atomic structures (RAM = 2.Z) can be worked back again to shell and atomic numbers.

Calculate and list the properties of all/any electron(s) in each shell and the properties of the Proton and the neutron required to maintain an atomic structure. Subsequently, explain why the system works.

Constants & Formulas

Isaac Newton's gravitational constant: G = 6.67359232004332E-11 m³/kg/s²
Coulomb's constant: k = 8.98755184732667E+09 N.m²/C²
Elementary charge unit: Qₑ = -Qp = -1.60217648753000E-19 C
Ultimate density: ρ = 7.12660796350450E+16 kg/m³

Calculations

Assumption (that will be proven in the calculations)

Protons and electrons provide electrical repulsion forces between themselves and attraction forces between each other.

Opposing forces; gravity and electrical charge

Fig 2. Opposing Forces between Proton and Electron (gravity vs Electrical Charge)

Fig 2 shows the ratio of attraction (φ) between Newton's gravitational law and Coulomb's electrostatic law

Electron Orbital Shape (half-parameter; 'p')

'n' shall represent a shell number
'Z' shall represent an atomic number
The following formulas are well known and proven by Rydberg and others:
Electron velocity in shell 1: v₁ = (2 . aₒ / mₑ)⁰˙⁵
Electron velocity in shell 'n': vn = v₁ / n
Newton's gravitational force: Fg = G.mp.mₑ / Rn²
Newton's gravitational energy: Eg = G.mp.mₑ / Rn
Newton's constant of motion: h = v.p
Newton's constant of motion in shell 'n'; hn = Fg.pn / mₑ.Rn
Shell orbit half-parameter; pn = n²
Shell orbit eccentricity (e); 0 = Rn.e² - pn.e + [(hn/h₁)² - Rn]

ShellFg (N)hn (m²/s)pnRn (m)e
13.63115175461575E-478.67914596934971E-0415.291772106700E-111
22.26946984663484E-482.16978649233743E-0442.116708842680E-101
34.48290340076018E-499.64349552149968E-0594.762594896030E-101
41.41841865414678E-495.42446623084357E-05168.466835370720E-101
55.80984280738519E-503.47165838773989E-05251.322943026675E-091
Table 1

As can be seen from the above Table, the eccentricity (e) of all orbits is exactly 1; i.e. a circle

Electron Velocities

Each shell contains a limited number of evenly spaced electrons (due to repelling electrical forces) all of which travel at the same velocity. This repulsion (see Electrical Forces and Energies) between electrons limits the number of available orbits (per shell) and also defines the radial distance between shells
(see Inter-Shell Electron Separation)
Shel1 1: 2
Shel1 2: 8
Shel1 3: 18
Shel1 4: 32
Shel1 5: 32#
# whilst shell 5 can hold more than 32 electrons, atomic numbers 1 to 92 occupy shells 1 to 5 with 32 electrons in the last shell

Perfect atoms are assumed (RAM = 2.Z) in the following calculations in order to verify the mathematics.

Shell Radius: Rn = Rn-₁ + aₒ.(2.n - 1)

Electron velocity in shell 'n': vn = v₁ / n

Electron orbital period; tn = t₁ . n³ {t₁ = 2.π.aₒ / v₁}

Electron angular velocity; ωn = 2.π / vn

The velocity details for the first 5 shells are listed as follows:

ShellRn (m)vn (m/s)tn (s)ωn (ᶜ/s)
15.291772107E-112187690.3511.519830480E-164.134135610E+16
22.116708843E-101093845.1751.215864384E-155.167669512E+15
34.762594896E-10729230.11684.103542295E-151.531161337E+15
48.466835371E-10546922.58769.726915070E-156.459586890E+14
51.322943027E-09437538.07011.899788100E-143.307308488E+14
Table 2

Every electron in each shell will perform according to the above Table.

Atomic Masses

The following particle details are used in these calculations:
Electron rest mass: mₑ = 9.1093897E-31 kg
Electron radius: rₑ = 1.45046059426276E-16 m
Proton rest mass: mp = 1.67262163783E-27 kg
Proton radius: rp = 1.77613270336827E-15 m
Neutron rest mass: mn = 1.6475621480E-27 kg
Neutron radius: rn = 1.76721793001688E-15 m
All of which are based upon a [universal] ultimate density (ρ) that was proven in the author's solution for Newton's gravitational constant; 'G'

Whilst 92 atoms have been analysed by the author, the following Tables (3 to 6) comprise the calculation results for the first 5 atoms occupying each shell, except for shell 1 which contains only 2 electrons.

ZShellZ.mₑ (kg)Z.mp (kg)Z.mn (kg)
119.1093897000E-311.6726216378E-271.6475621480E-27
211.8218779400E-303.3452432757E-273.2951242961E-27
322.7328169100E-305.0178649135E-274.9426864441E-27
423.6437558800E-306.6904865513E-276.5902485922E-27
524.5546948500E-308.3631081892E-278.2378107402E-27
625.4656338200E-301.0035729827E-269.8853728883E-27
726.3765727900E-301.1708351465E-261.1532935036E-26
1131.0020328670E-291.8398838016E-261.8123183629E-26
1231.0931267640E-292.0071459654E-261.9770745777E-26
1331.1842206610E-292.1744081292E-262.1418307925E-26
1431.2753145580E-292.3416702930E-262.3065870073E-26
1531.3664084550E-292.5089324567E-262.4713432221E-26
2942.6417230130E-294.8506027497E-264.7779302293E-26
3042.7328169100E-295.0178649135E-264.9426864441E-26
3142.8239108070E-295.1851270773E-265.1074426589E-26
3242.9150047040E-295.3523892411E-265.2721988737E-26
3343.0060986010E-295.5196514048E-265.4369550886E-26
6155.5567277170E-291.0202991991E-251.0050129103E-25
6255.6478216140E-291.0370254155E-251.0214885318E-25
6355.7389155110E-291.0537516318E-251.0379641533E-25
6455.8300094080E-291.0704778482E-251.0544397747E-25
6555.9211033050E-291.0872040646E-251.0709153962E-25
Table 3

Electrical Forces and Energies

The following Table comprises the electrical forces derived by Charles-Augustin de Coulomb along with their conversion to electrical energy:
Fₑ = k.Qₑ.Qp / Rn²
Eₑ = Fₑ.Rn

ZShellFₑ (N)Eₑ (J)
112.05968051240E-082.17987197685E-18
218.23872204961E-088.71948790740E-18
321.15857028823E-084.90471194791E-18
422.05968051240E-088.71948790740E-18
523.21825080063E-081.36241998553E-17
624.63428115291E-081.96188477916E-17
726.30777156923E-082.67034317164E-17
1133.07680669137E-082.93071676888E-17
1233.66165424427E-083.48779516296E-17
1334.29735810612E-084.09331515653E-17
1434.98391827693E-084.74727674958E-17
1535.72133475667E-085.44967994212E-17
2946.76637230832E-081.14579520783E-16
3047.24106430142E-081.22617798698E-16
3147.73184754851E-081.30928560610E-16
3248.23872204961E-081.39511806518E-16
3348.76168780471E-081.48367536424E-16
6151.22625138986E-073.24452145034E-16
6251.26678590235E-073.35177115160E-16
6351.30797951260E-073.46076475045E-16
6451.34983222061E-073.57150224687E-16
6551.39234402638E-073.68398364088E-16
Table 4

Gravitational Forces and Energies

The following Table comprises the gravitational forces and energies in each atom according to Newton's laws of motion.

Jₑ = ⅖.mₑ.Rₑ²
Fg = G.mn² / (2.Rn
PE = -Fg.2.Rn
KE = Z.(½.mₑ.vn² + ½.Jₑ.ωn²) {vn & ωn from Table 2 above}
Eg = PE + KE
K = Eₑ / Eg {Eₑ from Table 4 above}

ZShellFg (N)PE (J)KE (J)Eg (J)K
111.61726440178E-44-1.71163893009E-542.179871977E-182.179871977E-181
216.46905760710E-44-6.84655572038E-544.359743954E-184.359743954E-182
329.09711225999E-45-3.85118759271E-541.634903983E-181.634903983E-183
421.61726440178E-44-6.84655572038E-542.179871977E-182.179871977E-184
522.52697562777E-44-1.06977433131E-532.724839971E-182.724839971E-185
623.63884490400E-44-1.54047503709E-533.269807965E-183.269807965E-186
724.95287223044E-44-2.09675768937E-533.814775959E-183.814775959E-187
1132.41591348907E-44-2.30120345046E-532.664287972E-182.664287972E-1811
1232.87513671427E-44-2.73862228815E-532.906495969E-182.906495969E-1812
1333.37429239383E-44-3.21407754651E-533.148703967E-183.390911964E-1814
1534.49240111604E-44-4.27909732524E-533.633119961E-183.633119961E-1815
2945.31296625740E-44-8.99680212631E-533.951017958E-183.951017958E-1829
3045.68569516249E-44-9.62796898178E-534.087259957E-184.087259957E-1830
3146.07105894573E-44-1.02805313239E-524.223501955E-184.223501955E-1831
3246.46905760710E-44-1.09544891526E-524.359743954E-184.359743954E-1832
3346.87969114662E-44-1.16498424680E-524.495985952E-184.495985952E-1833
6159.62854534241E-44-2.54760338355E-525.318887624E-185.318887624E-1861
6259.94682297668E-44-2.63181601891E-525.406082503E-185.406082503E-1862
6351.02702758570E-43-2.71739796542E-525.493277382E-185.493277382E-1863
6451.05989039835E-43-2.80434922307E-525.580472261E-185.580472261E-1864
6551.09327073560E-43-2.89266979186E-525.667667140E-185.667667140E-1865
Table 5

The above Table shows that the ratio between Newton's kinetic energy for the electron and Coulomb's repulsion energy (between proton and electron: K) is exactly the atomic number (Z), proving that Newton's and Coulomb's laws together can be used to describe the distribution of and forces between electrons throughout an atom according to a simple and robust law.

Inter-Shell Electron Separation

The repulsion forces between adjacent electrons define both shell spacing and the limiting number of electrons in each shell. This limitation is dependent upon the separation distance between adjacent electrons whether in the same or an adjacent shell, and is calculated thus:
Shell volume: Vn = 4/3.π.Rn³
Shell area: An = 4.π.Rn²
Separation distance: dn = Vn / n.An
Repelling force: Fn = k.Qₑ² / dn²
Electrical balance distance: ℓn = Eₑ/Fn
Z = (ℓn/ℓ₁)⁰˙⁵

ZShellVn (m³)An (m²)dn (m)Fn (N)n (m)Z
116.20715E-313.51894E-201.76392E-117.41485E-072.93987E-121
216.20715E-313.51894E-201.76392E-117.41485E-071.17595E-112
323.97257E-295.63031E-193.52785E-111.85371E-072.64589E-113
423.97257E-295.63031E-193.52785E-111.85371E-074.70380E-114
523.97257E-295.63031E-193.52785E-111.85371E-077.34968E-115
623.97257E-295.63031E-193.52785E-111.85371E-071.05835E-106
723.97257E-295.63031E-193.52785E-111.85371E-071.44054E-107
1134.52501E-282.85034E-185.29177E-118.23872E-083.55725E-1011
1234.52501E-282.85034E-185.29177E-118.23872E-084.23342E-1012
1334.52501E-282.85034E-185.29177E-118.23872E-084.96839E-1013
1434.52501E-282.85034E-185.29177E-118.23872E-085.76215E-1014
1534.52501E-282.85034E-185.29177E-118.23872E-086.61472E-1015
2942.54245E-279.00849E-187.0557E-114.63428E-082.47243E-0929
3042.54245E-279.00849E-187.0557E-114.63428E-082.64589E-0930
3142.54245E-279.00849E-187.0557E-114.63428E-082.82522E-0931
3242.54245E-279.00849E-187.0557E-114.63428E-083.01043E-0932
3342.54245E-279.00849E-187.0557E-114.63428E-083.20152E-0933
6159.69867E-272.19934E-178.81962E-112.96594E-081.09393E-0861
6259.69867E-272.19934E-178.81962E-112.96594E-081.13009E-0862
6359.69867E-272.19934E-178.81962E-112.96594E-081.16684E-0863
6459.69867E-272.19934E-178.81962E-112.96594E-081.20417E-0864
6559.69867E-272.19934E-178.81962E-112.96594E-081.24210E-0865
Table 6

The above Table shows that Coulomb's repulsion energy between electrons within each shell and between adjacent shells leads directly to the atomic number and thus reinforces the fact that electron accommodation per shell is also explained according to a simple and robust law without any additional resources.

The following Table shows the relationship between atomic and shell numbers, where
N = the maximum permissible number of electrons in shell 'n'
...

Atomic NumberShell NumberShell Capacity
Z = Eₑn / Egnn = Rn / 3.dn = (ℓn/ℓ₁)⁰˙⁵N = 2.n²
111
211
328
428
528
628
728
11318
12318
13318
14318
15318
29432
30432
31432
32432
33432
61550
62550
63550
64550
65550
Table 7

... thus completing the calculation loop: From atomic and shell numbers, through all the energy and force relationships for all atoms and back to atomic and shell numbers; see Methodology above.

Summation and Conclusions

This sub-section is a summary of the properties of all/any/each sub-atomic particle.

References to 'mass' are to be interpreted as 'mass-energy'

References to 'velocity' are to be interpreted as 'linear and angular and vibrational' velocity unless stated otherwise

References to 'kinetic energy' are to be interpreted as 'linear and angular and vibrational' kinetic energy unless stated otherwise

References to 'thermodynamic' energy throughout this book are to be interpreted as 'thermodynamic and electromagnetic' energy unless stated otherwise

The author has concluded that there are only three sub-atomic particles; an electron, (e.g. a photon is simply a free electron), a proton and a neutron, each of which is a packet of energy

There is no such thing as mass as we know it. Mass is simply an energy component that varies according to the relativistic kinetic relationship described by Henri Poincaré and the author:
E = m.v² + J.ω²
which is a definition of its relative kinetic energy

All particles have the same rest-energy (@ 0K): -2.17987197684281E-18, which varies according to the following relationship:
Total Energy (@ 0K) + Thermodynamic Energy = Potential Energy + Kinetic Energy (linear and angular)
In which kinetic energy varies according to the following relativistic relationship:
ETOTAL = m.v² + J.ω²

The electron possesses linear kinetic energy
We know that an electron's natural velocity is linear because if it escapes from its atom, it will travel in a straight line, e.g. a photon. An electron cannot influence the rotation of its proton because of its circular orbit (spin theory).

The proton possesses angular kinetic energy
We know that a proton possesses rotational energy because it is a basic requirement of spin theory (necessary to drive orbiting electrons). Neutrons cannot be responsible for driving the orbiting electrons because the basic hydrogen atom contains no neutrons.

The neutron possesses vibrational kinetic energy
This is assumed because it is the only remaining kinetic energy available, and a neutron must possess kinetic energy to ensure compliance with the law of energy conservation.

The mass of each energy packet will differ according to its kinetic energy (½m.c² + ½J.ω²), which can be varied by a change in thermodynamic energy.

Sub-atomic particles are held together (in the form of an atom) by their inherent electro-magnetic charge, as defined by Coulomb. Even photons contain an electrical charge, which is revealed in the form of light.

The properties of all sub-atomic particles that never vary (constant) are as follows:
Electrical Charge: 1.60217648753E-19 C
Mass Density: 7.12660796350450E+16 kg/m³
Relativistic Kinetic Energy (@ 0K): 4.3597439537151E-18 J
Total Energy (@ 0K): -2.17987197684281E-18 J

When thermodynamic energy is added to any particle, its mass-energy is converted into velocity (linear and/or angular) and its potential energy will reduce with the mass. The greater the thermodynamic energy in a particle the faster it moves and the lighter it becomes.

All of the above is demonstrated in the following Tables at absolute zero (temperature = 0K):

Table 8.1 shows the dimensional properties of shells 1 to 5

NoCapacityRadiusAreaVolumeSeparation½ parametereccentricity
mm
n2.n²Table 2Table 6Table 6Table 6Table 1Table 1
125.29177E-113.51894E-206.20715E-311.76392E-1111
282.11671E-105.63031E-193.97257E-293.52785E-1141
3184.76259E-102.85034E-184.52501E-285.29177E-1191
4328.46684E-109.00849E-182.54245E-277.0557E-11161
5501.32294E-092.19934E-179.69867E-278.81962E-11251
Table 8.1: Dimensional Properties

The above Table shows that all electrons orbit the nucleus in circular paths (eccentricity = 1).

Table 8.2 shows the kinetic properties of any/all electrons in shells 1 to 5

NoMassRadiusLinear VelocityLinear PeriodAngular VelocityAngular Momentum
kgmm/ssᶜ/skg.m²
n(Emc - Jₑ.ωₑ) / vₑ²³√[3.m / 4π.ρ]Table 2Table 2Table 22/5.m.R²
19.10939E-311.45046E-162187690.3511.51983E-164.13414E+167.66586E-63
23.64376E-302.30246E-161093845.1751.21586E-155.16767E+157.72671E-62
38.19845E-303.01708E-16729230.11684.10354E-151.53116E+152.98514E-61
41.4575E-293.65493E-16546922.58769.72692E-156.45959E+147.78803E-61
52.27735E-294.24117E-16437538.07011.89979E-143.30731E+141.63856E-60
Table 8.2: Electron Kinetic Properties

Table 8.3 shows the kinetic properties of any/all electrons in shells 1 to 5

NoGravitational ForceElectro-Static ForceCentrifugal ForceNewton's Motion Constant (h)(hn/h₁)²
NNNm²/s
nG.mp.mₑ / R²k.Qp.Qₑ / R²m.vₑ² / R√[Fg.p / mₑ.R](hn/h₁)²
13.63115E-478.23872E-088.23872E-080.0008679151
29.07788E-485.1492E-092.05968E-080.0002169790.0625
34.03461E-481.01713E-099.15414E-099.6435E-050.012345679
42.26947E-483.21825E-105.1492E-095.42447E-050.00390625
51.45246E-481.3182E-103.29549E-093.47166E-050.0016
Table 8.3: Particle Binding Properties

Table 8.4 shows the energy any/all electrons in shells 1 to 5

NoLinear Kinetic Angular Kinetic Total KineticElectrical Potential Gravitational Potential Total EnergyRelativistic Energy
JJ JJJ JJ
n½.mₑ.vₑ² ½.Jₑ.ωₑ² KEv + KEωk.Q².ω₁/R.ωn G.mp.mₑ / REPQ + EPgmₑ.vₑ²+Jₑ.ωₑ²
12.1799E-18 6.5509E-30 2.1799E-184.3597E-18 1.9215E-57-2.1799E-184.3597E-18
22.1799E-18 1.0317E-30 2.1799E-184.3597E-18 4.8038E-58-2.1799E-184.3597E-18
32.1799E-18 3.4993E-31 2.1799E-184.3597E-18 2.135E-58-2.1799E-184.3597E-18
42.1799E-18 1.6248E-31 2.1799E-184.3597E-18 1.201E-58-2.1799E-184.3597E-18
52.1799E-18 8.9615E-32 2.1799E-184.3597E-18 7.6861E-59-2.1799E-184.3597E-18
Table 8.4: Particle Energy Properties

 

massAngular MomentumLinear VelocityAngular VelocityGravitational Acceleration
kgkg.m²m/sᶜ/sm/s²
EQ/c²2/5.m.(3.m/4π.ρ)⅔0√[(EQ-v)/J]G.mp/Rn
Proton1.67262E-272.11061E-5704.54492E+193.98616E-17
Neutron1.64756E-272.05817E-5751441.022103.92644E-17
Table 8.5: Proton and Neutron Dimensional Properties

 

Kinetic EnergyPotential EnergyElectrical PotentialTotal EnergyRelativistic Energy
JJJJJ
½.m.v² + ½.J.ω²G.mp.mn / (rp+rnQKE+PE+EPQm.v² + J.ω²
Proton2.17987E-185.19021E-501.60218E-19-2.34009E-184.35974E-18
Neutron2.17987E-181.89273E-571.60218E-19-2.34009E-184.35974E-18
Table 8.6: Proton and Neutron Energy Properties

The above Table shows that all three sub-atomic particles possess the same total and relativistic energies. Moreover, the difference between each particle is defined by its kinetic energy and therefore its mass. Their potential energy will reduce with mass.

The addition of thermodynamic energy to any and all sub-atomic particles will alter their kinetic energy and therefore their mass and therefore their potential energy, and their total and relativistic energies will vary according to the thermodynamic energy added.

Even a photon possesses mass: mass = Relativistic Energy ÷ c² = 4.85087E-35 kg; validating Henri Poincaré's formula. If mass is zero at light-speed the energy of a photon would also be zero and the 'conservation of energy' law wouldn't allow that.

According to Ludwig Boltzmann (KB = Rᵢ ÷ NA), the relativistic energy of 4.35974E-18J is reached for a photon if sufficient thermodynamic energy is added to an electron to raise its temperature from 0K to 315774.3836K, which would reduce its mass (according to Henri Poincaré's relativism), and therefore its potential energy (maintaining the conservation of energy).

Claims

Claim 1: There are only three particles in an atom; electron, proton and neutron

Claim 2: All three particles possess inherent kinetic and potential energies

Claim 3: Neutrons possess vibration; protons possess angular velocity; electrons possess linear velocity

Claim 4: Electrons follow circular orbits, in the same direction, around the surface of spherical shells

Claim 5: Electrons are evenly spaced within and throughout spherical shells due to balanced electrical repulsion and attraction forces between themselves and protons.

Claim 6: The –ve orbiting electrons generate a magnetic field around the atom's +ve nucleus

Claim 7: Neutrons contain the magnetic field generated by the electrons and the protons

Claim 8: Protons attract electrons and repel each other due to electrical forces

Claim 9: Electrons attract protons and repel each other due to electrical forces

Claim 10: All sub-atomic particles possess the same total and relativistic energies

Claim 11: The absorption of thermodynamic energy applies equally to each and every sub-atomic particle in identical measure in accordance with Boltzmann's law

Claim 12: The absorption of thermodynamic energy will increase a particle's velocity (linear, angular or vibratory) and reduce its mass according to kinetic relativism

Claim 13: Mass is a partial energy state that varies with kinetic energy according to the relativistic relationship: E = m.v² + J.ω²

Claim 14: The atom can be fully explained using Newton’s and Coulomb’s laws

Claim 15: There is no need for a sub-atomic unification theory

 

Further Reading

You will find further reading on this subject in reference publications(55, 60, 61 & 62)

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