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The Atom {© 17/04/18}

The following hypothesis, which is the culmination of Keith Dixon-Roche's work on Isaac Newton's laws of motion, describes a working model of the atom requiring neither quantum nor unification theories.

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 © 2018
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 pulls together all of the previous work compiled by the author with a view to describing the atom using Isaac Newton's laws of motion.
It is claimed (by the author) that, contrary to popular belief, Isaac Newton's laws of motion apply to all branches of science, including atomic, and that the atom is a far more elegant and simpler system than hitherto believed.
This study of Isaac Newton's work has revealed that there are most probably only three sub-atomic particles, i.e. there is no need for further sub-division into quarks, leptons, fermions, etc.

The purpose of this paper is to provide a literary description of the atomic model along with the energies that cause it to exist in its various states; gas, liquid and solid
The calculations associated with this paper provide the mathematical basis for;
1) inverse proportionality of electron velocity to its orbital radius
2) relationship between electron velocity and temperature
3) electron shells
4) source of the neutron

The Model

The atom is simple, elegant and a brilliant piece of engineering. Whilst all the information needed to understand it was available at the end of the 19ᵗʰ century, a total appreciation of its qualities has continued to elude us.

Atomic Particles

Atomic particles are pictorially represented here as solid spherical objects for convenience only. It is not proposed that they are in any way spherical, solid or a specific size.

The atom comprises only three atomic particles Fig 1 that between them hold it together and naturally attract or repel other atoms. They are:

The only three sub-atomic particles

Fig 1.

Electrons: non-polar magnetic packets of energy with negative electrical charge of fixed magnitude and perpetual but variable kinetic energy

Protons: non-polar magnetic packets of energy with a positive electrical charge of variable magnitude

Neutrons: protons and electrons combined through high temperature

The difference between electrical and non-polar magnetic, attractive and repulsive forces is 4.407E-40 (φ)

Electro-Magnetic Radiation

Electro-magnetic energy is what we regard as heat and light.
The various types of energy (light, radio, X, γ, etc.) are defined by an atom’s nucleic structure and radiated in different wavelengths and we perceive as colour, noise, etc.
The magnitude of a radiated energy wave; brightness, loudness, etc. is defined by its amplitude.

Orbiting electrons continuously collect electro-magnetic energy (heat) converting it into kinetic energy (increasing their velocity). In doing so, proton-electron pairs generate (and radiate) electro-magnetic energy, simultaneously reducing kinetic energy in the electrons. This process of energy transfer continues only whilst the orbiting electron holds a temperture-microstate greater than 1 (Nₜ>1) and/or continues to collect electro-magnetic energy.

As the velocity of an orbiting electron increases, its orbital radius decreases and the electro-magnetic energy radiated by its proton increases along with the magnetic attraction between the proton, the electron and the neutron (Fig 5). I.e. the strength of an atomic assembly rises with increasing kinetic energy in the electron (i.e. increasing temperature).

Electro-magnetic radiation is deflected as it passes a large body e.g. a planet or star because of magnetic attraction, i.e. what we currently understand as gravity.

Electron Shells

Each electron shell contains up to two electrons, both of which are identical. They are held in their shells by a balancing act between the electrical repulsion from each other (including those in the next shell(s)), and the attraction to their protons in exactly the same way as Newton described the balance between centrifugal force and gravitational force in an orbiting satellite and its force-centre.

How they work

Electrons and protons possess the same electrical charge when at rest (Nₜ = 1). The electrical charge in the electron never changes but that of the proton varies with the speed of its orbiting electron .

Electrical repulsion between adjacent protons

Fig 2.Proton Repulsion

Lone protons will always consistently repel each other with equal force due to their identical electric charges. This is the most basic form of matter; what we call hydrogen gas. Lone protons can never accumulate in solid or even liquid form because the repulsion force is constant everywhere within the volume they occupy
(Fig 2).

A proton can trap a slow-moving electron if it passes close enough to enable the opposite electrical charges to engage (Fig 3). Once trapped, the electron will remain in orbit around the proton until one of the two following events occur:

Proton trapping an electron

Fig 3.
Electron Trapping

1) An adjacent atom provides sufficient excessive electro[-magnetic] charge to cause it to swap orbits, or

2) Another electron impacts it with sufficient energy to knock it out of its orbit

An electron’s orbit is circular because the electron is providing its own kinetic energy; i.e. it is not generated by the potential energy between it and its proton.

A proton with an orbiting electron naturally generates a magnetic field with a positive (e.g. N) pole at one face of the orbit and a negative (e.g. S) pole at the other (Fig 4), empowering the proton-electron pair to attract a neutron. This is what we call deuterium (Fig 5).

As the kinetic energy in orbiting electrons rises, the [electro-]magnetic attraction between the protons and neutrons within the same electron shells increases and continues to do so as long as all protons within a nucleus are electrically isolated from each other by surrounding neutrons.

Fusion, the joining of separate proton-electron pairs to create a different element, is accomplished by applying sufficient pressure to force two nuclei together such that their combined electron shells locate them within the same [electro-]magnetic field.

The State of Matter

Electro-magnetic polar magnetism

Fig 4.Polar Magnetism

Magnetic and electrical charges are both active across atomic boundaries (outside the atomic shells), but whilst magnetic charges between neighbouring atoms are attractive, electrical charges are repulsive.

At relatively low temperatures, accumulative non-polar and [electro-]magnetic polar magnetic attraction is greater than the repulsion between adjacent atoms caused by the additional electrical charges generated in the protons. As the temperature rises, however, the increasing repulsive electrical charges will eventually force atoms apart. The temperature at which this occurs depends upon the size and structural matrix of the atomic nuclei concerned. As a general rule, the greater the number of proton-electron pairs in a single nucleus, the greater the magnetic attraction; i.e. the higher the melting temperature.

Solid matter is that in which magnetic attraction between adjacent atoms is greater than the electrical repulsion.

Liquid matter is that in which adjacent atoms repel each other via increasing electrical charge. The repulsion force (F = k.q²/R²) between adjacent atoms is less than that induced by magnetic (gravitational) attraction from the supporting planetary mass. Surface tension also plays its part in liquid retention but is not considered here.

Gaseous matter is that in which adjacent atoms repel each other via increasing electrical charge. The repulsion force (F = k.q²/R²) between adjacent atoms is greater than that induced by magnetic (gravitational) attraction from the supporting planetary mass. Each gaseous atom settles once the magnetic (gravitational) force due to its ‘height’ (distance from the supporting planetary mass) balances with the atomic separation force. Gaseous atoms only repel other atoms with the same magnetic charge (Dalton’s law)

Orbital radius inversely proportional to temperature

Fig 5. Orbit Radius

As the number of proton-electron pairs increases within an atom, its ability to attract adjacent atoms also increases but the less stable they become. The ability for atomic particles to remain together (within an atom) is strong up to and including the size of an iron atom (Z=26). Atomic nuclei larger than this tend to lose proton-electron pairs, e.g. the gradual reduction of uranium into lead. As a general rule (but there are exceptions; e.g. lead, zirconium) the larger the atom the faster the rate of disintegration, which is influenced by the nucleic structure

When matter, e.g. steel, is heated, we see the colour change with temperature. At low heat (electro-magnetic energy), only long (red) wavelengths are emitted. As the heat increases shorter (blue) wavelengths will be emitted (Fig 6). As temperature rises to a gaseous condition all wavelengths mix and the colour becomes white. It is important to note that very little electro-magnetic energy is emitted by cold material (<≈10K) and is the reason black-bodies emit negligible electro-magnetic radiation.


Isotopes are atoms with the same atomic number (Z) but with varying atomic mass due to unequal proton-neutron pairing.

For example; an atom of iron, with 26 protons and 26 neutrons is an isotope of 52. However, in nature, most iron atoms have more than 26 neutrons, each of which is given its own isotope, e.g. 57, 59, etc.

Colour variation with temperature

Fig 6.

Over time, the electro-magnetic magnetism generated by atomic nuclei will split surplus neutrons into their component parts, changing the atom into a different element. As the number of protons increases, the atoms will become less stable (stability is determined by nucleic structure) and subsequently divide into smaller atoms. The rate at which this occurs is referred to as the half-life of the atom. The half-life of any atom is a constant, it never changes.

Apart from oxygen all atoms naturally have more neutrons than protons.


Ions are atoms with the same atomic number (Z) but possess an electrical charge due to unequal proton-electron pairing.

Positive ions (atoms that have lost electrons) possess a positive electrical charge. Negative ions (atoms with additional electrons) possess a negative electrical charge. Negative ions are far less common than positive ions.

Only a few atoms exist naturally as negative ions and they are all non-metalsN except for two, which are semi-metalsS:

One additional electron (Group VIIA):
Fluorine (9N), Chlorine (17N), Bromine (35N), Iodine (53N)

Two additional electrons (Group VIA):
Oxygen (8N), Sulphur (16N), Selenium (34N), Tellurium (52S)

Four additional electrons (Group IVA):
Carbon (6N), Silicon (14S)

Any atom can become a positive ion simply by losing one or more of its electrons from impact with free electrons or a strong external positive electrical charge.

Negatively charged ions are a little more difficult to understand. Additional electrons need to be trapped by the positive charge in protons that do not exist in the nucleus, which shouldn't be possible. However, the nucleic structures of the above non-metal atoms probably have at least one exposed proton that is not protected by a neutron, which means that the additional electro-magnetic electrical charge generated in it is available to trap passing free electrons

Free Electrons

Electrons emitted from an atom will hold their linear (v) and angular (ω) velocities at the time of ejection in free flight until affected by impact, gravity and/or electro-magnetic energy. What we see in bubble chambers as post-impact spiral paths is simply the result of impacting electrons that can be visualised as spinning billiard balls obeying Newton’s laws of motion.

Angular velocity in an electron is: ω = 2π / orbital period (at the time of ejection)

Linear velocity of an electron is: v = √[2.KE / m] (at the time of ejection)

Atomic Modelling

Mathematical models of this atomic structure have been created for a number of atoms (including iron) at various temperatures using Coulomb’s law of electrical attraction, newton’s laws of orbital motion and the laws of thermodynamics.

It has been possible to mathematically construct the orbital models of all atoms (Z=1 to Z=92) using Newton's and Coulomb's laws at any temperature together with the heat transfer coefficient.

Density vs Temperature

Given that; temperature effects (e.g. gasification) are dependent upon a repulsive electrical charge between adjacent atoms and density is dependent upon an attractive magnetic charge between those same atoms, and that both charges are created by the same electro-magnetic energy generation process (electrons orbiting protons), density and temperature should follow similar patterns of behaviour according to the number of nucleic protons (atomic number (Z)).

This relationship, between electrical repulsion and magnetic attraction, can clearly be seen in the temperature/density vs atomic number plot shown below.

Relationship between temperature and density

Fig 7. Relationship Between Temperature/Density vs Atomic Number

The above-mentioned relationship is governed by the structure of the nucleus and is the last significant piece of the atomic puzzle. Whilst it can be resolved mathematically, it has not been addressed here because it is not part of Isaac Newton’s laws of orbital motion


Claim 1: Satellites in circular orbits generate their own kinetic energy

Claim 2: All heat (electro-magnetic energy) is radiated

Claim 3: Conduction is the transfer of radiated energy between electrons within a solid

Claim 4: Convection is the movement of a fluid to a position whereby its high electro-magnetic energy can be transferred (radiated); i.e. to a region of atoms at a lower temperature where atomic spacing is greatest [second law of dynamics]

Hypothesis 1: Electrons gain kinetic energy from electro-magnetic radiation, but they can only lose it via proton-electron pairing or impact.

Hypothesis 2: A lattice structure is dependent upon the atomic nucleic matrix

Hypothesis 3: Only atoms of identical nucleic construction can generate lattice structures

Hypothesis 4: Only atoms of identical magnetic charge can repel each other

The Theory

The symbols used in the following Tables can be found in; Symbols

The calculation results in the following Table have been derived from newton's laws of orbital motion

Table 1 Electron Velocities in an Hydrogen Atom at Various Temperatures
F̌ & F̂ are calculated using Newton’s law: F = G.m₁.m₂ / R²

The calculation results in the following Table have been derived from newton's laws of orbital motion incombination with Coulomb’s law: F = k.Q²/R²

Q₁1.60E-191.60E-191.60E-191.60E-191.60E-19C or A/s
Q₂1.60E-191.60E-191.60E-191.60E-191.60E-19C or A/s
Table 2 Electron Orbital Radii by Applying Coulomb’s Law to Table 5
F̌ & F̂ are calculated using Coulomb’s law: F = k.Q₁.Q₂ / R²

Kintetic Energy as Temperature

RAC = kB.Rᵢ.Qₑ = 96485.3317942156 C/mol (of electrons) Note: Faraday's constant = 96485.3317942158 C/mol {exact}

Rest condition @ Ṯ = 1K:
Nₜ = 1
Nᵥ = 1.5
Nᵨ = 2.5

RAMᵨ = Rᵢ.mᵨ/kB = 1.00727638277235 N
Note: RAMH = 1.00794 g/mol
RAMₑ = RAMᵨ . mₑ/mᵨ = 0.000548580318390698 g/mol
Rₐ = RAMₑ / Rᵢ = 15156.3563034308 J/g/K
R = Rₐ.mₑ = 1.38065156E-23 J/K
kB = 1.38065156E-23 J/K
kB.NA.Lₙ(Nₜ) = cᵨ.Lₙ(Ṯ).RAMₑ = 3.371231032 J/K/mol
exp(2.5xLₙ(Ṯ)) = 1

cᵥ = Nₜ.Rₐ = 22734.5344551462 J/g/K
Cᵥ = mₑ.cᵥ = 2.07097734E-23 J/K
cᵨ = cᵥ+Rₐ = 37890.8907585769 J/g/K
Cᵨ = mᵨ.cᵥ = 3.4516289E-23 J/K

KEₑ = kB.Ṯ.Nᵨ = 3.4516289E-23 J

X = Nₜ.RAC.e / Rᵢ.mₑ = 1.11157535506607E+12 C².s².K / kg².m²
Ṯ = X . v²/q² K

The Neutron

According to Newton's orbital motion formula; v = R/g
'v' will be the speed of light (c) (Table 6 below)
R = orbital radius of 1.4666666 x (rᵨ + rₑ) = 2.81773E-15m
g = G.mᵨ / φ.R² = 3.18988E+31m/s²

The heat transfer rate; Ṯ = X.v²
shows that at a temperature of 3229761K; v = c
and the iron atom (2.8E-10m) was measured at ≈-66.44°C
I.e a proton-electron pair will unite to create a neutron at the neutronic temperature and the neutronic radius
which occurs at the core of an active hydrogen star.

In close proximity to other neutrons and the electro-magnetic field generated by other proton-electron pairs, within the nucleus of an atom the neutron will gradually force the neutron to split apart into an electron and a proton. The rate at which this occurs is dependent upon the size and structure of the nucleus
A neutron therefore has no electrical charge but possesses a magnetic charge and its mass is that of a proton plus that of an electron

Electron Shells

orbital radiusRInput (from Table 6)
arc separation distancedπ/n . (4.π.R²) / (2.π.R)
linear separation distanceR.Sin(½.d/R)
gravitational acceleration at RgG.m₁ / φ.R²
electron velocityv√[g/R]
gravitational energyPEG.m₁.m₂ / R
gravitational forceFG.m₁.m₂ / R²
electrical force (check)Fₑk . (q/R)²
electron temperature in shell 1 (check)½.m₂.v² / Nᵨ.kB
Table 3 Electron Shell Distribution

The following calculations are for both electrons in shells 1 to 18 (Ṯ₁ = 1K)

Table 4 Electron in Shells 1 to 18

The following calculation results are for both electrons in an iron atom (Ṯ₁ ≈ 845K)

Table 5 Electrons in an Iron Atom (Ø = 2.8E-10m)
Average temperature of the atom in this condition is 206.7K

The following results are for an electron orbiting a proton at light speed (≈3.2E+06K)

Table 6 The Birth of a Neutron

Further Reading

You will find further reading on this subject in reference publications(55, 60, 61, 62, 63 & 64)

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