atom

This document is replaced by chapte4A in "Matter Unified", the HTML version. SEE :

http://www.newphys.se/elektromagnum/physics/Tedenstig/Own

By Ove Tedenstig/Sweden 1999

Web site : http://www.newphys.se/elektromagnum/physics/Tedenstig/own

A reworked document based on my complete work "Matter Unified" and some other separate written articles with start from 1981.

The article offer a new and detailed description of the quantum process in the atom. The Planck constant, the atomic fine structure constant, the Bohr quantum mechanical condition are derived with start from a pure theoretical basis.

THE QUANTUM ATOM

Some historical facts about quantum theory

Basic principles of quantum mechanical properties of matter based on new insights

Deducing basic atomic constants

Explanation of Bohr's quantum mechanical relation defined as m.v.D=h.n/(2 . p)
Schrödinger's wave equation of the atomic system
The atomic core structure

Current knowledge of matter on atomic level is founded on discoveries done over a long period of time. Some famous names are Ernest Rutherford, Max Planck, Niels Bohr, Ervin Shrödinger, Werner von Heisenberg and many others.

Max Planck is most known from his work of measurement and analyses of light and heat radiation from black radiating bodies. He formulated an energy distribution law and found that energy over different frequencies was emitted in a discontinuous way and not as a continuous stream. These revolutionary insights was the start of a new and very fruitful era in fundamental physics, the quantum mechanics.

Max Planck introduced a new physical constant bearing his name, "the Planck's constant", usually denoted by letter "h" and having a very small but defined value to 6.6260755(40)E-34 Ws(2) as given in the MKS(A) dimensional unit system.

At this time, the inherent structure of matter was very indistinct and unclear. Niels Bohr, using results from Planck, Rutherford, Balmer among others, was the man who by a simple formulated atomic model, for the first time in a theoretical way, succeeded to describe and explain some known light emission spectra from the hydrogen atom. In spite of the simplicity of this model, it was revolutionary and started up en intensive researching activity and development in this field of physical research, the quantum mechanics.

But the Bohr's model was just an approximation and of that reason the model later was improved by other physicists, using more sophisticated and more complex mathematical models. These models were able to describe more complex atoms than the relatively simple hydrogen system and beside that, was complemented by a set of rules which formed that we today name, the quantum mechanics.

However, if we proceed looking some closer to the Bohr's original model, we will find that Bohr was forced to make some pure hypothetical assumptions, not supported by any clear theoretical motivation. One of these hypotheses was the quantum mechanical relation, written m.v.D = h.n/(2.p), an expression which we shall be interpreted so that the electron orbit momentum, the product m.v.D, is an integer value of Planck's constant, h . Bohr never succeeded to give any plausible motivation to this relationship and got critics for it. But this shortcoming was excused by that his theory so well predicted and explained experimental results.

Picture atomp1.gif

This relationship still is not explained by the modern quantum physics, which clearly points on that the fundamental mechanisms of the quantum behavior of the atom, still not is understood.

Furthermore, Bohr's model was not able to explain the reason why the frequency of the emitted radiation not was the same as the orbital frequency of the radiating, orbiting electron.

Hence, in spite of all success with Bohr's model, it never was explained why matter showed up such an apparently very strange behavior, why energy only existed in some very narrow interval, or packets, within the atom. Why was matter quantified, why was not the energy of the atom permitted to be emitted or absorbed in a continuous way?

The answer of these questions was hidden in the quantum mechanical relationship m.v.D = n.h/(2.p), a pure hypothetical relation, only justified by the fact that it gave good agreement with experimental findings. The very fundamental reason why the matter behaved quantified (appeared in packets) never was explained and has not even since then been explained by the modern quantum mechanical research.

In addition with these fundamental questions, there are even further question marks of highly interest, associated to the quantum atom. For instance the presence of some very elementary constants, all the time present in the atomic, quantum mechanical mathematical relationships. That is Planck's constant, the atomic fine structure constant, Rydberg's constant among others.

Here it is the Planck's constant and the atomic fine structure constant which especially arouse our curiosity. These two fundamental constants never have been given any theoretical explanation or has not even been able to be derived from a pure theoretical basic, but has been surrounded by an aurora of mystics, being entities of matter of supernatural nature. We shall derive these very fundamental constants.

It is fully clear, that the existence of these very fundamental atomic constants says a lot of the atom and associated quantum mechanical processes in the atom. If we can understand these fundamental units, we can even undestand the atom. Of that reason we shall here spend some attention to these constants and even try to derive their physical value with start from some new basic ideas of the atomic system.

Atomic rules as rules for all matter

So, some points which we shall devote special attention to are as follows:

On pure speculative ground and without any mathematical, physical base, Bohr assumed that the electron's orbital momentum, equal to the product m.v.D was equal to h/(2.p), where m, is the electron rest mass, v , is the electron orbital momentary velocity, D , the momentary electron orbiting radius, h , the Planck constant and n, being the main quantum number 1,2,3,4…nx as defined by Bohr's original quantum theory.
The reason why the emitted (or absorbed) radiation of the atom not directly was related to the calculated frequency of the orbiting electron, was not either explained by the Bohr model and not by the modern quantum mechanic either.
The presence of some very fundamental atomic constants, the Planck's constant and the atomic fine structure constant, never have been given any physical motivation, not even the numerical values have been derived on pure theoretical basis.
The answers on these very fundamental questions are of extremely importance, not only concerning the behavior of matter on atomic level, but also in the fundamental understanding of how matter works and behave on all levels, in particular concerning the area of particle physics, where similar basic principles are involved.

Heisenberg's uncertainty principle says that conjugating physical quantities as for instance energy and time not simultaneously can be measured with the same degree of accuracy, where the product of energy and time always is a multiple value of Planck's constant. This very fundamental principle of the atomic system even has been transmitted as valid rules in quite different systems, as for instance being valid for the atomic core and for elementary particles, or groups/systems of such particles.

The principles have been used in the atomic nucleus when describing the fundamental nature of the strong nuclear force (Hideki Yakawa's meson theory) and even in the particle physics when describing the strong forces between elementary particles.

Another typical example of this trend. According to this idea each particle is associated with a wave, being related to the particle mass and the Planck's constant. That possibly can be true for electrons moving in an atom, but not true for free electrons which move in free space. Free elementary particles can move with arbitrary velocities and posses arbitrary energy levels not bounded to multiples of Planck's constant.

The Shrödinger's wave theory replaced Bohr's simple and visual model, describing matter in terms of a probability model. Even if this theory gave a more complete description of the phenomena in the atom, no deeper understanding of the quantum mechanical processes was achieved by this improvement.

As a summary we may conclude that too many rules have been extracted from the atomic quantum theory as general applicable rules usable for the whole area of fundamental physics. The reason for that is ignorance of fundamental basic principles behind the quantum phenomena in the atom. In the theory here presented we attend to change this situation and will offer answers on these questions.

The new quantum theory

Our atomic system being the base for our calculations, contains the following component and assumed properties:
The central particle in an atomic system is one or several proton particles as electromagnetic active parts, having a mass of 1836.15 times the electron mass.
As in the Bohr model, around the center particles, electron(s) move, having a relative mass of one mass unit compared with the proton mass.
Electrons and protons are electrically charged particles, creating a mutual interacting force between them, the Coulomb force. In every moment of time, this electrical force is balanced with the Newtonian mass inertial force created by the orbiting movement. Because the proton has a positive charge polarity and the electron having a negative charging polarity, they attract each other. The mass inertial force is directed outwards, hence is counter acting the electrical Coulomb force.
There are also neutrons in the core, but the strong forces which normally act on them is not acting on the orbiting electrons because of too large distances to the orbit shell.
Most of all that ( points 4-7) is already well known facts form established quantum theory. However, making it possible to proceed where Bohr and other researchers stopped, we must complete our atomic model with some complementary facts (or assumptions) which we assume being resonable. These assumptions or hypotheses are unique for our here presented theory and create a complete description of the Bohr model. Briefly we list these additional properties of the atomic system as follows :
All true elementary particles, to which electrons and protons belong, have the same mass density.
The electrostatic force surrounded a true elementary particle, is polarized so that a torque momentum appear on it when/or if the particle is turned out from a neutral angular position. This property ought to be compared with how a current loop will turn in a magnetic field.
The quantum behavior of the atomic system is primarily generated by that the proton oscillate in the common electromagnetic field between the proton and the electron as a result of interaction between the electrical field force and mass inertial forces acting on particles in the system.
The oscillating movement of the proton core gives, of reason of the polarized electrical field which surround the proton and the orbiting electron, the electron wavelike properties.
Some memory effect is assumed existing in the common electrical field between the core and the orbiting electron, creating a virtual track in space which the electron prefer to follow. Then it is assumed that the period of this trace is an integer multiple of the proton oscillating period.
When the electron jumps from one stable level to another stable level, the energy in the system change. During this time the jump is taking place, this energy difference is radiated/or absorbed by an associated oscillating frequency. This frequency is the mean value of the difference between two successive proton resonance frequencies.

In aim making it more easy to follow the proceeding calculations of our atomic quantum system, we make a list of definitions of variables necessary for our mathematical calculations:

Ekin

Etot

lout

Electron rest mass

Atomic core particle mass ( commonly a proton)

Orbit particle mass (commonly an electron, or even muon)

The standard velocity of light light

Momentan velocity of orbit particle

Radius of the electron particle

Radius of the orbiting particle, electron or muon

Radius of the proton particle

Radius of an individual central particle in the core

Distance between the central and the orbiting particle

Coulomb force between central and orbiting particle

Torsion force acting on the radius of the central particle

The kinetic energy in the orbiting system

The potential energy stored in the Coulomb field

The system's total stored energy Ek + Ep

The total number of active charged particles in the core

The total number of orbiting particles around the core

The total orbiting time for a turn around the core

The oscillating time period for the core particle

Wavelength of emitted/absorbed energy radiation

Planck's constant 6.626 075 5(40)E-34 J s

Atomic fine structure constant, value 1/137.035 989 5 (61)

Main quantum number as defined by common theory

Eff. number of charge units acting on the orbit particle

Eff. number of charge units acting on the center particle

To begin with, we establish that Bohr's simple atomic model in its main parts is correct, yet not complete for more complex atomic cores. We will accentuate that because Bohr's theory erroneously has been judged as wrong only for reason that it has been replaced by another, more sophisticated model using more advanced mathematics. Shrödinger's wave model is such an example, but we shall here show that Shrödinger's equation very well can be derived using parts of Bohr's model in addition to the here suggested new parameters.

Our model atom contains a number of protons in center and a set of single electrons in the orbit. Between these two collections of charged particles acts electrical forces in accordance with Coulomb's basic law for the electrical field.

Energy in the system

The orbital particle (commonly an electron) moves with velocity , vo. We suppose the velocity is small in relation to the light velocity, c , so the kinetic energy can be computed from Newton's simplified formula where the mass is invariant. Then this kinetic energy of the orbiting particle will be

Picture, atomF1.gif

The electron is situated in a force field and according to classical laws, it will correspond to a potential energy. The potential energy of the orbital particle is calculated to:

Picture atomF2.gif

In a system where the energy content is constant, unchanged, hence with no energy radiation losses, the sum of kinetic and potential energy is constant. The potential energy has negative potential sign in relation to the kinetic energy, hence:

Picture atomF3.gif

The oscillating proton in the core

We define two parameters for simplifying our mathematical description and analysis, Ko and Kc. Ko and Kc respectively, divided by the distance, D , squared, give the Coulomb force of particles involved. Ko is associated to electromagnetic force acting on the orbiting particles, Kc is associated to electromagnetic force acting on the center particles. Ko and Kc is multiplied with factors Zc and Zo respectively, being the number of active, united charges, in each point.

Picture atomF4.gif

The force Fc is acting on the center particle (commonly a proton) in the atomic core. The Coulomb force is polarized in such way, that if the proton tries to twist around its neutral axis, a torque momentum arises on it. The easiest way to see it is to reduce the proton mass to a point mass situated on a pendulum axis with radius, Rc = Rp, then calculate the torque force on it. For small amplitude in the oscillating, the torque force approximately will be in direct proportion to the relation s/Rp, where, s , is a very small angular distance on this circle which the pendulum axis describe.

When the proton oscillate in the electrical Coulomb field, mass inertial forces in accord with Newton 's basic laws is achieved. This force is equal to mass times acceleration. The torque force and the mass intertial forces are in balance, hence giving the following equations :

Picture atomf5.gif

We solve this harmonic differential equation, and get:

Picture artomF6.gif

where tc is the period time for the proton oscillation envelope in the electric field. We perform some further analysis of the factor "k" in the equation, and find :

Picture atomF7.gif

where we have used the fact that the mass density of a proton and an electron is the same (point 8 above).

The interaction process between the proton oscillation and the orbit movement

There is an interacting process between the proton oscillation and the orbiting particle. When the proton, electrical charged, oscillate, even the surrounding electric field will oscillate because of that the electrical field is polarized. The orbiting particle has a very small mass in comparison to the central particle (the proton), hence will be disturbed in its movement. The orbiting particle then will follow these disturbances, resulting in increasing/decreasing velocity fluctuations in the orbit movement.

Beside that, it is also assumed that there is some memory effect in the electric field from the proton, meaning that the field not disappear immediately, but stay some time. That create a virtual track in the space around the core, which will be a closed loop containing integer periods of the proton oscillating period. That means, that the proton oscillating time period multiplied with an integer value will be equal to the orbiting time period.

Above that, we also have a balancing situation, where the orbiting centrifugal force is in balance with the electrical Coulomb force. All that gives us the following set of formulas:

Picture atomF8.gif

The total energy in the system

Now we make use of these results to re-calculate the total energy stored in the system, in accord with the formula 3):

Picture atomF9.gif

When the orbital particle change its orbit (jump), the total energy also will change. The energy jump is occurred by change of quantum number, n , as seen in formula 9a). For two values of, n , n1 and n2, the corresponding total system energy will be E1 and E2 respectively. The difference dE= E1-E2 is that energy which the system looses or absorb at jump between two levels. We calculate this parameter:

Picture atomF10.gif

The frequency of the emitted/ or absorbed radiation

It's well known that the frequency of the emitted radiation from an atom (light) not directly is associated to the orbiting frequency of the electron, but differ from it. Between two successive energy states, the proton resonance frequency jumps from one frequency to another. But that process cannot occur on zero time, it's a successive change of frequency f1 to f2. As known from mixing frequencies in radio-receivers, a differential frequency is generated by f1-f2. That is also what happen here, the radiated/or absorbed frequency given/or taken by the atom will be a mean value of the difference. We make a calculation of the output frequency as result of already achieved results above:

Picture atomF11.gif

Calculating Planck's constant and the atomic fine structure constant

The relation between emitted/absorbed energy and emitted/absorbed light frequency is equal to "Planck's constant", denoted with letter, h .

Picture atomF12.gif

Regarding the Z-factors, see comments at the end of this article. Zo = Z(2) and Zc = Z. h then is a constant.

Calculation of the atomic fine structure constant

In established quantum theory, there is no idea about what the atomic fine structure constant ( a ) in the atom stands for. Here we have found that it stands for the relation between the electron mass and the proton mass, raised to power 2/3, approximately. Hence we make a summary:

Picture atomF13.gif

The Bohr's quantum mechanical relation m.v.D = h/(2.p)

As noted in point 1 above, the Bohr's quantum mechanical condition for the Bohr model, never was explained or motivated. We will here derive this relation from results received:

Picture atomF14.gif

Some special results from our theory

For an ordinary atom, where the orbital particles are electrons and the core particles are protons, there exist a limit value of the energy jump, equal to 13.6 eV (electron volts).

The radiated light from the atom has a wavelengt, lout , which inverse value has a limit value denoted "Rydberg's constant".

Picture atomF15.gif

Picture atomF16.gif

The Z-factors

Picture atom17.gif

Using these results will reduce achieved formulas to more simple forms where Zo and Zc are replaced by Z. Hence we find that Planck's constant as derived in formula 12b) will be an invariant entity. Zo and Zc are reduced in the following formulas to : 8c) times Z, 8e) times 1/Z, 9a) times Z(2), 12b) times 1 , 10d) times Z(2), 15) times Z(2) and 16) times Z(2).

Shrödinger's Wave Equation

Shrödinger's wave equation has been of central importance in the development of atomic quantum theory. The equation is represented by the "wave function y ", describing the probability of finding an orbital electron at a specific point of the atomic volume, or the energy distribution in the atom. Much has been speculated about what this "mystical equation" really stands for and what it represents or how it shall be interpreted physically.

However, it will here be shown, that Shrödinger's equation in pricniple is our equation 6a), describing the proton oscillation process. But the equation is transformed to be valid on the electron, orbital level, which means that the radiating frequency is a factor 1/2 of the proton frequency.

Shrödinger's equation appear in shapes, but one way to written it is as follows:

Picrute atomf18.gif

Is a wave function of probability of finding an electron of an atom at a specific point in space, or describing the distribution of energy within a specific space element.

Is the wavelength of the emitted radiation from the atom

Is a small distance element in space represented by a specific coordinate system x,y,z,O

We will here, from start by our proton oscillating equation 6a) derive this equation, where we note that the equation is transformed from the core to the orbit level by dividing the proton frequency with a factor 1/2.

Picture atomf19.gif

Picture atomf20.gif

The atomic core structure

The periodical system of the atom on chemical level is a mirror of the internal structure in the atomic core. Each electron on the orbital level interacts with each single proton in the core in a statistical manner, creating these energy levels which are seen in the atom's periodical system. The K,L,M,N,O,P,Q shells are located as rotating discs oriented along the X-axis and the different small energy fluctuations s,p,d,f along the Y-axis. Each single unit in the picture is equal to a 1/2 alpha particle, hence constituting of a proton and a neutron.

(end for now)