Mes livres :

Atomes et matière, ISBN 978-2919314-027, 360 pages, 34 €

Mécanique céleste et Cosmologie, ISBN 978-2919314-003, 158 pages, 18 €

Atoms and matter ISBN 978-2919314-034, 338 pages 34 €

Expédiés franco contre Chèque à la Commande à :

Iliade-édition, 8 route de Corcosse 17100 Courcoury 0546913153 ou 0971552233

A new way to consider atoms

By Emile Braunthal Weisman

Structure and mechanics of the atom.

Actually, the atom is thought as being made of a nucleus around which electrons turn like planets turn around the sun. In the present paper we will show that, if we allow that electrons in the atom, must not be considered as being point-like particles, we can better understand what is happening inside the atom and thus explain all the physical phenomena we observe in every day life.

This approach is very different to what the physicist was accustomed to when he studied Quantum Mechanics. Nevertheless, a little attention will convince him there is an alternative way to consider nuclear physics.

This is an abstract of a more than 300 pages book “Structure et mécanique de l’atome”, written in French and in need of an editor.

1- Structure of the atom.

We will study here the simplest atomic structure, the atom of hydrogen, built with one proton and one electron. Instead of what is usually accepted we will show that the electron is like the pulp of an apricot all around the proton. In this structure, the two components are concentric and they form a system I call in French: système electron proton or sep.

These two particles are of opposite electrical charges and this produce a result we will study.

2- Mechanic of the atom.

As the two particles are concentric their opposite charges will generate two kinds of interactions. A radial force, the force of Coulomb, and an axial force, a Moment of force, as we will show shortly.

First of all, we have to assume that these two particles are spinning around one of their axis. That is what physicists call the spin but, in actual physics, this movement is not allowed as to be a real one and “spin” is only employed as a mathematical operator.

When the two particles have the same angular velocity, they are at rest one to the other and then the attractive force, the Coulombian force, will predominate. Under the action of this attractive force the radius of the electron will decrease and the distance between them will also decrease. But if the electron is spinning, it has an angular momentum and if its radius decreases its angular speed will increase in the same way as a skater turns faster when he put his arms along the body. From this moment, the two particles will not have the same angular velocity and they will not be at rest relative to each other so the attractive force will not be as strong as it was previously.

If the two concentric particles have different angular velocity, this will generate an angular Moment of force, a torque, that will try to unify their angular speeds and then the electron’s electrical charge will induce this torque so as to increase the angular speed of the proton.

When the angular Moment of force increases, the radial attractive force decreases and we can show that the total sum of their squares is constant.

When the two particles have again the same angular speed, they will be at relative rest and then the attractive force will be preponderant and once again the radius of the electron will decrease. These successive steps of relative rest of the two particles are what physicists call the orbits of electrons in the atom.

The preceding is a simple description of the mechanic happening in a system of two elementary particles. This description is based upon the elementary laws of electricity and electrodynamics. We have not introduced any ad hoc hypothesis, we have simply deduced what may happen when we apply these laws in the configuration where two electrically charged particles are closed.

It is obvious that this phenomenon can receive a mathematical description but we have to remember that Mathematics gives only tools to quantify physical phenomena. Physics is not a branch of Mathematics and we must not reason in mathematical terms to deduce physical phenomena.

3- Fine-structure constant.

To express the physics of atoms in mathematical terms we first have to define the Fine- structure constant. Actually, it is admitted that this Constant a is given by a dimensionless ratio equal to e²/²c where e is the electron’s charge, ² the Planck’s constant and c the velocity of light.

We will see in the following that a must not be considered as a constant but as a coefficient, witness the degree of interaction between the electron and the proton. The mathematical expression of this coefficient appears to be:

a_i = (Sn_i^-2)^1/2 (1)

where n_i is the rank of the orbit described by the electron and the summation starts from 1 to this orbit.

As the Coulombian interaction has an infinite range and will never be equal to zero, the value of n_i is equal to 1 when the electron is on an external orbit far away from the proton. When the radius of the electron get smaller it describes smaller orbits which coefficients n will become 2, 3, 4…Thus, the Fine-structure constant of actual physics will be given by the approximate:

(2)

where the summation is made from 1 to 38. This means that the orbit of the electron in Bohr’s atom has the 38^th rank in the system we are proposing.

We can note that the actual meaning of the Fine-structure constant is somewhat mysterious and has no physical justification. The fact that its value can be given by a combination of a few universal constants can not be explained and the introduction of this constant, by Sommerfeld, with its actual formula equivalence is more due to accident rather than design.

4- Electricity / matter transformation

When the two electrical particles are interacting, their electrical charges appear to turn into matter, or what appears to be matter. When the interaction is tight the electrical characteristics of particles vanish. We can use the a coefficient to calculate the degree of transformation of electrical charge into matter. If q₀ is the value of the electrical charge of the free electron or proton, when they are interacting we can express their combined charge by:

q_i² = q₀²a_i (3)

where the indice i is the rank of the orbit.

In fact, the quantity of electrical charge is constant, the interaction of the electron with the proton does not lead to an emission of a part of these charges. It is only the electrical efficiency of the charges which decreases when the matter qualities increase. We have to point out that particles cannot have, at one and the same time, electrical and material characteristics. A free particle has electrical properties. When this particle is bound to an other one, they both have material properties. The characteristics, which make matter properties cannot belong to a single particle, it is only from the interaction of two particles of opposite charges that material properties can emerge.

In other respects, we see that we can’t make any direct equivalence between the quantity of matter and the energy this matter can produce. In the sep, the fusion of the electrical charges of the electron and of the proton does not lead to any emission of electrical radiation or generate any energy effect.

5- The spin

We said earlier that the particles in the sep were turning on themselves, that is what we call the spin. The angular velocity of this movement seems to be as great as the interaction is weak, when particles are far away one from the other, when the electrical properties are most important and when matter characteristics are non-existent.

Its seems that the angular velocity must be expressed:

w = ca_i/r_i (4)

where c is the light velocity, r the radius of the orbit of the electron and i, its indice. It is evident that we assume that this movement will have the speed of light on a very external orbit (with i=1) and that this speed will decrease on internal orbits, when material properties of the system will be greater.

.

6- Coulombian force.

The Coulombian force is given by the classical electrodynamics formula: f_c=q²/4pe₀r² where q is the electrical elementary charge, e₀ is the Dielectric constant and r the distance between the two charged particles. The law of Coulomb is suitable for two distant corpuscles. Here, the two charges are concentric and the force we have to consider is 4p times greater, so the Coulombian force of the sep will be:

(5)

but the sep is not isolated from the rest of the world. It has, in its close vicinity, other sep with which it will interact. The interaction with those sep will be as weak as the orbit is large and the proton deep inside the sep. Here again we can use the a coefficient to quantify the part of the force the system will exert on its vicinity. The external Coulombian force thus will be:

(6)

where f_c is the Coulombian force given by (5), and the internal force, which acts between electron and proton become:

(7)

7- Inertia of the sep.

The inertia (the quantity of electricity transformed into matter) of the sep increases when the system describes an internal orbit. The expression of the inertia seems to be:

(8)

It depends of the degree of interaction between the two particles and of the spin velocity.

8- Movements in the sep.

When the two particles spin with the same angular velocity, the Coulombian force exerts an attraction on the electron and the radial speed (toward the center of the sep) increases. So the Coulombian force induces an acceleration of the radial movement of the electron. But at the same time, as the radius of the electron decreases, the angular velocity of the movement of spin increases. The axial speed of a point on the equator line of the electron (in the following, we will call it: the point P) must vary from:

(9)

the angular velocity is greater on the inside orbit of rank (i+1) but, as the radius of this orbit is smaller than the radius of the orbit of rank (i), the axial (tangential) speed of the electron will be smaller. This is normal because the inertia of the system has increased.

At the beginning of the radial movement, radial acceleration is very important but, as the radius decreases, angular acceleration increases and axial speed will soon reach the maximum possible speed on that orbit: ca_i+1.

The analysis of the movement of the point P during this jump from one orbit to the first inside orbit shows that this point is describing a circular movement as shown on the following drawing.

			i
			i+1
	step 1	step 2

Fig. 1 – Movement of point P during a jump.

In the next step while the electron will induce a torque on the proton to bring it to the same angular velocity, the angular velocity of the electron and its radius seem to be constant. At the end of step 2, both particles have same angular velocity, they are at relative rest and a new jump towards an inside orbit will occur. This movement will again occur at the end of step 4 and to generalize, we can illustrate this movement in Fig. 2:

	i

i+3

i+2

i+1

i+n

step 1 step 2 3 4 5 6 7…..T_R

Fig. 2 - Movement of the point P during a period.

As we can see, the sep is getting infinitely small. We do not know what is the ratio V of the radius of orbit i to the next orbit of rank i+1 but reasonably it must be: 1<V>2 .So:

z = r_i / r_i+1 with 1< z >2 (10)

This ratio may also be different for each atomic element or for sep inside a same atom whether the electron of this sep is on an inside or an external orbit as it will be seen in studying heavy atomic structures.

The representation of fig. 2, also shows the first external orbits or any inside orbits.

9- Duration of movements in the sep.

Each jump from an orbit to the next one takes a certain time. This time will depend on the speed of the point P and of the distance to cover. Therefore:

(11)

because the speed varies during this movement from ca_i to ca_i+1 and it appears that the average speed c(a_i +a_i+1)/2 is a good approximation.

We can assume that the second step during which the proton gets the same angular velocity as the electron is of equal duration. So when the sep starts from an external orbit of rank p to an internal orbit of rank k, the total time will be:

(summation from k to p) (12)

But it is obvious that the sep can not infinitely shrink down to the smallest orbits. It has to stop somewhere and return to an outer orbit. That is what happens when an interaction with an other sep becomes possible. I will not explain here how this interaction occurs. It would take to much time and will require the introduction of some other new notions.

The time necessary for the electron to go back to an external orbit will be:

(13)

because the particles are not yet tied and this movement is made at the speed of light. We have to remember that the electron keeps its angular movement during this phase of return. So, the total time for a complete movement of the sep is:

(14)

10- Period and wave lengths of the sep.

We can show that this formula gives the periods of pulsation of the sep. But this method is not suitable to obtain the periods of the modes of vibration of the atom of hydrogen for instance. The sep is a theoretical object. In real atoms, even in the molecule of hydrogen, sep are interacting and in gas or in matter they are submitted to pressure which prevent their free expansion. Anyhow the study, with this method, of emission spectrum of atomic elements in pressure and temperature conditions, may help understanding the mechanic of heavy atomic elements.

For these calculations we will take the Bohr’s radius equal to 5.29.10^-11 m. on the 38^th orbit of our system. The indices k and p are used to design internal and external orbits as it is done in actual atomic physics but here, with these indices, we can design any orbit. This is illustrated below.

The calculation of the periods of a sep pulsating between an orbit p to an orbit k is easier

when we use a coefficient b_i given by:

(15)

where the summation is made from the i orbit to the most internal possible. In the Table 1, we choose the indice i=80 so as to have a most precise result. We have to start summing from the high indices so as to obtain significant differences between two levels. It would not be the case in starting summation from the outer orbit.

The period T_pk and the wave length l_pk will then be given by :

T_pk = r₃₈c^-1(b_p-b_k) l_pk = r₃₈(b_p-b_k) (16)

For a sep pulsating between orbits 34 and 50 with a ratio z=1.8 for instance, with the values given by Table I, we obtain:

T_34-50 = 5.29.10^-11(1.874.10⁴-2.6679)/3.10⁸= 3.304.10^-15

l_34-50 = 5.29.10^-11(1.874.10⁴-2.6679)=9.912.10^-7

We see that these results are coherent. We obtain them without any ad hoc hypothesis.

Sep can go far into the center of the atom, on an orbit as high as 60 or even more, that’s why the capture section of neutrons may be very little for some atomic elements.

The inner orbit is reached when the electron is kept by the proton of an other sep, when the radius of these two particles are compatible to interact in preference to their previous companions. This capture may happen on several internal orbits, that explain the hyperfine structure of light spectrums. The most outer orbit depends of the pressure conditions in which atoms are confined. In an heavy atomic structure sep are all at different degrees of contraction so they are never at the same time on a same orbit.

11- Conclusion.

Even if the present proposition does not allow the accurate calculation of periods and of wave lengths of pulsating atoms, it gives a better understanding of how the atom is made and how it works than can do the actual mechanics.

Atom is not a small planetary system. It is not vacuum and particles are not point-like objects. In the description we give, we find a model that looks like the wave function of Schrödinger. In an atom, particles are not at the same time corpuscles and waves, they are continuously varying from one state to the other.

This model of atom allows explanation of electromagnetic emission, of weak and intense interaction forces, of cohesion forces in macroscopic materials, of pressure of gases, of heat transfers phenomena, of electrical conduction…My book, Structure et mécanique de l’atome deals of all these problems. It will be soon available in English.

Table 1. Values of b in regard to values of V

Indice	Alpha	Z=1,2	Z=1,4	Z=1,6	Z=1,8	Z=2
1	1,0000E+00	4,0990E+05	3,5131E+07	2,6845E+09	1,4573E+11	5,6306E+12
2	4,4721E-01	4,0207E+05	3,2687E+07	2,3326E+09	1,1764E+11	4,2213E+12
3	2,6726E-01	3,8924E+05	2,9318E+07	1,9141E+09	8,8253E+10	2,9047E+12
4	1,8257E-01	3,7243E+05	2,5565E+07	1,5083E+09	6,3026E+10	1,8908E+12
5	1,3484E-01	3,5268E+05	2,1801E+07	1,1532E+09	4,3442E+10	1,1837E+12
6	1,0483E-01	3,3096E+05	1,8260E+07	8,6128E+08	2,9153E+10	7,1982E+11
7	8,4515E-02	3,0809E+05	1,5069E+07	6,3143E+08	1,9159E+10	4,2803E+11
8	7,0014E-02	2,8478E+05	1,2283E+07	4,5598E+08	1,2382E+10	2,5002E+11
9	5,9235E-02	2,6158E+05	9,9084E+06	3,2518E+08	7,8929E+09	1,4394E+11
10	5,0965E-02	2,3892E+05	7,9216E+06	2,2946E+08	4,9740E+09	8,1873E+10
11	4,4455E-02	2,1712E+05	6,2844E+06	1,6047E+08	3,1043E+09	4,6099E+10
12	3,9223E-02	1,9642E+05	4,9520E+06	1,1136E+08	1,9213E+09	2,5733E+10
13	3,4943E-02	1,7696E+05	3,8789E+06	7,6752E+07	1,1806E+09	1,4257E+10
14	3,1388E-02	1,5884E+05	3,0224E+06	5,2587E+07	7,2088E+08	7,8470E+09
15	2,8398E-02	1,4209E+05	2,3439E+06	3,5841E+07	4,3772E+08	4,2943E+09
16	2,5854E-02	1,2671E+05	1,8101E+06	2,4313E+07	2,6448E+08	2,3381E+09
17	2,3669E-02	1,1267E+05	1,3925E+06	1,6423E+07	1,5909E+08	1,2672E+09
18	2,1775E-02	9,9927E+04	1,0675E+06	1,1052E+07	9,5318E+07	6,8398E+08
19	2,0121E-02	8,8408E+04	8,1581E+05	7,4113E+06	5,6903E+07	3,6782E+08
20	1,8666E-02	7,8041E+04	6,2165E+05	4,9545E+06	3,3859E+07	1,9714E+08
21	1,7379E-02	6,8745E+04	4,7245E+05	3,3026E+06	2,0087E+07	1,0533E+08
22	1,6233E-02	6,0439E+04	3,5817E+05	2,1956E+06	1,1884E+07	5,6124E+07
23	1,5207E-02	5,3040E+04	2,7093E+05	1,4561E+06	7,0128E+06	2,9827E+07
24	1,4286E-02	4,6467E+04	2,0450E+05	9,6354E+05	4,1288E+06	1,5814E+07
25	1,3453E-02	4,0644E+04	1,5406E+05	6,3626E+05	2,4256E+06	8,3658E+06
26	1,2699E-02	3,5497E+04	1,1586E+05	4,1933E+05	1,4222E+06	4,4166E+06
27	1,2012E-02	3,0958E+04	8,6974E+04	2,7586E+05	8,3227E+05	2,3273E+06
28	1,1386E-02	2,6964E+04	6,5189E+04	1,8117E+05	4,8621E+05	1,2242E+06
29	1,0812E-02	2,3456E+04	4,8788E+04	1,1880E+05	2,8358E+05	6,4286E+05
30	1,0284E-02	2,0379E+04	3,6462E+04	7,7782E+04	1,6515E+05	3,3706E+05
31	9,7983E-03	1,7686E+04	2,7214E+04	5,0857E+04	9,6038E+04	1,7647E+05
32	9,3495E-03	1,5333E+04	2,0286E+04	3,3208E+04	5,5773E+04	9,2268E+04
33	8,9339E-03	1,3279E+04	1,5104E+04	2,1657E+04	3,2349E+04	4,8179E+04
34	8,5483E-03	1,1489E+04	1,1234E+04	1,4107E+04	1,8740E+04	2,5127E+04
35	8,1896E-03	9,9313E+03	8,3459E+03	9,1794E+03	1,0844E+04	1,3089E+04
36	7,8553E-03	8,5770E+03	6,1944E+03	5,9665E+03	6,2680E+03	6,8113E+03
37	7,5431E-03	7,4011E+03	4,5931E+03	3,8743E+03	3,6194E+03	3,5407E+03
38	7,2511E-03	6,3812E+03	3,4027E+03	2,5134E+03	2,0880E+03	1,8387E+03
39	6,9775E-03	5,4975E+03	2,5186E+03	1,6291E+03	1,2034E+03	9,5400E+02
40	6,7206E-03	4,7326E+03	1,8627E+03	1,0550E+03	6,9297E+02	4,9453E+02
41	6,4792E-03	4,0711E+03	1,3765E+03	6,8262E+02	3,9871E+02	2,5613E+02
42	6,2518E-03	3,4995E+03	1,0165E+03	4,4135E+02	2,2922E+02	1,3255E+02
43	6,0375E-03	3,0062E+03	7,5004E+02	2,8514E+02	1,3168E+02	6,8544E+01
44	5,8351E-03	2,5806E+03	5,5308E+02	1,8409E+02	7,5589E+01	3,5419E+01
45	5,6438E-03	2,2138E+03	4,0757E+02	1,1877E+02	4,3361E+01	1,8289E+01
46	5,4627E-03	1,8979E+03	3,0015E+02	7,6574E+01	2,4857E+01	9,4377E+00
47	5,2911E-03	1,6260E+03	2,2090E+02	4,9339E+01	1,4240E+01	4,8669E+00
48	5,1283E-03	1,3922E+03	1,6249E+02	3,1772E+01	8,1532E+00	2,5082E+00
49	4,9736E-03	1,1912E+03	1,1945E+02	2,0447E+01	4,6652E+00	1,2919E+00
50	4,8266E-03	1,0185E+03	8,7765E+01	1,3152E+01	2,6679E+00	6,6500E-01
51	4,6867E-03	8,7031E+02	6,4450E+01	8,4548E+00	1,5249E+00	3,4212E-01
52	4,5535E-03	7,4315E+02	4,7304E+01	5,4324E+00	8,7111E-01	1,7592E-01
53	4,4264E-03	6,3412E+02	3,4703E+01	3,4887E+00	4,9737E-01	9,0412E-02
54	4,3051E-03	5,4067E+02	2,5446E+01	2,2394E+00	2,8385E-01	4,6443E-02
55	4,1893E-03	4,6062E+02	1,8649E+01	1,4368E+00	1,6191E-01	2,3846E-02
56	4,0785E-03	3,9209E+02	1,3661E+01	9,2141E-01	9,2315E-02	1,2238E-02
57	3,9726E-03	3,3345E+02	1,0003E+01	5,9064E-01	5,2611E-02	6,2776E-03
58	3,8712E-03	2,8328E+02	7,3206E+00	3,7845E-01	2,9971E-02	3,2188E-03
59	3,7740E-03	2,4040E+02	5,3550E+00	2,4239E-01	1,7066E-02	1,6498E-03
60	3,6808E-03	2,0374E+02	3,9151E+00	1,5518E-01	9,7141E-03	8,4524E-04
61	3,5914E-03	1,7243E+02	2,8608E+00	9,9312E-02	5,5271E-03	4,3287E-04
62	3,5055E-03	1,4570E+02	2,0892E+00	6,3530E-02	3,1436E-03	2,2161E-04
63	3,4231E-03	1,2288E+02	1,5246E+00	4,0623E-02	1,7873E-03	1,1341E-04
64	3,3438E-03	1,0340E+02	1,1118E+00	2,5964E-02	1,0158E-03	5,8015E-05
65	3,2675E-03	8,6795E+01	8,0990E-01	1,6587E-02	5,7709E-04	2,9668E-05
66	3,1940E-03	7,2634E+01	5,8929E-01	1,0590E-02	3,2773E-04	1,5167E-05
67	3,1233E-03	6,0564E+01	4,2812E-01	6,7567E-03	1,8603E-04	7,7504E-06
68	3,0552E-03	5,0280E+01	3,1041E-01	4,3071E-03	1,0555E-04	3,9591E-06
69	2,9895E-03	4,1519E+01	2,2447E-01	2,7422E-03	5,9842E-05	2,0215E-06
70	2,9261E-03	3,4060E+01	1,6175E-01	1,7428E-03	3,3898E-05	1,0316E-06
71	2,8649E-03	2,7710E+01	1,1598E-01	1,1048E-03	1,9174E-05	5,2595E-07
72	2,8058E-03	2,2307E+01	8,2601E-02	6,9753E-04	1,0821E-05	2,6779E-07
73	2,7488E-03	1,7709E+01	5,8258E-02	4,3769E-04	6,0833E-06	1,3602E-07
74	2,6936E-03	1,3799E+01	4,0512E-02	2,7195E-04	3,3970E-06	6,8773E-08
75	2,6403E-03	1,0475E+01	2,7578E-02	1,6625E-04	1,8743E-06	3,4467E-08
76	2,5887E-03	7,6488E+00	1,8154E-02	9,8866E-05	1,0114E-06	1,6969E-08
77	2,5387E-03	5,2471E+00	1,1290E-02	5,5916E-05	5,2254E-07	8,0476E-09
78	2,4904E-03	3,2066E+00	6,2911E-03	2,8548E-05	2,4564E-07	3,4996E-09
79	2,4435E-03	1,4734E+00	2,6515E-03	1,1113E-05	8,8831E-08	1,1817E-09
80	2,3981E-03	3,9489E+00	6,4696E-03	2,5113E-05	1.8830E-07	2,3724E-09

On my site : http://perso.wanadoo.fr/ebraw I publish some other papers in French but soon available in English.

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