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Books and publications on the interaction of systems in real time by A. C. Sturt
Economics, politics, science, archaeology. Page uploaded 7 December 2004

 



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An Electrodynamic Model of Atomic Structure

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by A. C. Sturt

 

 

 

 

 



Summary

1. Introduction

2. An alternative physical model

3. The equivalence of forces

a.      Gravity

b.      Definition of force

c.      Electrical charges and magnetic poles

d.      Possible interactions

4.Uniform motion in a circle

5.Proposed model of the simplest atom

a.      Basic structure

b.      Displacement of the electron

6. Magnitude of electromagnetic quanta

7. Elliptical orbits

a.      Ellipse in the same plane

b.      Ellipse in an inclined plane

8. The helium atom

a.      Proposed structure of helium nucleus

b.      Atomic radius of helium

c.      Magnetic field in the helium atom

d.      Deflection of electron

e.      Potential interaction of helium atoms

9. Atomic structures from lithium to neon

10. The first complete sphere

11. Higher atomic numbers

12. Atomic radii and chemistry

13. Discussion

References

Addendum – fission of nuclei

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary

1. Introduction

2. An alternative physical model

3. The equivalence of forces

e.      Gravity

f.        Definition of force

g.      Electrical charges and magnetic poles

h.      Possible interactions

4.Uniform motion in a circle

5.Proposed model of the simplest atom

c.      Basic structure

d.      Displacement of the electron

6. Magnitude of electromagnetic quanta

7. Elliptical orbits

c.      Ellipse in the same plane

d.      Ellipse in an inclined plane

8. The helium atom

f.        Proposed structure of helium nucleus

g.      Atomic radius of helium

h.      Magnetic field in the helium atom

i.         Deflection of electron

j.         Potential interaction of helium atoms

9. Atomic structures from lithium to neon

10. The first complete sphere

11. Higher atomic numbers

12. Atomic radii and chemistry

13. Discussion

References

Addendum – fission of nuclei

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary

1. Introduction

2. An alternative physical model

3. The equivalence of forces

i.         Gravity

j.         Definition of force

k.       Electrical charges and magnetic poles

l.         Possible interactions

4.Uniform motion in a circle

5.Proposed model of the simplest atom

e.      Basic structure

f.        Displacement of the electron

6. Magnitude of electromagnetic quanta

7. Elliptical orbits

e.      Ellipse in the same plane

f.        Ellipse in an inclined plane

8. The helium atom

k.       Proposed structure of helium nucleus

l.         Atomic radius of helium

m.    Magnetic field in the helium atom

n.      Deflection of electron

o.      Potential interaction of helium atoms

9. Atomic structures from lithium to neon

10. The first complete sphere

11. Higher atomic numbers

12. Atomic radii and chemistry

13. Discussion

References

Addendum – fission of nuclei

 

 

 

 

 

 

 

 

 

 

 

8.       The Helium Atom

 

The hydrogen atom is unique in having a nucleus consisting of a single proton, which makes it more difficult to introduce the concept of the separation of charges required if the spinning nucleus is to counteract the field effect of the orbiting electron. However, all other atoms have more than one particle in the nucleus, which introduces an obvious distance of separation.

 

The helium atom comprises two electrons orbiting a nucleus containing two neutrons and two protons, which give electrical neutrality. There are no stable nuclei with a single neutron and two protons, and so it seems unlikely that the role of the neutron is simply as a separator of protons. Otherwise they could just line up, with the protons sandwiching the neutron.

 

a.      Proposed structure of helium nucleus

 

The most likely arrangement of the four particles is shown in Figure 2.

 

The radii of protons and neutrons is assumed to be the same i.e. rp. The nucleus is planar with an axis of rotation at the centre. If the radius of rotation of the nucleus about its axis is rn, then

 

 

This represents the minimum radius of rotation, assuming the particles do not penetrate each other i.e. they are like billiard balls. They may, of course, be held apart by a balance of attractive and repulsive forces, which would increase rn.

 

The two electrons are likely to be in the same orbit, given the identical forces attracting them to the nucleus i.e. diametrically apart. They travel in the same sense, staying as far apart as possible, because of the repulsion of their negative charges. By the same argument as before, the axis of their orbit coincides with the axis of rotation of the nucleus.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


b.      Atomic radius of helium

 

The forces attracting each electron are considerably greater than in the hydrogen atom. The nucleus has four times the mass, and so gravitational attraction is increased fourfold, plus the gravitational attraction of the opposing electron. The electrical charge on the nucleus has doubled, so that the electrical attraction is doubled, but there is a repulsive force from the opposing electron.

 

Given these increased forces, the a first approximation of the new radius may be made as follows.

 

 

 

The gravitational force attracting the electron towards the nucleus has increased by , say, 4¼ times. The square of the new radius, which is the radius of the helium atom, is therefore decreased by 4¼ times, so that

 

 

and

 

 

If the radius of the hydrogen atom is taken as 0.46nm, then

 

 

 

 

However, the electrical force of attraction increases according to the same argument, say, by a factor of 1¾. Considering only the electrical forces,

 

 

so that

and

 

 

 

These are higher than the accepted figure for the atomic radius of helium by a factor of 2 and 3.

 

However, if both gravitational and electrical forces are taken into account, and on the hypothesis that they are of equal magnitude, the force pulling the electron towards the nucleus increases, say, by a factor of (4¼ + 1¾) or six times, which gives

 

so that

and

 

 

This is not too far from the quoted atomic radius of helium of 0.122nm, which suggests that the basic model is reasonable.

 

Both calculations assume that gravitational and electrical forces are independent of speed.

 

In any case the result is that the electron is pulled much closer to the nucleus, which means it orbits much faster. There is twice the charge and four times the mass acting at only about a third of the distance. The electrical forces holding the nucleus and orbiting electrons in a plane are therefore more than 30 times greater than for the hydrogen atom. The helium atom is that much more resistant to deflection from a planar configuration.

 

c.       Magnetic field in the helium atom

 

According to Laplace’s Law, the magnetic intensity H at the centre of a circular coil of radius r is

 

 

 

 

i.e. magnetic intensity is proportional to the electric current through the coil and inversely proportional to the distance over which it acts.

 

The orbiting electrons of helium constitute an electric current, which generates magnetic intensity at the centre of the atom. The helium atom is electrically neutral, because of the positive charges on the nucleus. The hypothesis here is that there these positive charges separate on the nucleus as it rotates, so as to generate an equal and opposite magnetic intensity to that generated by the electrons.

 

The magnetic fields are then proportional to the relative rates of rotation and inversely proportional to the distance of their charges from the centre of rotation i.e. the centre of the atom.

 

If

 

-         relectron is the radius of the orbit of the electrons i.e. the atomic radius,

 

-         nelectron is the number of orbits which an electron makes per second,

 

-         rnucleus is the radius of the nucleus,

 

-         nnucleus is the number of revolutions which the nucleus makes per second,

 

then,

 

and rearranging

 

from which

 

 

 

The radius of the electron orbit is the radius of the helium atom, which has been measured at 0.12 nm.

 

The radius of the nucleus is 2.4 times the radius of a proton according to the geometrical model proposed above. The radius of the proton is measured at 10-15m i.e. 10-6nm. This gives a figure of 2.4x10-6nm for the radius of the nucleus.

 

If the value of nnucleus = 1, then

 

 

 

 

 

Thus the nucleus at the centre of the helium atom rotates twice for 105 orbits of the electron to maintain equal and opposite magnetic intensities, and so a stable configuration. The nucleus spins in the direction in which the electrons orbit.

 

The angular momentum of this ‘disc’ is much greater than for the hydrogen atom, and so the helium atom will need much greater force to deflect its axis i.e. to make it precess.

 

 

d.      Deflection of electron

 

An electron deflected to an orbit of greater radius in the same plane distorts the whole structure of the atom to some extent, but the distortion disappears as it accelerates back towards the nucleus. However, the ground state orbit of helium is already occupied by the other electron. This is travelling at the same constant velocity as before, but the deflected electron has a lower velocity until it reaches the ground state orbit.

 

Thus when the deflected electron reaches the ground state again, the two electrons will not be quite diametrically opposite. Their mutual repulsion will cause one electron to slow and the other to accelerate to reach their stable configuration at opposite ends of a diameter. This acceleration will be accompanied by the emission of a quantum of electromagnetic radiation, which will cause both electrons to settle down to the constant ground state velocity in the same sense but diametrically opposite.

 

e.      Potential interaction of helium atoms

 

The proposed electronic structure of the helium atom suggests the possibility that under some conditions helium atoms may associate in ordered structures. Normally thermal motion would cause them to repel each other because of the negative charges carried by their electrons. However, if they are cooled sufficiently to allow them to approach, their electronic orbits may synchronise, so that an electron is shared between atoms as in Figure 3.

 

 

 

 

 

 

 

 

 

 

 

 

 


All the electrons are travelling at the same speed. Their orbits are synchronous but 90° out of phase and in opposite senses. This is because orbiting in the same sense would require electrons to approach each other at some point in their orbits, and their like charges make this unlikely. The link between the atoms is the attraction which the joint electron has for both nuclei at the point shown. This falls short of covalency, which requires paired electrons, but nevertheless the association between the atoms is not  random.

 

If this sort of link occurs, there is no reason why another atom should not join the first two atoms to form a line. In fact the process could continue indefinitely to form long strings of helium atoms. Thermal motion is likely to be the limitation. Helium structures formed in this way seem likely to have unusual angular momentum and magnetic properties, with each atom opposing the next. It might be possible to detect such properties spectroscopically.

 

The “discs” formed by the helium atoms have been drawn in the same plane, but the lines could equally well be formed of “discs” perpendicular to each other i.e. one “disc” in the plane of the paper and the next perpendicular to it, as in Figure 4.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


In this case each atom is 90° out of phase with the adjoining atoms.

 

In principle the “discs” may interact at any angle, and even rotate independently, as long as they retain their proximity. However, if the orbits are in the same plane or orthogonal, as shown in Figures 3 and 4, the structures may be extended in two or even three dimensions.

 

The essential conditions are enough mobility to manoeuvre into alignment, and the appropriate phasing. Since these imply opposite temperature requirements, there will be an optimum temperature for satisfying both. This temperature will be very low, probably close to absolute zero.

 

The electronic structure which permits such links is unique to helium. No other atom has the electronic balance and potential for synchronous orbits. Confirmation that such structures are possible might be relevant to the formation of cosmological structures from gases.

 


 



 
extension of model to helium


 








proposed structure of nucleus

 

 

 

 

 

 

 

 


 

 
 

 



 


 




 

 





 


 


 

 
atomic radius




 


 





 

 





 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

orders of magnitude

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

reasonable values

 

 

 

assumptions

 

 

 

 

 

 

 

 

 

 

 

Laplace

 

 

 

 

magnetic intensity

 

 

nuclei spin

 

magnetic fields

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

nucleus

 

electron

 

 

 

 

 

relative rates of spin

 

 

 

 

 

 

 

 

 

mechanism of return of electron after deflection

 

 

 

 

 

 

 

 

 

 

potential for association of helium atoms

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

formation of lines and

discs

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

optimum temperature low

 

 

 

unique to helium

 

 

 

Copyright A. C. Sturt 27 September 2001

continued on Page 5

 

 

Churinga Publishing

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