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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

by A. C. Sturt

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7. Elliptical orbits

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5.       Proposed Model of the Simplest Atom

a.      Basic structure

The simplest atom, hydrogen, is a stable entity composed of a nucleus in the form of a proton around which an electron circulates. The line velocity of the electron is a significant fraction of the speed of light. The atom is filled with the medium of space, which according to our previous analysis provides inertial resistance. The mass of the nucleus (mp) is much greater than that of the electron (me), but their charges are of equal and opposite magnitude.

The electron is held at a distance r0 from the nucleus by the balance of the attractive gravitational and electrical forces and the centrifugal force of the circular orbit. This is the ground state. Thus The term for gravitational attraction is included because the process takes place in the presence of the gravitational field. The orbit is not necessarily circular; it may be an ellipse of nearly zero eccentricity, but it can be treated as a circle to a first approximation.

The assumption is that the total effect is the sum of the gravitational and the charge effects, but there may be an interaction which could be important if both increase in magnitude with velocity.

The electron circulates at a constant line velocity, and so there is no electromagnetic emission. The electron is an electric current, which by convention is considered to flow in the opposite direction, and according to Laplace’s Law it generates a magnetic intensity which exerts a force on a positive charge at the centre of the atom along the axis. The direction of the force is given by the corkscrew rule.

The hypothesis is that there is a separation of charge on the nucleus, the corollary of which is that charge moves on the surface of the particle. The nucleus rotates in the same sense as the electron moves in orbit, which is equivalent to an electric current in the opposite direction to that represented by the electron. It rotates at such a rate, and the separation of charges is such, that it generates a magnetic field equal and opposite to that generated by the electron. When the electron and proton have approached close enough to form a stable entity, the magnetic effect holds them so that the electron orbits the nucleus in a plane i.e. the atom takes the form of a disc.

Since the disc has a mechanical axis of rotation, and its components have mass, it has angular momentum and may undergo precession.

However, it cannot be assumed that the axis of the rotating proton entity always coincides with the axis of the atom. It seems likely that the nucleus wobbles like a star and a planet, which itself may add to the separation of charge if, for instance, the positive charge is on the outside of the nuclear orbit as a result of the attractive influence of the electron.

b.      Displacement of the electron

If the electron is deflected by some means, it orbits further away from the nucleus, but still within the same plane. There is no increase of line velocity of the electron during deflection, and so there is no emission of electromagnetic radiation from that cause. However as the forces of attraction begin to pull the electron back towards the nucleus, line velocity in the medium of space increases until the activation energy of emission is reached, and a quantum of electromagnetic radiation hf is emitted.

The emission of the quantum of energy stops acceleration for an instant at a distance of, say, rn-1 from the nucleus, and leaves the electron with kinetic energy ½m(vn-1)2  where constant velocity vn-1>vn.

The electron immediately resumes its acceleration. When its line velocity reaches the activation energy of emission, it emits another quantum of electromagnetic radiation. This quantum of energy is greater than the first, because it is emitted at an increased line velocity, according to the factor R in the inertial field analysis. The higher energy manifests itself as higher frequency radiation.

The emission of the quantum of energy leaves the electron closer to the nucleus at distance rn-2 with kinetic energy ½m(vn-2)2 as before, but the value of the constant velocity is now greater than before the quantum was emitted i.e (vn-2)>(vn-1). And so on.

Thus the emission of quanta determines the distance between ‘orbits’. These ‘orbits’ represent the instants of constant velocity at which no quantum of electromagnetic radiation is being generated and emitted. The progressive increase of the energies of quanta emitted as the electron descends to ground state results from the progressive increase of velocities at which the emission takes place through interaction with the inertial field. The model is shown schematically in Figure 1 The process is summarised in Table 1 below. Velocity, kinetic energy and emitted quantum energy increase as the electron approaches the ground state. Quanta are labelled according to the ‘orbit’ into which the electron falls.

 Electron velocity vn

##### Table 1 Succession of Quantum Emissions

Thus

-         The line velocity of the electron and hence its kinetic energy increase as it drops back towards the nucleus.

-         One quantum hfn is the energy generated in the inertial resistance field and emitted as the electron drops back from the ‘orbit’ rn, in which the velocity is constant, to the ‘orbit’ rn-1 at which line velocity is also constant, but greater.

-         It is the quantum hfn-1 which determines the difference between rn and rn-1.

6.       Magnitude of Electromagnetic Quanta

The forces which attract the electron back towards the ground state accelerate it from one constant velocity to another with emission of a quantum of electromagnetic radiation. The magnitude of this quantum of radiation can be calculated from the work done against the inertial field during the process of increasing velocities.

According to the analysis of inertial resistance (3), the energy Wf  required to overcome the inertial field in accelerating from v to v+dv is the difference between the total energy expended and that which is consumed in increasing the Newtonian kinetic energy. This is given by the following expression: where R is the Inertial Resistance Parameter.

In the model of the atom proposed here, the parameter Wf  is the energy of the quantum of light emitted.

Using the notation developed above, the quantum of energy emitted in accelerating an electron from velocity v to velocity vn-1 is therefore 7.       Elliptical Orbits

The electron may be deflected entirely out of a circular orbit into an ellipse, which has eccentricity. Two possibilities result from this: the ellipse may be in the same plane as the circular orbit, or it may be inclined at an angle to the plane.

a.      Ellipse in the same plane

The line velocity in an elliptical orbit is no longer constant, but greatest when the electron approaches its closest to the nucleus. The increase of velocity as it orbits the nucleus causes the emission of a quantum of radiation. The magnitude of the quantum is smaller than in circular orbit, because the velocity is lower. The reduction of energy may thus cause a sequence of emissions which brings the electron back to circular orbit, from which it drops back to ground state. The orbit may also rotate in the plane as the Earth around the Sun, but this additional motion may not involve enough energy to cause a change in the pattern of emissions.

The nucleus responds to deflection of the electron through the forces of attraction by changing the rate of rotation, changing the separation of charges and greater oscillation within the plane.

b.      Ellipse in an inclined plane

If the deflection causes the electron to orbit out of the plane of the circle, the change of angular momentum causes precession of the elliptical orbit. This also causes the nucleus to precess. The result is a different series of changes of velocity and emission of quanta of electromagnetic energy to bring both rotations back into the same plane. This is followed by the sequence of emissions which brings the orbit back to a circle. This compares with Bohr’s hypotheses for the hydrogen atom, which were that:

-         Only orbits for which mrω x 2πr were a multiple of Planck’s constant did not emit radiation.

-         Each of these orbits was characterised by a number in order of increasing energy.

-         A single quantum of electromagnetic radiation was emitted when the electron dropped from an orbit to the orbit with the next lower number.

-         The orbital number determined the size of the quantum of electromagnetic radiation emitted.

However, these hypotheses were not justified by reference to physical mechanisms.

hydrogen

proton

electron

balance of forces

ellipse

no e.m. emission

Laplace

hypothesis separation of charges on nucleus

magnetic effect

angular momentum

wobbles

electron acceleration back towards nucleus produces e.m. emission

quantum

stepwise descent

velocity increase

emission of quanta is ‘distance’ between orbits

quanta and velocities

quantum of energy emitted

eccentric orbits

different quanta

Bohr model assumptions

not justified by physical mechanisms

 Copyright A. C. Sturt 27 September 2001

 Churinga Publishing