Predicting the spectra of Hydrogen

When you excite hydrogen gas by passing an electric current through it, it produces a particular kind of light which is composed of only certain frequencies. See:

http://hyperphysics.phy-astr.gsu.edu/hbase/tables/hydspec.html

One of the successes of quantum mechanics is its ability to reproduce the formula for the hydrogen spectra.

The cubic atomic model can reproduce the Balmer formula which predicts the spectra of hydrogen as well as the QM Schrodinger equations can. A description of the Balmer formula can be found at:

http://www.colorado.edu/physics/2000/quantumzone/balmer.html

It can be expressed as: v = 1/l = R (1/n1^2 - 1/n2^2)

In this formula l = wavelength, v = frequency and R is the Rydberg constant. The values n1 and n2 represent any 2 integer values representing the electron energy levels. Using this formula, you can precisely calculate the frequencies that are in the light produced by hydrogen.

Conventional quantum mechanics explain this as the result of an electron moving from one “electron shell” to another. The problem with this picture is how do you explain why the electrons maintain these “shells”? In atoms with dozens of electrons flying about, why don’t they collide and scatter? What could possibly hold them in their proper places? Quantum mechanics does not explain this and I think that it is impossible for the electrons to maintain any “shells”.

The cubic atomic model does not assume that the electrons are outside of the nucleus. It assumes that they are an integral part of the nucleus. So how is the spectra of hydrogen generated if there are no electron shells to generate the spectra?

The way I derive this is by assuming that space is quantized, that is, space is made out of fixed sized grains, like the grains of sand in a beach. Lets say we call L, the diameter of the grain of space. This restricts the movements of electrons to only move in whole integer distances n*L from the nucleus of the atom.

When you excite an atom, electrons are knocked loose from the nucleus and they can only travel integer distances away from the nucleus. So the main reason why electrons appear to have specific energy levels is because they can only exist at specific distances away from the nucleus. So there is no need to postulate that these electrons somehow exist in a mysterious “energy shell” floating around the nucleus with no apparent support. Instead when an atom is in the ground state, all the electrons fall straight into the nucleus and stop.

To derive the Balmer formula using the cubic atomic mode, we can trivially calculate the force between a hydrogen nucleus and an electron using Coulomb's law:

F = KQ1Q2/R^2 where r = n*L and Q1, Q2 are the charges of a proton and an electron.

Since we're dealing with hydrogen with a single +1 charge and -1 charge, it simplifies to:

F = K/R^2

I claim that the energy of the electronic transitions is exactly proportional to the difference in electrostatic force as calculated by Coulomb's law for any 2 values of r where R = n*L.

So for a transition from 2 to 3, we calculate the difference. For simplification, we take L=1 (the diameter of an aether particle) in arbitrary units. Since we are only talking about proportionality, the constant K can be anything, so let us set it to K=1 so it drops out as well:

Difference in force for a 2->3 transition = 1/2^2 -1/3^2

If we were to take a different transition, say 3 to 5, we get:

Difference in force = 1/3^2 -1/5^2

In general, we have:

Difference in force = 1/n1^2 -1/n2^2 where n1 is the starting level and n2 is the finishing level.

Now note that this is EXACTLY, the same format as the Balmer formula!

Since I claim proportionality, we can add in any constant, so we can add the Rydberg constant R and equate it directly to energy.

Energy = R(1/n1^2 -1/n2^2)

An since energy is inversely proportional to wavelength for light, we can write the complete Balmer fomula as:

1/wavelength = R(1/n1^2 -1/n2^2)

This interpretation immediately solves some questions about the Balmer formula. The use of 1/r^2 terms is not just happenstance, it is a directly result of the forces calculated by Coulomb's law. It also answers how an electron should actually be perceived when it is radiating. It is simply an electron, moving fixed distances towards and away from the central proton as it being ionized. When it is not ionized, the electron falls to the lowest level basically resting on the proton. The quanization is not due to some magical something that forces the electron into fixed sized orbits, it is space itself which does the quantization. A concept, which I think is much easier to accept. Balmer himself could not justify how electrons maintain their stately orbits around the nucleus, but this derivation solves that problem by forcing the electron to only exist at fixed distances away from the nucleus for short periods of time due to the granular nature of space itself.

The derivation of the Balmer formula is based on the Cubic Atomic model which can be found at : http://franklinhu.com/atmpics2.html

This is part of my Theory of Everything which can be found at: http://franklinhu.com/theory.html