[Richard777 (OP)]

The binding energy of the Hydrogen electron is well documented. The ratio of binding energy and wavelength gives a force which acts upon the electron.
It is reasonable to assume that two forces (reciprocal forces) are required to balance the electron in a steady state. It is convenient to name one force the “binding force” (derived from binding energy) and the opposing force is called the “reciprocal force”.
The binding vector is a vector of force. The components of force may be associated with; heat, light, electric charge, and inertia. Two states of force may be defined; an orbital state and an emissive state.
Can a vector represent different states of hydrogen?

[chris]

bump

[evan_au]

The binding vector is a vector of force. The components of force may be associated with; heat, light, electric charge, and inertia.

The proton in a hydrogen atom creates an electric field; this field defines a vector of force which attracts the electron to its nearest proton.
- If this hydrogen atom is in a hydrogen molecule, the presence of the other proton and electron affects this electric field.
- If this hydrogen  molecule is in a hydrogen gas, the motion of nearby hydrogen molecules also affects this electric field.

It is reasonable to assume that two forces (reciprocal forces) are required to balance the electron in a steady state.

One of the findings of quantum theory is that there is a "ground state" of hydrogen, where the electron can sit undisturbed, and it can't fall into a lower orbital.

One simplified way of imagining this is to think of the electron as a wave, which oscillates as it travels around the proton.
Only certain orbits will have an integer number of oscillations and be stable; all others will interfere with each other, and be unstable.

The ground state has just one oscillation around the orbit; there are no lower stable orbits in which the electron can exist.

This discovery solved a paradox in pre-quantum physics: "If the negative electron is attracted so strongly to the positive proton, why doesn't it plunge into the nucleus, radiating enormous energy in the ultraviolet before it disappears?". This was called the "ultraviolet catastrophe".

You are asking the same question - but the good news is that the solution was found by Plank and Einstein in discovering the quantized nature of light, which then relates to the quantized levels of electron orbitals. 

There is no need for a reciprocal force based on heat, light and inertia.

[puppypower]

Two opposite charges will attract via the electrostatic force. While a charge in motion will give off a magnetic field. In the case of the hydrogen atom, we have an electron and proton attracting each other via the electrostatic force, resulting in a motion situation that will create magnetic repulsion. A positive and negative charge moving in opposite directions; toward or away from each other, is analogous to two electrons moving in the same direction. The result is magnetic repulsion. 

As the electrons of the hydrogen atom lower energy level, the velocity of the electron increases, causing the electron's magnetic field to get stronger. The closeness in distance increases the electrostatic attraction between the proton the electrons, causing the proton to move toward the electron and vice versa. This causes magnetic repulsion which comes to an equilibrium at the lowest energy level. This is where electrostatic attraction and magnetic repulsion balance each other. We would say the EM force, which is the sum of the two, is at its lowest energy level.

The theoretical moral of this story is,  atomic nuclei should have their own version of orbitals to optimize proton motion, that will reflect the optimized electron orbitals, so there is balance between magnetic and electrostatic forces. Conceptually, if you could tweak the nucleus orbitals, you could generate exotic atomic states. The vice versa should also be true, with exotic oxidation states able to tweak nucleus orbitals, to cause nuclear rearrangement reactions.


\

[evan_au]

Two opposite charges will attract via the electrostatic force. While a charge in motion will give off a magnetic field. ...The result is magnetic repulsion.

It is true that the Hydrogen nucleus has a small amount of magnetism (we call it a "magnetic moment", even though it lasts a long time), and the electron orbiting the hydrogen nucleus also has a small magnetic moment.

However, electrons do not orbit the nucleus in a flat plane, in the same direction, like planets orbiting the Sun (as some simplified models of the atom show it). This would indeed produce a strong magnetic field. In fact, the electrons orbit the nucleus in three dimensions, and do not have a specific position or direction. So these orbits do not produce a strong magnetic field that would repel the electron from the nucleus.

The magnetic field of the nucleus can be thought of as the "spin" of a tiny, electrically charged proton. And the magnetic field of the electron can be thought of as the spin of an electrically charged electron. These fields are far too weak to repel the electron from the nucleus, and far too weak to overcome the electrostatic attraction of electron and nucleus.

We can illustrate the relative strength of the electrostatic and magnetic forces as follows:
- When an electron drops into the ground state, it emits an ultraviolet photon. The Lyman alpha line has a frequency of 2.47×10¹⁵ hertz.
- When an electron of the Hydrogen atom is in the ground state, it can transition from "parallel" to the nucleus to "anti-parallel". This emits a photon at the "Hydrogen Line" with a frequency of 1.42 x 10⁹ Hz
- So the electrostatic energy in the ground state is about 2 million times greater than the magnetic energy involved.
- So the magnetic field cannot prevent the electron from collapsing into the nucleus.
- The electron orbit is protected by quantum effects, not magnetic effects.

magnetic repulsion

The assumption here is that the magnetic field will always repel.
However, when a Hydrogen atom emits a photon at the Hydrogen line, any magnetic repulsion will now turn into a magnetic attraction. If this magnetic field was previously stopping the hydrogen atom from collapsing, it should now accelerate the immediate collapse of the electron into the nucleus!

But because the magnetic effect is so weak compared to the electrostatic effect, it really doesn't change the orbit of the electron by a noticeable amount..

See: https://en.wikipedia.org/wiki/Hydrogen_line

In the case of the hydrogen atom, we have an electron and proton attracting each other

While hydrogen atoms (proton+electron) do exist in the near-vacuum of space, in our environment hydrogen atoms rapidly join up with other nearby atoms to produce molecules such as hydrogen gas, water and organic molecules.

When hydrogen forms covalent bonds, it shares an electron with an adjacent atom. These electrons have opposite spins, cancelling the magnetic field due to electron spin. If this theory of magnetic repulsion actually worked, hydrogen atoms would collapse as soon as they formed a molecule with another atom.

This does not occur, so we can be sure that magnetism is not counterbalancing the electrostatic force between proton and electron.

Conceptually, if you could tweak the nucleus orbitals, you could generate exotic atomic states.

Magnetic Resonance Imaging (MRI) routinely tweaks the magnetic field of the hydrogen nucleus, by subjecting it to radio frequency magnetic fields inside a strong superconducting magnet.

This does not generate exotic exotic states inside your body.

See: https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance#Nuclear_spin_and_magnets