The Pre-Quantum World

The Pre-Quantum World

Let's review the infamous 'Thomson Plum-Pudding Model' first. When I tried doing some study on the model, I was amazed. Blown away, to be exact - not by the fact that the model is (now) deemed to be absurd, (its lack of scientific backing notwithstanding) but by the issue of how Thomson could come up with a solution to how the electrons could distance themselves so as to minimize the interaction between themselves.

On further exploration, I came across this article on 'The Thomson Problem'. The question goes as follows:

"Given N electrons on the surface of the unit sphere that exhibit interactions that follow Coulomb's Law, find the configuration of minimum potential energy."

This problem, apparently, is a subset of a larger question on arranging objects that interact with each other according to the inverse-square law. Now, let us, for a moment forget about the solution to such a problem. Intuitively, symmetrical structures like a line that connects the electrons (in the case of a two electron system), whose length is the diameter of the pudding or a regular tetrahedron (for 4 electrons) can solve the issue. 

Note: We are dealing with an environment that has rid itself of the surrounding positive charge.

But here is one question that crept in. As we increase the number of electrons, the rigidity of the structure of energy equilibrium increases, i.e., the degrees of freedom of the electrons go down drastically. So we are dealing with a situation where even the most electro-negative elements would be unwilling to give in to an excitation of the electron, simply because the rigidity of the structure leads to a collapse of the equilibrium state, on disruption. An enormous amount of energy would hence be required for excitation, to take into account the re-establishment of equilibrium of the remaining electrons.

The Thomson Model is a failure today, but that was just some food for thought on a topological problem.