[zewqywan] Electrostatic repulsion in the nucleus

In 1911, Rutherford discovered the atom has a nucleus.  Let's assume that from his discovery he deduced a model for the atom consisting of electrons somehow wandering around the entire volume of the atom, and a positively charged nucleus occupying a tiny space in the center.  The linear scale of that tiny space is approximately 100000 times smaller than the diameter of the atom.  (We'll mention an alternative possible model at the end.)

A fun mathematical exercise -- did Rutherford try this? -- then is to calculate the potential energy in the electrostatic repulsion of that much charge crammed into that tiny volume of the nucleus.  There are two possible simple models: all the positive electric charge is uniformly spread out over the surface of a sphere of that volume, or all the charge is uniformly spread out within the interior of a sphere.  These calculations are probably easy, though I haven't done them.

The answer, the total electrostatic potential energy locked into the nucleus of an atom, is likely shockingly huge, especially when multiplied up to a macroscopic quantity of material.  How did scientists react to such huge numbers?  It was probably an exciting time, as the universe had revealed itself to be profoundly weird.

Scientists then of course realized that there must be a very strong force, now called the nuclear force or the residual strong force, that cancels out (and them some) electrostatic repulsion within the nucleus.  If the nuclear force were to disappear, how much energy would it take to assemble an atomic nucleus?  (This energy is equivalent to the electrostatic potential energy.)

How does this energy compare to the mass-energy of the atom itself? The "mass defect" is not quite what we want: it sums the potential energies of attractive nuclear force and the repulsive electrostatic force, so there's some canceling out of signs going on.   We want just the electrostatic component. 

If the nuclear force were to disappear, how much force would it take to hold together one atomic nucleus against electrostatic repulsion?  This might be a human-scale number.

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It might have been that Rutherford's gold foil alpha particle experiment only yielded a ratio between the size of the nucleus and the space between, while the absolute atomic scale remained unknown until X-ray crystallography later.  When did we first realize how weird the atomic nucleus is?

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It's also possible that scientists considered models in which the electrons and the nuclear positive charge were both contained in the nucleus, eliminating the difficulty of huge electrostatic forces within the nucleus.  However, this would require some sort of magic to permeate the empty space between atoms, keeping atoms separated by typical atomic distances.  Though in retrospect, such magic subjectively seems less preposterous than the nuclear force.