It takes @2000 electrons to equal the mass of one proton, according to a quick google search. The electrons, however, have 2000 times more electrostatic force than the proton; although the amount of force could be argued to vary, I think, according to the volume of the 2000 electrons. So if you began with some arbitrarily large volume for the 2000 electrons and began compressing them, their expansive force would increase in somewhat the same way a spring's potential energy increases as it is compressed. What I wonder is at what volume would the expansive potential of the 2000 electrons equal the amount of energy contained in the mass of a proton according to E=MC^2?

 

I am wondering about this because I am interested if there is some relationship between volume and different kinds of energy/force. For example, the volume of a H2 molecule may constitute the highest possible stable density for two protons unbonded by strong force. A He atom would be the highest possible density when strong force bonds them. Presumably if the 2000 electrons were floating through a vacuum, their gravity would stabilize the cloud they form at some volume as well. So, I'm trying to look at the relationship between forces, mass, and volume. Thanks for any input.

It occurred to me after posting this thread that since electrons have mass, the mass-energy equivalency of the mass of 2000 electrons would be the same as a proton. Then, if their electrostatic repulsion was equivalent to the energy of their mass, they would have double the energy of the proton. So the question becomes how would you find an equivalent amount of energy to the energy of 1 proton in electrons at what volume? My idea is that it's possible to compare energy of force-repulsion with energy of mass and that this would provide some clue about the relationship between different forces. Crackpottery?