My textbook asks me to derive an equation for the potential energy (U) of sphere (r0) filled with an electric charge of uniform density (P) [expressed in terms of the total charge Q] The equation can be derived by treating the potential energy (U) as the total work it would require to build the sphere and computing an integral (which I won't show unless somebody wants me to, that is not why I am asking this question).

Here is the kicker: In the next part of the question, it asks us to set our result (U = (3/5)((Q^2)/r0)) equal to mc^2, and attempt to calculate the proper radius of an electron [it does not work, it is three orders of magnitude too large].

***Now, it asks us to explain why this theory does not adequately analyze the proper radius of an electron, or to find out what the defect in this theory is. I really do not know, I wouldn't have used this method in the first place. Any thoughts here?