No equations led to ⟨R_m^2 ⟩=6/G(0) [at]_(t=0)=12/(m_s^2 ) in which both sides of the equation are dimensionally at odds. It is appropriate to dare challenge the flaw in the procedure that produced 0.55 fm as the mass radius with many models and solutions because the charge radius and, more recently, the proton's mass radius are inconsistent. The objective is to develop an alternative theory that combines the idea of the mass-energy equivalence principle with a kinetic basis. Proving that 0.55 fm is a fabrication and demonstrating that the proton's charge radius might equal the mass radius of one up and one down quark combined are only a few of the objectives. Results were generated through theoretical and computational methods. The mass radii of protons were between 1.019699 and 1.10254513 fm; the sum of mass radii of up and down quarks was 0.8349190666 fm; the mass of the hypothetical particle was 8.911586959 exp. (−32) kg; mass radii of up and down quarks were 0.5881268197 and 0.246803591 fm, respectively; the mass radius of an electron was 0.06278280228 fm; and nucleon size—based radii of the electron are 0.08993727541 and 0.09001990394 fm, corresponding to the proton and nucleon, respectively. The idea that the charge radii may represent the mass radii of quarks is supported by the total (0.8349190759 fm) of the radii of up and down quarks in this research. The new model equation for calculating the mass radii of the electron and proton is supported by the intraproton radius (0.08993727541 fm) of the electron, which is provided by〖 ((R_mP^3)u20441836.152673)〗^⅓, where proton mass radius, R_mP = 1.10254513 fm. Since ⟨R_m^2 ⟩ ≠12u2044(m_s^2 ), 0.55 fm was a fabrication. It is almost half of 1.10254513 fm and was used to support the false claim that the proton charge radius equals its spatial extent, thereby refuting Bohr’s radius.