From a theoretical viewpoint, this investigation examined fractional energy levels and velocities that surpass the speed of light in a vacuum. These phenomena have received limited attention. Using a classical framework, the study aims to validate these phenomena by computing relevant parameters using fundamental constants and their multiples in derived equations. The presence of fractional energy levels and superluminal velocities (SVs) is validated within a classical framework aligned with the mass-energy equivalence principle. SVs are directly proportional to the masses of fundamental and baryonic particles when the first energy level is set to one. Conversely, if a constant luminal velocity is considered, the irrational energy levels (n_i) are proportional to the square of the particles' masses. For example, the values for the proton and the top quark are 3.022436467 exp. (+8) and 556.3297886 exp. (+8) m/s, respectively. The corresponding energy levels are 1.0164718078 and 34,436.83251, respectively. With the first atomic energy level, the energy levels are equal to the corresponding atomic numbers. For each atomic number, the fractional energy levels are inversely related to the subluminal kinetic energy. From Z=1 to Z=4, however, the energy levels showed an increasing trend. Even though the classical theoretical framework considers the distance between two centers of mass, determining the mass radius of the proton remains a possibility at specific fractional energy levels for certain atomic numbers. Future research may explore achieving the proton's mass radius at higher atomic numbers and lower fractional energy levels (below 0.1).