Cobalt nanoparticles were synthesized using the gamma radiolytic technique, and the particle size was found to be reduced from $12\pm 1$ to $7\pm 1$ nm by increasing the dose from 10 to 60 kGy. The UV-visible absorption spectra were measured and exhibited a steady absorption maxima at 517 nm in the UV region, which blue-shifted toward a lower wavelength with a decrease in particle size. By taking the conduction electrons of an isolated particle that are not entirely free but are instead bound to their respective quantum levels, the optical absorption of the cobalt nanoparticles can be calculated and simulated via intra-band quantum excitation for particle sizes comparable to the measured ones. We found that the simulated absorption maxima of electronic excitations corresponded to the measured absorption maxima. Moreover, the structural characterizations were performed utilizing dynamic light scattering (DLS), transmission electron microscopy (TEM), and X-ray diffraction (XRD).