Stable, catalytically active palladium nano particles of various average diameters (1.9-7.4 nm) have been synthesized and characterized by X-ray diffraction, spectroscopy, and microscopy techniques to demonstrate remarkable size-dependent and renewed catalytic activity toward the Suzuki-Miyaura coupling reaction in green protocol. The catalytic activity is found to depend on the amount of the reducing agent, stabilizer-precursor ratio, solvent composition, and aryl halides used. The product obtained by this reaction is characterized by H-1 NMR, (CNMR)-C-13, and IR spectroscopy, analyses. A newly developed kinetic equation illustrates that while the catalyst particles of the lowest dimension are gradually exposed to the reactants and hence activated due to partial removal of capping polymer from the catalyst surface, others are deactivated due to agglomeration during the progress of the reaction, as conformed by the microscopic profiles of the used and unused catalysts.