All of the responses you provided highlight important aspects of how the study of the atom contributed to the understanding of the periodic table of elements. However, the most comprehensive answer among them is:
Experiments that identified characteristics of atoms provided scientists with atomic weights and atomic numbers, which were used to organize the periodic table.
This statement emphasizes the critical role that atomic characteristics, such as atomic weight and atomic number, played in the development and organization of the periodic table. The classification of elements based on these atomic properties allowed for a systematic arrangement that reflects their chemical behavior and relationships.