Final answer:
Evidence for the existence of atoms includes periodic table patterns, Mendeleev's predictions of undiscovered elements, and consistent physical and chemical properties of elements.
Step-by-step explanation:
Three pieces of evidence for the existence of atoms include the patterns observed in the periodic table, the confirmation of Mendeleev's predictions about undiscovered elements, and the properties of elements such as melting point, boiling point, and behavior in chemical reactions. The periodic table shows a clear pattern where elements are organized by their properties and atomic number, which suggests a repetitive and organized underlying structure made up of atoms.
Mendeleev's accurate prediction of the discovery of elements like gallium and germanium based on gaps in his periodic table further supports the existence of atoms because it implies that the properties of elements are determined by their atomic structure. Additionally, properties such as melting points, boiling points, and reactivity in chemical reactions are consistent with the behavior of atoms as the basic units of matter.