What characteristic of an atom is determined by the number of protons?

The characteristic of an atom that is determined by the number of protons is indeed the element it represents. The number of protons in an atom's nucleus is known as the atomic number, and it uniquely identifies the type of element. For example, an atom with one proton is hydrogen, while an atom with six protons is carbon. This means that the atomic number corresponds directly to the element on the periodic table, effectively labeling it and distinguishing it from all other elements.

In contrast, characteristics like specific isotopes relate to the number of neutrons rather than protons. Atomic mass includes both protons and neutrons, and charge is determined by the balance between protons and electrons. Therefore, while those other concepts are influenced by protons, only the number of protons in an atom directly identifies which element it is.