What characteristic of an element determines its specific isotope?

The characteristic of an element that determines its specific isotope is the number of neutrons. Isotopes are variants of an element that have the same number of protons (which determines the element's identity) but different numbers of neutrons. This variation in neutron number gives rise to different isotopes of an element, which may have slightly different atomic masses. The number of protons in an atom determines its atomic number, while the sum of protons and neutrons determines its atomic mass.