How are isotopes defined?

Isotopes are defined as atoms of the same element that have the same number of protons but different numbers of neutrons. This distinction is essential because the number of protons defines the element, while the variation in the number of neutrons leads to different mass numbers for those isotopes. For example, carbon has isotopes like carbon-12 and carbon-14, where both have six protons (making them carbon), but carbon-12 has six neutrons whereas carbon-14 has eight neutrons.

The other statements do not accurately capture the definition of isotopes. Atoms that have the same number of neutrons but different numbers of protons would not be isotopes of the same element but rather would represent different elements entirely. Atoms of different elements sharing the same mass would not be isotopes either, as isotopes pertain specifically to variations of the same chemical element. Finally, variations in electron configurations relate to the chemical behavior of atoms, but do not define isotopes, as these variations do not affect the atomic nucleus where the neutrons reside.