Which of the following statements is true about isotopes?

Isotopes are defined as variants of the same element that have the same number of protons, which is indicated by their atomic number, but differ in the number of neutrons they contain. This variation in neutron number leads to different mass numbers for each isotope. For instance, carbon-12 and carbon-14 are both isotopes of carbon; they share the same atomic number of 6 (indicating they are both carbon), but carbon-12 has 6 neutrons while carbon-14 has 8 neutrons.

Understanding the correct statement about isotopes highlights their defining characteristics. The fact that they can have different mass numbers due to varying neutron counts is a fundamental aspect of isotopic behavior, which supports the selection of this answer. Additionally, the presence of isotopes includes both stable and radioactive forms, thereby expanding their importance in fields such as chemistry and nuclear science.

This explains why the other statements do not hold true; they either misrepresent isotopic characteristics or impose incorrect limitations on their behavior.