Isotope
Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons, and so different masses.
Definition
Isotopes are versions of the same element with different numbers of neutrons; they have the same number of protons, so they are the same element, but different mass numbers. They are named by mass number, such as hydrogen-1, hydrogen-2 (deuterium), and hydrogen-3 (tritium), and some are stable while others are radioactive. Because chemistry depends on electron configuration, isotopes of an element behave almost identically in reactions, with only small kinetic isotope effects from their mass difference. Radioactive isotopes decay with a characteristic half-life, and stable isotope ratios serve as tracers in geology, medicine, and climate science.
Example
Carbon-12 has $6$ neutrons and carbon-14 has $8$; both are carbon, but carbon-14 is heavier. Hydrogen-1 has no neutrons, hydrogen-2 has one, and hydrogen-3 has two, and all three form water with oxygen, though heavy water made from hydrogen-2 is about $10\%$ denser. Carbon-14 decays by beta emission with a half-life of $5{,}730$ years, so a sample with $25\%$ of its original carbon-14 has passed two half-lives and is about $11{,}460$ years old.
Key Insight
Extra neutrons change the weight, not the behavior. Carbon dating works because living things take in carbon-14 while alive and it decays at a known rate after death, turning atoms into clocks. Uranium-235 and uranium-238 are chemically inseparable, so enriching uranium relies on the $1.3\%$ mass difference in gaseous $UF_6$ spun in centrifuges; isotope separation is a physics problem, not a chemistry problem.