Isotopes were first discovered through the study of radioactive decay chains.
Discovery of Isotopes: Clues from Radioactive Decay
The initial suggestion of isotopes came in 1913 from radiochemist Frederick Soddy. Soddy's work on radioactive decay chains, specifically his observations of radioactive elements between uranium and lead, revealed a puzzle. He identified roughly 40 different "radioelements"—radioactive species that behaved chemically like elements—but the periodic table only had space for about 11 elements in that region.
The Radioactive Element Puzzle
This discrepancy indicated that multiple radioelements could occupy the same position on the periodic table, meaning they had identical chemical properties but different atomic masses. Soddy coined the term "isotope" (from the Greek isos meaning "same" and topos meaning "place") to describe these differing forms of the same element.
Example of Isotopes
For example, different isotopes of lead (Pb) are produced in different radioactive decay series. These isotopes of lead have the same number of protons (defining them as lead) but different numbers of neutrons, leading to different atomic masses.
Summary
In short, isotopes were found through investigations of radioactive decay, which revealed that some elements existed in multiple forms with the same chemical properties but different atomic masses, thereby filling fewer "places" on the periodic table than there were discovered radioelements.