According to the National Science Foundation, isotopes are important both to help scientists understand the makeup of atoms in a theoretical sense as well as due to the unique characteristics isotopes of certain elements may have. Isotopes can be unstable and provide opportunities for fission, or they may decay into entirely new isotopes or elements. The specific isotopes present in molecules can serve as atomic-level fingerprints, as well.
The discovery of isotopes led to a new understanding of atomic structure, explaining why different samples of a given element might behave in different ways. For example, there are three stable isotopes of oxygen, and water molecules containing the lighter isotopes evaporate slightly faster than the heavier versions. Heavier oxygen molecules tend to condense out of water vapor more quickly, as well, so the water that falls from rain clouds tends to become atomically lighter as the storm progresses.
Isotopes can also be unstable, such as the radioactive elements that power nuclear fission. When these atoms decay, the particles and energy they emit can be harnessed in weapons as uncontrolled reactions or nuclear reactors as controlled reactions. Isotopes are also important in forensics because the ratio of isotopes in a given sample of material can identify its origin. If two samples of lead contain the same mix of isotopes, for instance, it is likely that the samples came from the same source.