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Isotopes are variants of a particular chemical element that have the same number of protons in their atoms but a different number of neutrons. Some isotopes are deemed unstable, commonly known as 'radioactive isotopes'.

These unstable isotopes are characterized by excess nuclear energy that results in inherent instability. The nucleus of an atom wants to reach a state of equilibrium or lowest energy, and for unstable isotopes, this means undergoing radioactive decay. During this process, they emit radiation in the form of alpha particles, beta particles, or gamma rays, each corresponding to different types of decay.

Examples of unstable isotopes include Uranium-238 and Carbon-14, both of which play a crucial role in scientific methods like radiometric dating that allow us to date materials and artifacts.

The transformation of an unstable isotope into a stable one is not always direct. Often, it involves a series of steps – a 'decay chain'. During these steps, the original isotope, known as the parent, decays into a new isotope, known as the daughter. If the daughter isotope is still unstable, it, too, will decay, continuing the chain.

This sequential process can include a variety of decay types along the way until a stable isotope, which no longer undergoes radioactive decay, is finally produced. An example of a decay chain is the Uranium Series, which starts with Uranium-238 and ends with Lead-206, after many intermediary isotopes and decay events.

Understanding decay chains is essential for many fields, including geology, archeology, and nuclear physics, as they help determine the age of rocks and fossils and are used in the management of nuclear materials.

In contrast to unstable isotopes, stable isotopes do not exhibit radioactivity. These isotopes have a balanced nuclear composition that does not release excess energy through radioactive decay. As such, they remain constant over time.

Stable isotopes are common in nature and are used in a variety of scientific applications. For example, they serve as tracers in environmental studies and in medical diagnostics where they can help trace biochemical pathways without the risk associated with radiation.

Examples of stable isotopes include Carbon-12 and Oxygen-16. The presence of stable isotopes at the end of a decay chain signifies that the chain has reached its completion, and the material will no longer undergo radioactive changes.