The most common isotope of plutonium found in nuclear reactors and weapons is plutonium-239 (Pu-239). It has a half-life of approximately 24,110 years. This means that it takes about 24,110 years for half of the Pu-239 sample to decay into other elements.
Regarding an RTG (Radioisotope Thermoelectric Generator) powered by plutonium, the half-life of Pu-239 is important because it determines the rate at which the plutonium decays and produces heat. The heat generated by the radioactive decay of plutonium is converted into electricity by the RTG.
As the plutonium decays over time, its radioactivity decreases, and subsequently, the amount of heat it produces also decreases. Eventually, after several half-lives, the plutonium will have decayed to such an extent that it no longer generates enough heat to be useful for powering the RTG effectively.
Typically, for practical purposes, an RTG powered by plutonium is considered to have reached the end of its useful life when the power output drops to about half of its original value. Since the half-life of Pu-239 is approximately 24,110 years, it would take multiple half-lives for the plutonium to decay to the point where the power output diminishes significantly.
To provide a rough estimate, assuming we consider an RTG to be no longer functional when the power output reaches 50% of its original value, and considering the half-life of Pu-239, it would take several tens of thousands of years for an RTG powered by plutonium to cease functioning due to decay of the plutonium into other elements. The exact duration would depend on the specific design of the RTG and the initial amount of plutonium present.