Some radioactive substances, including all of the actinides, are subject to decay chains. This means that a radioactive substance is transformed initially to another element that is itself radioactive and will undergo further decays until a stable isotope is obtained. For all of the actinides, including natural uranium and thorium, a stable nuclide is not reached until there have been many decays resulting finally in an isotope of either lead or bismuth.
The specific activity (the amount of nuclear decays per unit mass) of the daughter product is almost different for the decay daughter, and the chemistry is different. In general after isolation of a nearly pure radioactive substance, the concentration of the daughter nucleus will rise to a maximum, after which the daughter will be decaying as fast as formed. The time it will take for this to happen is related to the half-lives of both the parent nuclide and the daughter nuclide. For nuclear calculations, the actual number that is used is the decay constant, which is the natural logarithm of 2 divided by the half-life in whatever units of time are convenient. If we use the letter l to designate the decay constant, the time required is given by the following relationship:
t = ln(l
1/l
2)/(l
1 - l
2)
"ln(x)" refers to taking the natural logarithm of a number x, in this case the ratio of the decay constants.
From a health perspective, the most important example of this case has little to do with nuclear power but is related to the properties of uranium containing geologic formations, including soils. Because sufficient time has passed in uranium formations for them to be in radioactive equilibrium with all of their decay daughters, all of the daughters are present in concentrations related to their half-lives in comparison to the half-life of the parent uranium. One decay daughter in the uranium series, arising from the decay of U-238, is the gaseous element radon, which is highly radioactive, having a half-life of a few days. While the equilibrium concentration of this element is small, it is very mobile and diffuses easily, particularly in soils which have large surface area to mass ratios. Some of this radon diffuses into structures built by human beings, in places like basements. As a result people can be exposed to fair amounts of radiation. In fact radon from the decay of uranium is one of the major sources of background radiation to which all humanity has been exposed since the beginning of time. The average exposure of a citizen of the US is said to be about 360 millirems per year, 200 of which derive from radon. After cigarette smoking and air pollution, exposure to natural radon is thought to be the third largest contributor to lung cancer.
http://extranet.urmc.rochester.edu/radiationSafety/WebTraining/Modules/Natbkg.html#Natural%20BackgroundMost of the external cost now attached to the use of nuclear power comes from the assumption that the uranium will eventually decay to radon in whatever form so called "nuclear wastes" are stored. This assumption is based on the once through uranium cycle. It is easy to show that continuous recycling will actually result in a decrease in exposure to radiation in less than 1000 years of use.
However in the "once through" cycle, although the risk of most fission products falls below the risk of uranium ores within a few hundred years, the risk associated with the actinides can remain slightly higher than uranium ores for much longer periods. For the short term, the first several hundred years the risk of actinides actually
rises because of equilibrium effects, owing to the decay of plutonium-241, which is always formed in nuclear reactors, into americium-241, an effect controlled by equilibrium effects. This state is achieved after about 200 years. After 1000 years the risk of actinides is dominated by neptunium-237, the decay daughter of americium-241.
This is a strong argument for abandoning the "once-through" fuel cycle and fissioning
all of the actinides that are mined. Nuclear engineers around the world are developing programs to do exactly just this. I have no doubt that this is the approach that will ultimately embraced by humanity should humanity survive global climate change. The use of continuous recycling will destroy all of the uranium before it has an opportunity to decay into radon thus eliminating the vast majority of the radon risk.
None of these issues have any bearing on the fact that all fossil fuels are more dangerous by many orders of magnitude than nuclear fuels, fossil fuels all being unacceptably dangerous, and nuclear fuels having almost no impact in a relative sense.