Radioactive isotopes (radionuclides to be more correct) are thermodynamically able to change into another nuclide, this decay has to be an exothermic event. For example if we consider beta decays for nuclides with mass numbers of 130. It is clear that Cadmium-130 atoms can be transformed by beta decay into lower energy atoms such as tellurium-130 by beta decay. But Xenon-130 is unable to convert itself into cesium-130.
The rate of the transformation (radioactive decay) is proportional to the number of the nuclei of the radionuclide in question. While with exceptionally high decay energies the decay rate is often higher, there not a clear relationship between decay energy and rate of decay. Things like odd vs even proton / neutron numbers and magic numbers are important.
The rate constant for the reaction is normally written as "lambda" the value of the constant varries greatly between very large (such as beryllium-8) and very small (such as thorium-232, bismuth-209 and plutonium-244).
The activity (A in Bq which is events per second) is given by the equation
A = lambda N
Where N is the number of atoms
You calculate lambda by dividing ln(2) by the half life in seconds
When fission of uranium or plutonium atoms occurs a vast range of different nuclides are created. The final decay products of these range from zinc through to the middle of the lanthanide series. You can imagine that a very wide range of different nuclides exist in the decay chains of the different initial fission products. If we consider if a zirconium-110 nucleus is formed by the fission process, all the radionuclides in the decay chain which leads to palladium-110 have short half lives (less than 15 seconds). So if a short pulse of fission such as a nuclear bomb detonation occurs then all the atoms with the mass of 110 will have decayed to the palladium in about two minutes.
If we were to make a solution of enriched uranium nitrate and deliver a strong neutron pulse to it and then five seconds later we were to separate the ruthenium from this mixture then the specific activity of the ruthenium in terms of Bq per mole would be exceptionally high. But given a minute or so then the radioactivity level of the ruthenium in the neutron bombarded uranium will be far lower.
Now if we were to leave uranium after a dose of neutrons and leave it it for millions of years then the vast majority of the fission products will decay away and then the radioactivity of the uranium will be larger than the fission products. There is a place in Africa where a series of natural nuclear reactors operated many millions of years ago. The vast majority of the fission products and the transuranium elements (such as plutonium) formed by these prehistoric reactors have decayed away to either stable nuclides (in the case of fission products) or uranium in the case of the plutonium which the reactor formed.
In the samples of the African fossil reactor materials clear signs of nuclear fission exist, while for a while (a long time ago) the fission product radioactivity was far greater than the either the uranium or plutonium radioactivity. The fission product radioactivity and then the plutonium radioactivity have no decayed away. Leaving the slowly decaying uranium still in the samples.