Why radioactivity decreases with time ?

Radioactivity decreases with time, but at different rates for different radioactive species. The lifespan of a radioactive material may be longer than that of a human being. As the material decays, in one or more steps depending on the decay chain, its radioactivity decreases until the material is fully transformed into a stable and therefore non-radioactive substance.

 

Two researchers (Rutherford and Soddy) demonstrated that a material made up of a given radioactive species loses half its radioactivity, i.e. half the atoms in the material disintegrate, over a period time that is specific to the species. This duration is referred to as the half-life of the given radionuclide.

Thus, if one gram (100%) of a substance is present to start with, and the half life is X days, only half a gram (50%) will still exist after X days; only a quarter gram (25%) will exist after 2X days and only an eighth of a gram (12.5%) will exist after 3X days (see figure to the right). It is, of course, the radioactivity that decays, not the mass, so this statement is true only when applied to pure radioactive materials. It is not strictly when discussing other materials, such as Uranium as an ore. 

Shorter half-lives indicate species that are more radioactive and longer half-lives indicate those that are less so. Compare, for example, 1 gram of Plutonium-239 with 1 gram of Plutonium-241. Plutonium-239 has the longer half-life that corresponds to a radioactivity level of 2.29x106 Becquerel per gram (0.062 Curies per gram), and Plutonium-241 has the shorter half-life that corresponds to a much higher radioactivity level of 4.14x109Becquerel per gram (112 Curies per gram). Thus, Plutonium-239, which stays active for a long time, has only 2.29x106 Becquerel per gram whereas Plutonium-241 has 4.14x109 Becquerel per gram, compensating by decaying rapidly.