It is clear that a radioactive element will lose its activity after a infinite time and all radioactive element are identical in this respect. To distinguish one radioactive element from other as far as its activity is concerned we use the concept of half life. Half life T of a radioactive element is the time in which the initial number of radioactive atoms is reduced to half, i.e. N = N0/2 ; t = T. Therefore
We define the concept of mean life to represent the above mentioned facts from a statistical point of view. We have already seen that it it only after an infinite time that the radioactivity of an element disappear completely. Hence out of disintergrating atoms some will disintegrate almost immediately and some other will disintegrate after an infinite time.
Thus actual life of a disintagrating atom can vary from 0 to ∞. We thus introduce the numerical average of the ages of the atoms as the number of atoms decreases from N0 to 0. Mean life is then the ratio of the combined ages of all the atoms and the total number of the atoms in the disintegratinng atom. Refering to figure we can write , \(\tau\) , the mean life of a radioactive element as
on inegrating above expression we have \(\tau = \frac{1}{λ}\)
We thus have T = 0.693 \(\tau\)
The curie is the unit of radioactive disintegration. We have
1 curie = 3.7 x 1010 disintegration per second
