The Law of Radioactivity Disintegration:
Let, N be the number of atoms present in the radio element at a given instant t. Then the rate of decrease,
Here, λ is the disintegration constant. It is defined as the ratio of the amount of the substance which disintegrates in a unit time to the amount of substance present.
The equation (i) can be written as, 
Integrating,
Let, there are 
number of atoms present initially.
Then, when t=0, N=N0
Substituting the value of C in equation (ii),
Thus the number of atoms of a given radioactive substance decreases exponentially with time.