Suppose an element A disintegrates into another element B.
Let number of atoms of A when t = 0 is N0.
A undergoes continuous disintegration into B and hence the number of atoms of A goes on decreasing.
Let the number of atoms of A left undisintegrated in time t be N
If dN atoms of A disintegrates in a small time dt, then the rate of disintegration (i.e., rate of decrease) of A into B is equal to 
and is proportional to N.
where l is a constant of proportionality which is called by Rutherford and Soddy as Radioactive (or decay or disintegration) constant.
The rate of disintegration has a negative sign showing that the number of atoms of A decreases with time.
In the differential form, the equation is
Integrating, we have
Substituting in (i), we get
Converting in equation (ii), natural logarithm to base 10, we have
Kinetically radioactive decay process is a first order reaction.
