THEREFORE for A,

........................................................1

when the parent nuclei decays the daughter nuclei is formed, therefore

the rate of formation of B,

ALSO THE RATE AT WHICH THE DAUGHTER nuclei decays is

  therefore

multiply both side of the above equation by the integrating factor

 ..............................*

the value

adding up exponential part of the right hand side of the above equation

Integrating the equation

...................................................2

where C is the integration constant,  when t=0 ,

thus

Substituting  in equation 2 above

 IF the half life of thee parent A, is very large, we can neglect , and  with respect to

THUS

If the half life the parent atom is so large compared to the time of our observation the exponential decay  will almost be equal to unity and

Therefore, from the above equation,  the rate at which  the parent nuclei disintegrate is equal to the rate at which the daughter nuclei is formed , the rate at which a radioactive element decays is equal to the rate at which the next one is formed in a natural decay series.