Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is:
Assume that we start with 1000 38S nuclei at time t = 0. The number of 38Cl is of count zero at t = 0 and will again be zero at t = ∞. At what value of t, would the number of counts be a maximum?
Given
The reaction given in this scenario is
The number of 
nuclei = 1000, the initial time taken = 0, the number of 
at time
, half-life of 
and half-life of
. Hence, to find the value of time t when it is maximum, we use the relation of decay rate and number of live atom with respect to time.
Formula used
According to the Radioactive Decay Law or Rutherford Soddy Law the decay rate of a nucleus is given by the formula of
,
where
is the rate of decay of the nucleus with respect to time, 
is the decay rate constant of the nucleus and N is the number of active nuclei.
Explanation
The radioactive decay of Sulphur and Chlorine is given as
The number of active Sulphur nuclei
The decay rate constant of Sulphur
The number of active Chlorine nuclei
The decay rate constant of Chlorine
With the formula of radioactive decay in terms of initial and final number of atoms both before and after decay is
The rate of decay of active number of nuclei of Chlorine is
_______________ (1)
Multiplying 
on both sides and integrating we get the sides as
______________ (2)
Now since at time
, the number of chlorine nuclei (
) = 0. Therefore, the equation now stands as
The value of C = -
Hence, putting the value of C in equation (2) we get:
______________ (3)
To find the maximize value of the chlorine, we integrate the equation (3) on both side with respect to time and putting
, we get
Integrating, the above equation to find the value of t in terms of 
which leads to the time, when the number of nuclei 
is maximum
_____________________ (4)
Now to find the value of time t, we put the value of 
in equation (4),
Therefore, the time at which the value of active nuclei of Chlorine will be maximum is 1.648 h.