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?
If we consider and
as the disintegration constants for S38 and Cl38 respectively.
Therefore, dN1/dt = – N2
dN2/dt = rate of decay of Cl38 + rate of formation of Cl38
again, dN2/dt = N2+
N1
edN2 +
N2e
dt =
N0e(λ2 –
)dt
If we integrate the above equation, we will get:
t = 1.65 h