# How to approximate the activity of radioactive product in chain decay?

I am trying to understand how do I get approximation for the activity for a radioactive nuclide that produced during a chain while the activity of the source is given at time $$t_0$$. For example lets take Sr90 wich decay to yittirium90 through $$\beta ^-$$ decay and the yittirium90 decay to zirconium-90 through a $$\beta ^-$$ decay.

Lets say that the activity of sr90 at its time production $$t_0$$ is given as $$B(t_0)[Bq]$$ Now, if I want to find the actvity of sr90 at time $$t$$ is just equal to $$B(t)= \frac{N(t)}{N_A}\cdot M$$ while M is the molar mass of sr90, $$N_A$$ is avogadro's number and $$N(t)$$ is the number of sr90 atoms in the material at time $$t$$, which given by $$N(t)=N_0 \cdot e^{-\lambda t}$$, $$\quad\lambda$$ is the probability per unit time of a single sr90 atoms to decay and can be taken from internet.

The above is clear for me, what I would want to know now is how do I get an estimate for the activity of yittirium90 at time $$t$$.

• Growth & decay of radioactivity page 129 -> Sep 14, 2022 at 21:52
• Thank you very much Sep 15, 2022 at 6:23
• The multiple decay equation is called the Bateman equation Sep 15, 2022 at 6:53
• @Farcher I am getting in my calculations that sometimes the activity of one of the daughters radioactive nuclide is higher than the parent radionuclide activity. I understand that there is a relation to the half life time but Im not sure I can understand how is it possible intuitively. Do you have any nice explanation? Sep 15, 2022 at 7:59
• Imagine short lived parent atoms which decay into long lived daughter atoms. After a time the short lived parent atoms all but die out leaving the long lived parent atoms still decaying. Sep 15, 2022 at 8:05