Understanding the determination of Radon activity

Question

When we want to determine the radioactivity of a nucleus, we usually determine the counts detected using say a Geiger counter. The count rate is then usually used as the disintegration rate i.e. the activity of the nucleus.

However, say now we wish to measure the activity of Radon 222 using alpha spectroscopy. Here is the part I don't understand:

If we use say RAD7, a detector with inbuilt alpha spectroscopy, we have to wait for activity equilibrium between the parent Radon nucleus and the daughter nuclei (those who decay via alpha particle emission) before an accurate Radon concentration (measured in $\mathrm{Bq/m}^3$) can be calculated. Why do we have to wait for equilibrium? And if we do wait for equilibrium, then the Radon concentration will only involved counts obtained from Po-218 after around 10mins and only after 3h will counts from both Po-214 and Po-218 be involved. Why is it okay to calculate the Radon concentration this way even though different contributions occur at different times?

Answer 1

The RAD7 manual (pdf) is actually really nicely written, does it answer your question?

Now introduce some radon into the RAD7. What do you see? At first, maybe nothing. But within a few minutes, you begin to get counts in the A window. The RAD7 chirps merrily with each count. That's polonium-218, a result of the decay of radon-222 within the RAD7 sample chamber. For the first 5 minutes or so, the count rate increases, then begins to approach a steady level. After about 10 minutes, we say that the polonium-218 daughter has reached close to equilibrium with the radon-222 parent.

Etc. if you wait longer. If you do a full fit on the grow-in of activity you wouldn't need to wait, but for simplicity, once you waited for equilibrium, you don't need any differential equations any more, thus simplifying the interpretation of the counts.