Understanding the determination of Radon activity

[user1139]

Homework Statement:

This is a conceptual question.

Relevant Equations:

As it is conceptual in nature, no equations will be used in the 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?

 

[gleem]

Even if you had an isotopically pure sample of Rn222 how would the production of Po218 affect the rate of decay of Rn?

Besides ever since the formation of the Earth's supply of U238 daughter nuclei have been/are being produced
Because of the extremely long half-life of U238 and the relatively short half-lives of the daughters an equilibrium has occurred in the population of the daughters. At any time the amount of daughter isotopes naturally occurring is constant.

 

[Astronuc]

Homework Statement:: This is a conceptual question.
Relevant Equations:: As it is conceptual in nature, no equations will be used in the question.

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 ) can be calculated. Why do we have to wait for equilibrium?

One should look at 'secular equilibrium', where the parent isotope decays slower (has a longer half-life) than the daughter radionuclide.
https://en.wikipedia.org/wiki/Secular_equilibrium

Secular equilibrium can occur in a radioactive decay chain only if the half-life of the daughter radionuclide B is much shorter than the half-life of the parent radionuclide A. In such a case, the decay rate of A and hence the production rate of B is approximately constant, because the half-life of A is very long compared to the time scales considered. The quantity of radionuclide B builds up until the number of B atoms decaying per unit time becomes equal to the number being produced per unit time. The quantity of radionuclide B then reaches a constant, equilibrium value. Assuming the initial concentration of radionuclide B is zero, full equilibrium usually takes several half-lives of radionuclide B to establish.

https://upload.wikimedia.org/wikipedia/commons/a/a1/Decay_chain(4n+2,_Uranium_series).PNG
https://physicsopenlab.org/2016/02/07/radon-2/