Decay analysis of Ra226 with Bi-214

[abotiz]

Hi,

I have a question regarding the possibilities of analyzing the activity of Ra-226 in a sample from a collected spectrum with HPGe detector, by studying the peaks of Bi-214?

The most common energy peak for Ra-226 is the 186 keV with yield 3.6%, the difficulties of determining the activity is due to the large noise and scatter registred at these low energies/channels in the detector. However, in the same decay chain one can find Bi-214. The gamma with 609keV and yield 46% is easily spotted in the spectrum, and the acitivty can therefore be determined (through a calibration) with good statistics.

I feel that mathematically, it should be possible to relate the activity of Bi-214 to the activity of Ra-226. I know the measuring time of the sample and the half-life of the nuclides in the chain. However, iam not sure how to set up the equation(s). Basically, one Ra-226 nucleus produce one Bi-214 nucleus, however, with a delay, and if I multiply that delay with the activity of Bi-214, iam sure I would get the activity of Ra-226.

Please, any help is much appreciated.

Best regards

 

[mfb]

If the decay products of Ra-226 do not leave your sample, the concentration of Bi-214 will reach an equilibrium after a few weeks (with nearly one Bi-214 decay per Ra-226 decay), and you can use this decay to estimate the number of Ra-226-decays.
The intermediate Rn-222 could be tricky - radon is a gas, so it could escape your sample.

 

[abotiz]

Hi,

Thanks for your reply!
In my education, I learned that if the mother nucleus deacays very slowly and the dotter nuclide decays very fast, then the mother activity = dotter activity. This seems to be the case here, now that you mention it.
Is there a rule of thumb like, if the longest decay time of the dotter nuclides in the chain is like 10 days, one have to wait about 30 days (3 T_1/2)? For example in the fig below, to reach equilibrium with Bi-214 I would wait about 3*3.8 days. If I wanted equilibrium with Bi-210 I would then have to wait 3*22 years? i.e. 3 times the longest decay time until the interested nuclide?

Thank you!

 

[mfb]

In my education, I learned that if the mother nucleus deacays very slowly and the dotter nuclide decays very fast, then the mother activity = dotter activity. This seems to be the case here, now that you mention it.

Right (it is daughter, by the way).

In a mathematical analysis, it will never exactly give an equilibrium - just better and better approximations. After 3 half-lifes of Rn-222, the activity is about 7/8 of the equilibrium value. After 4, it is about 15/16 and so on, if the initial sample had pure Ra-226.