Answer to Question #11530 Submitted to "Ask the Experts"
Category: Radiation Basics — Radionuclides
The following question was answered by an expert in the appropriate field:
We have a thorium dioxide (ThO2) quantitative microanalysis standard that is 1.6 mm by 1.6 mm in size. I've read that thorium produces mostly alpha particles, but I also recently read that thorium decays to many daughter radionuclides that generate beta and gamma rays.
Does ThO2 produce beta and gamma rays? If so, is there software available that can estimate the amount of beta and gamma radiation produced over time?
Thorium-232 (232Th) is present in significant amounts in the Earth's crust and is an alpha-emitting radionuclide, which decays to radium-228 (228Ra), which is a beta emitter with a half-life of about six years; it emits no significant gamma radiation. The 228Ra ultimately decays through multiple radioactive progeny, four others of which decay by beta emission with the associated emission of various gamma rays, to stable lead-208 (208Pb). So, yes, the decay of thorium through its radioactive progeny does produce significant gamma and beta radiation.
You can find a large number of graphical and tabular displays of the 232Th decay chain on the Internet. Here is a link to one that shows the decay chain with decay modes and half-lives for all the radionuclides and some gamma emission information for a major radionuclide in the chain (thallium-208 [208Tl]), and here is a second that includes all the significant and minor gamma radiation and beta radiation from the radioactive progeny in the chain.
At the latter site above, if you click on a specific radionuclide, you will see the detailed information for gamma and beta energies and yields for that radionuclide. The yields shown in this case are based on the assumption that sufficient time has passed since the separation of the 232Th from other materials that secular equilibrium exists between the progeny and the parent thorium. "Sufficient time" here means that roughly seven half-lives of the longest lived progeny, 228Ra, have passed, implying an elapsed time of about 40 years. In this time, under a secular equilibrium condition, the 228Ra and all subsequent progeny that are not produced through a branch decay (one of two or more alternative decay routes) of a precursor radionuclide would have the same activity as that of the long-lived parent, 232Th. The progeny, polonium-212 (212Po) and 208Tl, are produced in respective yields of about 0.64 and 0.36 from the branch decay of bismuth-212 (212Bi). Therefore, under secular equilibrium conditions, these two radionuclides would have respective activities equal to 0.64 and 0.36 of the activity of the chain parent 232Th.
If considerably less time than 40 years has passed since the thorium in your source was separated from its progeny, the decay progeny would not be in secular equilibrium, and you could not make the above simple assumptions regarding relative activities. The linear first-order kinetics that govern the decay processes are well known and analytical solutions for any progeny member in a series decay can be determined. The original equations that show how the progeny activities are related to the chain parent and to each other are credited to Bateman, and you can find many references to him and his results by searching the Internet.
Many people have devised simple computer programs to solve the equations. A convenient and effective calculator program is available at the Uranium Wise site. Type "Th-232" (without the quotation marks) in the first chart in the "Series Name" box, accept "Th-232" for the "Nuclide Name," specify a nominal activity for the 232Th, and select "Pure" as the state of the 232Th (i.e., no progeny present). Then specify a start and stop elapsed time in the second chart, select "line chart" in the "Chart Type" box, select "all individual nuclide activities" in the "Chart Detail" box, and leave the "Chart Axes" box set for the log-log display. Click "Calculate" below the chart, and you will see the results for each of the expected activities for all members of the chain along with the decay/ingrowth curves for each member of the series. It is then a simple matter to get the expected beta and gamma emission rates for specific-energy beta particles and specific-energy photons from a specific radionuclide in the chain by multiplying the activity by the respective beta yield or gamma yield for the radionuclide of interest. The calculating software also allows the user to change various parameters to see how they affect the results.
George Chabot, PhD