Well it is very easy to work out the amount of the first radioisotope in a simple decay chain such as P-32 decaying to S-32
For the a unstable daughter such as in Mo-99 to Tc-99m to Tc-99, it is quite easy to work out the Tc-99m activity.
For the second radioactive daughter such as Tc-99 it is quite hard (big equation) to work out the activity at a given time.
What about for a third radioactive daughter such as U-234 in the following chain, where we start with pure U-238.
U-238 to Th-234 to Pa-234 to U-234
There are several solutions to the Bateman equation published, including one that uses Markov chains for solution. A very useful solution is found at
http://wordpress. MrReid.org/decay-chains/.
Thanks very much, I am now looking at the excel file to see how the calculatons were done. I will then get to work.
I didn´t know the exel sheet from Joseph. I´ve tried to find an own solution for a simple case 1 daughter nuclide, only one possible decay channel. I attend a chapter from one of my textbooks handling your problem. Look at page 139ff.
Hanno, Mark
Attached is a Markov method and a spreadsheet as described in the article.
Dear Joseph,
The paper on the build up of radon does explain how to use the Bateman equations very well, I think it is more clear than the paper published by A. Reid. That one does not explain so much about the general method of doing the calculations.
we can use Bateman equations to determine the activity of the 4th radionuclide in a decay chain? actually, Bateman equation can be used for any radionuclide (5th, 6th, 7th ........ nth) in the decay chain.
The answer provided by J. Alvarez is the best solution. Further study into the answer(s) and a more rigorous treatment of the answer can be found in the classical textbook by G. Gerhard Friedlander and Kennedy.
other solution to the Bateman equation published is a useful solution founded at http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/modern/radiactive_dacay.pdf
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