Let's just say it involves jars and is not very pleasant. The jars' contents are then analyzed by gamma spectroscopy primarily, although I would expect they would also be doing alpha monitoring as well since reactor fuel could possibly have been taken internally.
The reason it takes so long is because of the biological half life, i.e. the time it takes the body to eliminate half of the radioactive elements through normal bodily functions.
Thank you for the insight. I completely forgot about the biological half life. I thought ‘uptake’ isotopes like Strongtium would not be eliminated from the body well. Strontium to the bones - cesium to the muscle etc. So is there a rule of thumb how much the body eliminates - ie is it really half or in general half? Thanks in advance.