The term for implanting radioactive materials into tissues for treatment is called brachytherapy.
unstable, radioactive
The phrase, "fall out," is a military term; an order from a superior, to troops in formation at attention. It is also a term in nuclear warfare referring to the radioactive dust created by a nuclear explosion.
The generic term would be "irradiated", which is also used to mean illuminated but can be identified by its context. This is similar to the use of "contaminated" to mean radioactive.
"The radioactive decay of certain unstable isotopes is used to calculate the age of objects."
no
brain scan
I suppose you must mean uranium, it is slightly radioactive.
Radioactive decay is the process in which unstable nuclei release radiation in the form of alpha particles, beta particles, or gamma rays.
If it is related to Nuclear studies, then the answer would be fusion.
Radioactive elements.
The medical term you are looking for is "nuclear medicine." This branch of medicine uses radioactive substances to diagnose and treat various diseases and conditions in the body.