The isotope Uranium-238 has a half life as long as 4.5 billion years whereas the half life of Thorium-234 is as little as 24 days.
The animation below explains the half life of a radioactive isotope.
The age of the ancient organic materials can be found by measuring the amount of Carbon-14 that is left.
The most common tracer is called Technetium-99 and is very safe because it only emits gamma rays and doesn't cause much ionisation.
Radioisotopes can be used for medical purposes, such as checking for a blocked kidney.
To do this a small amount of Iodine-123 is injected into the patient, after 5 minutes 2 Geiger counters are placed over the kidneys.
The release of radiation is also a random event and overtime the activity of the radioactive material decreases.
Over the next 2 days 2500 of the remaining radioactive nuclei undergo decay.This is half of the remaining 5000 radioactive nuclei.