The thing with radioactivity is: it may be invisible but it is luckily very well detectable. Gamma ray spectrometers are super sensitive but that does not mean the detected levels are actually posing a threat to humans.
What is relevant here is either alpha (stopped by a couple of cm of air), beta (stopped by a sheet of plastic, heavy clothing, or a couple of micrometers of metal) and gamma radiation. These are the radiations we measure to monitor fallout.