Clarification...
The gamma rays found in storms have nothing to do with radioactive materials.
The charged particles (alpha and beta) generated by the decay of nuclear wastes and natural radioactive materials often tend to be quite weak, and don't travel far (gamma rays are a different matter.) Space-originating particles are far more energetic.
Nuclear explosions and active fission reactors generate powerful streams of neutrons that do interact with surrounding material, and can create new radioactive substances. This is not common.