>>12938021The seperated components of a radioactive atom are moving at high speed and interact with other atoms.
They can break chemical bonds, like the kind that hold your body together, by interacting with their charge, momentum and can change the chemistry entirely by changing the chemical elements via fision and fusion.
When these components are in the form of an atom they are 'perfectly safe' as you say because they are bound together and not moving at high speed.
They are big, slow and clumsy compared to fast moving smaller particles but are dangerous is other ways like toxicity and reactivity.