Can a radioactive material transffer it's radioactivity to another substance?

I recently purchased a small sample of radioactive uranium ore for testing out my geiger counter and learning to use it, I am aware that it isn't a deadly amount of radiation that is being emitted from the sample but nonetheless am a bit worried about it. I am wondering if the sample being stored out side of a lead lined box can transffer it's radioactivity to say dust or even the cardboard box it is stored in, thanks!