It’s important to note that *not all* radiation can penetrate everything. Alpha radiation can only travel a few feet and is stopped by paper. Radio waves are oftentimes blocked/scrambled by metallic frames.
Otherwise, it’s similar to how a pebble can get dropped in a pool of water and sink to the bottom without leaving any holes. It has enough mass and energy to push through the water. In the case of radioactive particles traveling “through matter”, it’s really traveling through the gaps and space in the individual atoms and molecules that make up the objects you see.
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