"Alpha particles are so large that they tend not to penetrate well, so the packages of nearby chips will protect them from alpha particles emitted elsewhere within the room. Beta particles (electrons) and cosmic rays can penetrate the package of chips, but those are from the solar wind not radioactive decay of anything local. I'm not sure that a radiation counter will detect alpha particles from the packaging materials. The situation I've seen is with the bonding agent emitting alpha particles, which is a "goo" inside the package which cushions the die and the wires between the silicon die and the pins on the package. The particles which hit the silicon die can cause errors, while the plastic of the package surrounding the goo would tend to absorb the rest." - DGentry