The irradiation the coins were subjected to made them temporarily radioactive.
A silver dime is 90% silver. That silver is actually two different stable isotopes in roughly equal quantities, silver-107 and silver-109. Neutron bombardment turned a small amount of the isotope silver-109 present in the coin into radioactive silver-110 which, with a half-life of a mere 22 seconds, decays into stable cadmium-110. Likewise, some of the silver-107 forms metastable silver-108 (half-life 400 years) which eventually decays to cadmium-108. A tiny amount of the copper present would be similarly eventually transmuted to stable isotopes of nickel and zinc, with half-lives in minutes or hours.
After just a few days, the radiation would have been undetectable by a Geiger counter. You'd certainly need an extremely sensitive detector to find anything above normal background radiation from the coin today. But the transmutation of a few trillion silver atoms inside the coin into cadmium atoms would be permanent. In theory, an advanced modern analytical device ought to be able to tell the difference between a once-irradiated dime and a never-irradiated dime, just by measuring the cadmium levels, especially by measuring the ratio of cadmium-110 to other stable cadmium isotopes not related to silver transmutation reactions, such as cadmium-114.
