Actually, the radiation of the scattered "unused" plutonium is negligible compared to the amount of radiation generated by the fission products.
An unexploded (or scattered) plutonium bomb consists of 300-600 Curies. But the amount of fission products from a 1kt detonation are (the list is only partial):
160,000 Curies of Iodine-131
38,000 Curies of Strontium-89
190 Curies of Strontium-90
200 Curies Cesium-137
15 Curies of Carbon-14
But that's only the near-term story. Plutonium has a (far) longer half-life than the fision products, which means that after sufficient time has passed, the residual Plutonium will continue to be a lasting radiation threat even after the fission products have decayed away to unremarkable levels.