In a system and a method for making carrier-free radioactive isotopic Gallium-68, stable enriched Zinc-68 is formed into a solid target of very high purity. The solid target of enriched Zinc-68 is exposed to a proton beam provided by irradiation in a cyclotron to change the enriched Zinc-68 into Gallium-68. After irradiation, the solid target contains high concentrations of Gallium-68 with only trace amounts of enriched Zinc-68 and isotopic Gallium-67. Gallium-68 is then further purified to remove the impurities resulting in a Gallium-68 composition with high purity and specific activity and without Germanium-68, Also provided are radiopharmaceutical agents that are labeled with the Gallium-68 compositions made by solid targeting in a cyclotron.