Final answer:
Large impacts breaking the lunar surface allowed magma with radioactive material to reach the surface, and subsequent impacts distributed this material, forming the current lunar soil.
Step-by-step explanation:
One way that radioactive material reached the surface of the moon after it already formed is through the process of large impacts allowing magma to rise through cracks. These impacts were so powerful that they broke the surface rocks and created pathways for the deeper lunar magma, which can contain higher concentrations of radioactive elements, to ascend to the surface. The moon's surface is a testament to this violent past, with its heavily cratered highlands indicating a history of such significant impacts. Through the ages, this material was further distributed by smaller impacts that pulverized rocks and mixed the surface layers, resulting in the fine-grained lunar soil that covers the moon today.