According to the theory of relativity, an object with mass cannot reach or exceed the speed of light. As an object with mass approaches the speed of light, its relativistic mass increases, requiring an infinite amount of energy to reach the speed of light. Therefore, it is not possible for a piece of radioactive material, which has mass, to travel at the speed of light.
However, let's consider a hypothetical scenario where we imagine a piece of radioactive material traveling at a speed very close to the speed of light. In this case, the behavior of radioactive decay would still occur, even though time dilation and length contraction effects would come into play due to the relativistic motion.
From the perspective of an observer at rest relative to the radioactive material, the rate of decay would appear to slow down due to time dilation. Time would pass more slowly for the moving object relative to the observer. However, from the perspective of the moving radioactive material, time would continue to pass normally, and the decay would occur at its usual rate.
It's important to note that this scenario is purely hypothetical since objects with mass cannot reach or exceed the speed of light. The behavior of radioactive decay is well-described in non-relativistic frameworks and doesn't rely on objects approaching the speed of light to occur.