How many half-lives are generally required to reduce the radioactivity of a radionuclide to about 1% of its original value?

To determine how many half-lives are needed to reduce the radioactivity of a radionuclide to about 1% of its original value, we need to understand the concept of half-lives in radioactive decay. Each half-life period reduces the remaining quantity of a radionuclide by half.

After one half-life, 50% of the original quantity remains. After two half-lives, 25% remains, then after three half-lives, it drops to 12.5%. Continuing this process, we evaluate the following:

• After four half-lives, 6.25% remains.

• After five half-lives, 3.125% remains.

• Finally, after six half-lives, only 1.5625% remains.

At this point, we have determined that by the end of six half-lives, the amount of radioactivity is already slightly above 1%. Since the question asks for the point at which the radioactivity is about 1%, six half-lives would indicate a dramatic reduction, allowing us to approximate down to that threshold.

Thus, the answer indicating that approximately seven half-lives would bring the remaining radioactivity down to less than 1% (as it would be