After how many half-lives would only approximately 12.5% of a radioactive substance remain?

To determine when approximately 12.5% of a radioactive substance remains, it's essential to understand the concept of half-lives in radioactive decay. After one half-life, only 50% of the original substance remains.

After two half-lives, you would have:

• 50% remaining after the first half-life
• 50% of the remaining 50% after the second half-life, which is 25% of the original amount.

After three half-lives, the remaining quantity would be:

• 50% after the first
• 25% after the second
• 12.5% after the third half-life, because 50% of the previous 25% is 12.5%.

This process demonstrates that after three half-lives, only 12.5% of the original substance remains. Each half-life represents a halving of the previous amount, leading to the final conclusion regarding the quantity that remains. Thus, the correct answer is that approximately 12.5% of a radioactive substance remains after three half-lives.