After 7 half-lives have passed, what percentage of the original amount of a radioactive substance remains?

• A. 0.78%
• B. 50%
• C. 6.25%
• D. 12.5%

Answer: (A)

Verified step by step guidance

1. Understand that the amount of a radioactive substance remaining after a certain number of half-lives can be calculated using the formula: \(\text{Remaining fraction} = \left(\frac{1}{2}\right)^n\), where \(n\) is the number of half-lives elapsed.
2. Identify the given number of half-lives, which is 7 in this problem.
3. Substitute \(n = 7\) into the formula to find the fraction of the original substance remaining: \(\left(\frac{1}{2}\right)^7\).
4. Calculate the fraction value (without final numeric evaluation here) to understand how much remains relative to the original amount.
5. Convert the fraction to a percentage by multiplying the fraction by 100 to express the remaining amount as a percentage of the original.