To determine how much of a radioactive substance remains after a certain period, we can use the concept of half-life. The half-life is the time it takes for half of a sample of a radioactive substance to decay. In this case, the half-life of the substance is 5 years. ### Step-by-Step Explanation 1. **Understanding Half-Life**: - The half-life of a substance is the time required for half of the radioactive atoms in a sample to decay. After one half-life, only half of the original amount remains. 2. **Calculating the Number of Half-Lives**: - We need to find out how many half-lives fit into the total time period of 15 years. - Given that the half-life is 5 years, we can calculate the number of half-lives in 15 years: \[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{15 \text{ years}}{5 \text{ years}} = 3 \] - This means that 15 years is equivalent to 3 half-lives. 3. **Calculating Remaining Amount**: - We start with an initial sample of 16 grams. After each half-life, the amount of substance remaining is halved. - After the first half-life (5 years): \[ \text{Remaining amount} = \frac{16 \text{ grams}}{2} = 8 \text{ grams} \] - After the second half-life (10 years): \[ \text{Remaining amount} = \frac{8 \text{ grams}}{2} = 4 \text{ grams} \] - After the third half-life (15 years): \[ \text{Remaining amount} = \frac{4 \text{ grams}}{2} = 2 \text{ grams} \] 4. **Final Calculation**: - After 15 years, the remaining amount of the radioactive substance is 2 grams. ### Conclusion The correct answer is **A. 2 grams**. ### Explanation of Other Options - **B. 4 grams**: This would be the amount remaining after 10 years (2 half-lives), not 15 years. - **C. 8 grams**: This is the amount remaining after 5 years (1 half-life), not 15 years. - **D. 1 gram**: This amount would not be reached in this scenario; it would require more than 15 years to decay to this level. ### Common Pitfalls - **Misunderstanding Half-Lives**: Students often confuse the number of half-lives with the total time. It’s crucial to divide the total time by the half-life to find the correct number of half-lives. - **Forgetting to Halve the Amount**: Some may forget to halve the amount for each half-life, leading to incorrect calculations. ### Revision Summary - The half-life is the time taken for half of a radioactive sample to decay. - To find the remaining amount after a certain time, calculate the number of half-lives that fit into that time. - Halve the initial amount for each half-life to find the remaining quantity. - After 15 years (3 half-lives), a 16-gram sample reduces to 2 grams.