Final answer:
Approximately 1.98g of the original 10g sample of cesium-137 will remain after 80 years, calculated using the half-life decay formula and considering two full half-lives and an additional period of decay.
Step-by-step explanation:
The original question is about the radioactive decay of cesium-137, which has a half-life of 30 years. The student wishes to know how much of a 10-gram sample of cesium-137 will remain after 80 years. To determine this, we must use the concept of half-lives, knowing that after each half-life period, half of the remaining substance will have decayed. After the first 30 years, the 10 grams will be reduced to 5 grams. After the second 30 years (60 years in total), the sample will further reduce to 2.5 grams. As 80 years consists of two full half-lives and a partial one-third half-life, we calculate the remaining mass after two half-lives and then apply the formula for exponential decay ({0.5}^(80/30)) for the remaining years.
So, after 80 years, the calculation would be:
- After 60 years: 10g * (1/2)^2 = 2.5g
- After 80 years: 2.5g * {0.5}^(20/30) ≈ 2.5g * 0.7937 ≈ 1.98g
Therefore, approximately 1.98g of the original 10g sample of cesium-137 will remain after 80 years.