Final answer:
After 40 years, which is 2.5 half-lives of a radioactive element with a half-life of 16 years, only 12.5 grams of the initial 100 grams will remain due to radioactive decay.
Step-by-step explanation:
The question involves the concept of radioactive half-life, which is the time it takes for half of a radioactive substance to decay. Given a half-life of 16 years, after 40 years (which is 2.5 half-lives), the amount of the radioactive element remaining can be calculated. To find out how much remains after each half-life:
- After the first 16 years (1 half-life), 50% remains.
- After 32 years (2 half-lives), 25% remains.
- After 40 years, which is 2.5 half-lives, you would multiply the remaining amount after two half-lives by 0.5 once more.
Therefore, after 40 years, 100g × 0.5 × 0.5 × 0.5 = 12.5 grams will remain.