To determine how much zinc remains in the fossil after 500 years given its half-life is 100 years, we can use the following formula:
In this case:
- Initial amount = 200 g
- Time elapsed = 500 years
- Half-life = 100 years
First, calculate the number of half-lives that have passed in 500 years:
Now we can calculate the remaining amount of zinc:
Calculating
Now plug this value back into the formula:
Thus, after 500 years, the amount of zinc remaining in the fossil is approximately 6.25 grams.