The half life of zinc is 100 years. A fossil started with 200g of zinc. When the fossil was discovered it was 500 years old! How much zinc does the fossil have remaining?

1 answer

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:

Remaining amount=Initial amount×(12)time elapsed/half-life

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:

Number of half-lives=500 years100 years/half-life=5

Now we can calculate the remaining amount of zinc:

Remaining amount=200,g×(12)5

Calculating (12)5:

(12)5=132

Now plug this value back into the formula:

Remaining amount=200,g×132=200326.25,g

Thus, after 500 years, the amount of zinc remaining in the fossil is approximately 6.25 grams.