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:

\[ \text{Remaining amount} = \text{Initial amount} \times \left(\frac{1}{2}\right)^{\text{time elapsed} / \text{half-life}} \]

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:

\[ \text{Number of half-lives} = \frac{500 \text{ years}}{100 \text{ years/half-life}} = 5 \]

Now we can calculate the remaining amount of zinc:

\[ \text{Remaining amount} = 200 , \text{g} \times \left(\frac{1}{2}\right)^5 \]

Calculating \(\left(\frac{1}{2}\right)^5\):

\[ \left(\frac{1}{2}\right)^5 = \frac{1}{32} \]

Now plug this value back into the formula:

\[ \text{Remaining amount} = 200 , \text{g} \times \frac{1}{32} = \frac{200}{32} \approx 6.25 , \text{g} \]

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