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?

Answer 1

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.