Questions: All dating schemes that are presently used to determine the absolute age of Earth material involve the decay or breakdown of an unstable parent element to a more stable daughter element. The time it takes for half of the original parent material to be converted to daughter material is referred to as the half-life. Assuming a given parent/daughter dating scheme has a half-life of 2,000 years, what would be the age of an object where only 12.5% of the parent remained?
- 15,000 years
- 50,000 years
- 100,000 years
- 6,000 years
- 25,000 years
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All dating schemes that are presently used to determine the absolute age of Earth material involve the decay or breakdown of an unstable parent element to a more stable daughter element. The time it takes for half of the original parent material to be converted to daughter material is referred to as the half-life. Assuming a given parent/daughter dating scheme has a half-life of 2,000 years, what would be the age of an object where only $12.5 \%$ of the parent remained?
15,000 years
50,000 years
100,000 years
6,000 years
25,000 years
Solution
Solution Steps
Step 1: Understand the Problem
The problem involves determining the age of an object based on the percentage of the parent element remaining. The half-life of the parent element is given as 2,000 years, and we need to find the age of an object where only 12.5% of the parent element remains.
Step 2: Identify the Relevant Data
From the graph, we can see that 12.5% of the parent element remains after 3 half-lives.
Step 3: Calculate the Age
Since each half-life is 2,000 years, and it takes 3 half-lives for the parent element to reduce to 12.5%, we calculate the age as follows:
\[ \text{Age} = 3 \times \text{half-life} = 3 \times 2,000 \text{ years} = 6,000 \text{ years} \]