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

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
Transcript text: Copyright O The McGraw-Hal Companies, Inc. Permission required for reproduction or display. 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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Solution

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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: \[ \text{Age} = 3 \times \text{half-life} = 3 \times 2,000 \text{ years} = 6,000 \text{ years} \]

Final Answer

The age of the object is 6,000 years.

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