Question
Multiple Choice Question
The half-life of C-14 is 5470 years. If a particular archaeological sample has one-quarter of its original radioactivity remaining, what is the best estimate for its age?
A.
5470 years
B.
10940 years
C.
16410 years
D.
21880 years
Answers
GPT-4o mini
The half-life of Carbon-14 (C-14) is 5470 years. If a sample has one-quarter of its original radioactivity remaining, it means that two half-lives have passed.
Here's the breakdown:
1. After the first half-life (5470 years), the sample would have half of its original radioactivity remaining.
2. After the second half-life (another 5470 years), the sample would have one-quarter (1/2 of 1/2) of its original radioactivity remaining.
Thus, the total time that has elapsed is:
\[ 2 \times 5470 \text{ years} = 10940 \text{ years} \]
So, the best estimate for the age of the sample is:
**B. 10940 years**.
Here's the breakdown:
1. After the first half-life (5470 years), the sample would have half of its original radioactivity remaining.
2. After the second half-life (another 5470 years), the sample would have one-quarter (1/2 of 1/2) of its original radioactivity remaining.
Thus, the total time that has elapsed is:
\[ 2 \times 5470 \text{ years} = 10940 \text{ years} \]
So, the best estimate for the age of the sample is:
**B. 10940 years**.