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A grain sample was found in a cave. The ratio of 14 6 c/ 12 6 c was 1/64 was the value in a fresh grain sample. How old (in yr) was the grain in the cave? The half-life of C-14 is 5600 years .
Accepted Answer
The grain sample is approximately 22,400 years old. Here's how to calculate that:
Radioactive Decay: Carbon-14 (¹⁴C) decays with a known half-life of 5600 years. This means that after 5600 years, the amount of ¹⁴C in a sample reduces to half its initial value.
Ratio Calculation: The ratio of ¹⁴C/¹²C in the cave sample is 1/64. This means the ¹⁴C content has decreased by a factor of 64.
Number of Half-Lives: Since each half-life reduces the ¹⁴C content by half, a decrease by a factor of 64 indicates that 6 half-lives have occurred (2⁶ = 64).
Age Calculation: The total age of the sample is 6 half-lives
5600 years/half-life = 22,400 years.
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