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Radiometric Dating Mastering Biology Answer: Carbon-14 Half-Life

A 12.5% remainder equals one-eighth of the starting carbon-14, or three half-lives, so the fossil's calculated age is 17,190 years.

Question

Carbon-14 has a half-life of 5,730 years. A fossilized leaf contains 12.5% of the carbon-14 that was present when the fossil formed.How old is the fossil? Express the answer numerically in years and show how the remaining fraction gives the number of half-lives.

Answer

Convert the percentage to a fraction:

12.5%=0.125=18.12.5\%=0.125=\frac{1}{8}.

Each half-life multiplies the remaining amount by 12\frac{1}{2}:

  • after one half-life: 12=50%\frac{1}{2}=50\%;
  • after two half-lives: 14=25%\frac{1}{4}=25\%;
  • after three half-lives: 18=12.5%\frac{1}{8}=12.5\%.

The leaf has therefore undergone three half-lives:

age=3×5,730 years=17,190 years.\text{age}=3\times5{,}730\ \text{years}=17{,}190\ \text{years}.

Answer: 17,190 years.

Evidence boundary

The calculation uses the values stated in this problem: a 5,730-year carbon-14 half-life and 12.5% remaining. It assumes the measured carbon belongs to the leaf, that the sample remained a closed system after death, and that 100% represents the starting amount specified by the exercise. Real laboratory dating also requires calibration, contamination control, and uncertainty analysis, which are not supplied here.

Sources

These references support the concepts and methods used in the explanation above.

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