Carbon dating can be applied to organic materials up to 5.0 × 10⁴ years old.What percentage of the original $ { }_{6}^{14} \mathrm{C} $ is present in a sample after this much time? The half-life of $ { }_{6}^{14} \mathrm{C} $ is 5730 yr.

Question

Quizplus · Accepted Answer

Using the formula for exponential decay, we can calculate the fraction of $ { }_{6}^{14} \mathrm{C} $ remaining after 5.0 × 10⁴ years as: $N/N_{0} = (1/2)^{(t/T)}}$ where: - N is the remaining amount of $ { }_{6}^{14} \mathrm{C} $ - N0 is the initial amount of $ { }_{6}^{14} \mathrm{C} $ - t is the time elapsed (5.0 × 10⁴ years in this case) - T is the half-life of $ { }_{6}^{14} \mathrm{C} $ (5730 years) $N/N_{0} = (1/2)^{(t/T)}} = (1/2)^{(5.0\times10^{14}\mathrm{years}/5730\mathrm{years})} \approx 0.0024$ This means that approximately 0.24% of the original $ { }_{6}^{14} \mathrm{C} $ is present in a sample after 5.0 × 10⁴ years. Therefore, the answer is B.

Carbon Dating Can Be Applied to Organic Materials Up to 5.0