The radioactive nuclide ¹⁴C decays with a t_1/2 of 5730 yrs. An archaeologist is studying a woven mat using radiocarbon dating. If calculations related to the mat's original ¹⁴C content reveal that there was 5.83 × 10²² atoms of ¹⁴C present in the plant used to weave the mat, how long ago was the mat woven if modern spectroscopy was used to determine that 7.11 × 10²⁰ atoms of ¹⁴C now exist in the sample?

Question

Quizplus · Accepted Answer

The decay of ¹⁴C follows first-order kinetics. Using the formula N = N₀ * (1/2)^(t/t_1/2), where N is the remaining amount, N₀ is the initial amount, and t_1/2 is the half-life, we can solve for t. Substituting the given values, we find t ≈ 3.6 × 10⁴ yrs.

The Radioactive Nuclide 14C Decays with a T1/2 of 5730

The Radioactive Nuclide ¹⁴C Decays with a T_1/2 of 5730