The radioactive nuclide ¹⁴C decays with a t _1\2of 5730 years. An archaeologist is studying a woven mat using radiocarbon dating. If calculations related to the mat's original ¹⁴C content reveal that there were 5.83 × 10 ²²atoms , how long ago was the mat woven? Modern spectroscopy was used to determine that 7.11 × 10 ²⁰atoms of ¹⁴C exist in the current 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 current number of atoms, N₀ is the original number of atoms, t is the time elapsed, and t_1/2 is the half-life, we can solve for t. Substituting the given values, we find that t ≈ 3.6 × 10⁴ years.

The Radioactive Nuclide 14 C Decays with a T

The Radioactive Nuclide ¹⁴C Decays with a T