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

Multiple Choice

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?

A) 8.3 × 10⁴ yrs
B) 4.1 × 10² yrs
C) 3.6 × 10⁴ yrs
D) 5.0 × 10⁶ yrs