Answer to Question #263506 in General Chemistry for geoerge

Question

A living tree contains 14C (half-life, 5730 years) and has a specific activity of 750 counts per hour. A wooden artifact recovered from an archeological site gives a count of 210 counts per hour. The age of this artifact is most nearly

Answer 1

Given:

Half life = 5730 year

use relation between rate constant and half life of 1st order reaction

k = (ln 2) / k = 0.693/(half life)

= 0.693/(5730)

= 1.209×10^-4 year-1

use integrated rate law for 1st order reaction

ln[[A]] = ln[[A]]o - k×t

ln(220) = ln(750) - 1.209×10^-4×t

5.39 = 6.62 - 1.209×10^-4×t

1.209×10^-4×t = 1.23

t = 10141 year