Question

A wooden object from an archeological site is subjected to radiocarbon dating. The activity due to C-14 is measured to be 11.6 disintegrations per second. The activity of a carbon sample of equal mass from fresh wood is 15.2 disintegrations per second. The half-life of C- 14 is 5715 year. What is the age of the archeological sample

Answer 1

$k= -\frac{1}{t}\ln(\frac{N_t}{N_o})\\ k= -\frac{1}{2.00 yr}\ln(\frac{0.59}{1.000})\\ k= -\frac{1}{2.00}(-0.0481)=0.0241 yr^{-1}\\ t_{\frac{1}{2}}=\frac{0.693}{k}=\frac{0.693}{0.0241}=28.8 yr$