Question

Archeologists can determine the age of artifacts made of wood or bone by measuring the amount of the radioactive isotope 14C present in the object. The amount of isotope decreases in a first-order process. If 27.4% of the original amount of 14C is present in a wooden tool at the time of analysis, what is the age of the tool? The half-life of 14C is 5730 yr.

Answer 1

K = 0.693/t_1/2

half life = 5730 yr

K = 0.693/5730 = 1.2094*10^-4 Yr^-1

K = 2.303/t log[A₀]/[A]

1.2094*10^-4 = 2.303/t log100/100-27.4

                   = 2.303/t*1.8609

t               = 2.303*1.8609/1.2094*10^-4

                = 3.5436*10⁴ = 35436 yr >>> answer

Age of tool 35436yr