Question

The half-life of carbon-14 is 5,730 years. An artifact produces 13.3 disintegrations of 14C per minute per gram of carbon in the sample. Estimate the age of this sample assuming that its original radioactivity was 15.3 disintegrations per minute per gram of carbon.

Answer 1

The radioactive decay follows first order kinetics and

rate law is

k = [2.303/t] log a /a-x

= [2.303/t] log initial acitivity /activity now

as activity is proportional to concentrations

given

half life = 5730yrs

thus k = 0.693/5730 /yr

initial acitivity = 15.3 disintegrations /min

= 15.3 x 60 x 24 x 365 /yr  

sample activity = 13.3 disintegrations /min,

= 13.3 x60x24x365 /yr

thus 0.693/5730 = [2.303/t] x log 15.3 /13.3

time t = 1158.51 yrs

The age of artefact is 1158 yrs.