Question

The radioactivity due to carbon-14 measured in a piece of a wooden casket from an ancient burial site was found to produce 20 counts per minute from a given sample, whereas the same amount of carbon from a piece of living wood produced 160 counts per minute. The half-life of carbon-14, a beta emitter, is 5730 years. Thus we would estimate the age of the artifact to be about?

Answer 1

17202.6 years

Step-by-step explanation:

Activity of the living sample (Ao) = 160 counts per minute

Activity of the wood sample (A) = 20 counts per minute

Half life of carbon-14 = 5730 years

t= age of the artifact

From;

0.693/t1/2= 2.303/t log Ao/A

Then;

0.693/ 5730= 2.303/t log Ao/A

Substituting values;

0.693/5730= 2.303/t log (160/20)

Then we obtain;

1.209×10^-4 = 2.0798/t

t= 2.0798/1.209×10^-4

Thus;

t= 17202.6 years

Therefore the artifact is 17202.6 years old.