Answer to Question #76713 in Atomic and Nuclear Physics for Osama Sulaiman

Question

living matter has an activity of 260 bq/kg due to carbon 14. if a sample of wood from burial site has an activity of 155 bq/kg, estimate the age of the site. half-life of carbon 14 is 5730 years

Answer 1

Activity of the sample is decreasing as: A=A_0 2^(-T/T_(1/2) )
T_(1/2)=5730 years-halflife time.
A_0=260 bq/kg-initial activity
A=155 bq/kg-activity at time T
So, A=A_0 2^(-T/T_(1/2) )→T=T_(1/2) log_2⁡〖A_0/A〗=5730*log_2⁡〖260/155〗=4276 years

So, the age of the site is 4276 years.