Question

An old sample of wood from an archaeological excavation was found to have a radioactivity of about 140.8 counts per minute due to ${}^{14}C(t_{1/2}=5730$ years) as against 281.6 counts per minute for that of a freshly cut piece of wood. What is the age of the old sample of wood (in millennia, 1 millennium= 1000 years)?

Answer 1

Age of the wood sample = $t=\frac{1}{\lambda }ln\frac{\text{initial activity}}{\text{final activity}}=\frac{t_{1/2}}{ln2}ln\frac{281.6}{140.8}$ $=\frac{5730}{ln2}ln2$ = $5730=5730years$