Question

A piece of wood from an' archaeological sample has $5.0$ counts $\min ^{-1}$ per gram of $C-14$, while a fresh sample of wood has a count of $15.0 \,min ^{-1} \,g ^{-1}$. If half-life of $C-14$ is $5770\, yr$, the age of the archaeological sample is

• A. 8,500 years
• B. 9,200 years
• C. 10,000 years
• D. 11,000 years

Answer 1

Answer: (B)

9,200 years

Answer 2

Age of archaeological sample,
$t=\frac{2.303}{k} \log \left(\frac{N_{0}}{N}\right)$
(Here, $N_{0}=$ initial activity,
$N=$ remaining activity)
and
$k=\frac{0.693}{t_{1 / 2}}$
(where $t_{1 / 2}=$ half-life)
$=\frac{0.693}{5770} yr ^{-1}$
$\therefore t=\frac{2.303 \times 5770}{0.693} \log \left(\frac{15}{5}\right)$
$=19175.0 \,\log \,3 \,yr$
$=9148 \,yr \approx 9200 \,Yr$