Question

Wooden artifact and freshly cut tree are $7.6$ and $15.2$ ${min}^{-1}{g}^{-1}$ of carbon $(t_{1/2}=5760years)$ respectively. The age of the artifact is:

• A. $5760$ years
• B. $5760\times \frac{15.2}{7.6}$ years
• C. $5760\times \frac{7.6}{15.2}$ years
• D. $5760\times (15.2-7.6)$ years

Answer 1

Answer: (A)

$5760$ years

$k=\frac{0.693}{t_{1/2}}=0.0001203125$
now use
$A\left(7\right)=A_o{e}^{-kt}\ln \left(\frac{A_o}{A\left(7\right)}\right)=ktt=\frac{\ln \left(\frac{A_o}{A\left(7\right)}\right)}{R}\frac{\ln \left(1/2\right)}{0.0001203125}=5760years\left(optionA\right)$