Question

A sample of ancient wooden boat is found to undergo $9$ $dpm$ $g^{-1}$ of ${}^{14}C$. What is the approximate age of the boat? The rate of disintegration of wood recently cut down is $15$ $dpm$ $g^{-1}$ of ${}^{14}C$.

• A. $4246.5$ yrs
• B. $5384$ yrs
• C. $4628$ yrs
• D. $2684$ yrs

Answer 1

Answer: (A)

$4246.5$ yrs

$t_{1/2}=5760$

$t=\frac{2.303\times t_{1/2}}{0.693}log\frac{a}{a-a_0}$

$t=\frac{2.303\times 5760}{0.693}\times log\left(\frac{15}{9}\right)$

$t=4246.5$ years