Question

What is the age of an ancient wooden piece if it is known that the specific activity of $C^{14}$ nuclide in its amounts is $3/5$ of that in freshly grown trees? Given the half of $C$ nuclide is $5570yr$.

• A. $1000yr$
• B. $2000yr$
• C. $3000yr$
• D. $4000yr$

Answer 1

Answer: (D)

$N_0=\frac{3}{5}{N}_0{e}^{-\lambda t}$
$e{\lambda }^t=\frac{5}{3}$
$\therefore log{e}^{\lambda t}=lo{g}_e\frac{5}{3}$ or $\lambda t=lo{g}_e\frac{5}{3}$
or $t=\frac{1}{\lambda }lo{g}_e\frac{5}{3}$
$=\frac{T}{0.693}\times 0.5\left(\because T=\frac{0.693}{\lambda }\right)$
$=\frac{5570\times 0.5}{0.693}yr$
$=4018.7yrs$
$=4000yr$