Question

What is the age of an ancient wooden piece if it is known that the specific activity of $C^{14}$ nuclide in it amounts to 3/5 of that in fresh trees? Given: the half life of C nuclide is 5570 years and $lo{g}_e\left(5/3\right)=0.5$

• A. 1000 years
• B. 2000 years
• C. 3000 years
• D. 4000 years

Answer 1

The correct option is D 4000 years

We know that: $|\frac{dN}{dt}|=|\frac{d{N}_0}{dt}|e^{-\lambda t}$

According to question: $\frac{|\frac{dN}{dt}|}{|\frac{d{N}_0}{dt}|}=3/5$

So, $e^{-\left(0.693/t_{1/2}\right)t}=3/5$

Taking $lo{g}_e$:

$-\left(0.693/5570\right)t=lo{g}_{e}3/5=-lo{g}_{e}5/3$

$\left(0.693/5570\right)t=lo{g}_{e}5/3=0.5$

$t=4000$ years