Question

The amount of ${}_6{C}^{14}$ isotope in a piece of wood is found to one fourth $\left(1/4\right)$ of that present in afresh piece of wood. Calculate the age of the piece of wood $(t_{1/2}of{}_6{C}^{14}=5770years)$

• A. $7999$ year
• B. $11540$ year
• C. $16320$ year
• D. $23080$ year

Answer 1

The correct option is B $11540$ year

$K=\frac{0.693}{t}log\left(\frac{N_0}{\frac{N_0}{4}}\right)$

As we know ,

$k=\frac{0.693}{t_{1/2}}$

$\Rightarrow k=\frac{0.693}{5770}$

Putting the value of k in above equation , we get

$\frac{0.693}{5770}=\frac{0.693}{t}log\left(4\right)$

$\therefore t=11540$ year

Hence , option B is correct .