Question

A piece of wood was found to have $ {{C}^{14}}/{{C}^{12}} $ ratio $ 0.7 $ times that in a living plant. The time period when the plant died is (half-life of $ {{C}^{14}}=5760\,\,yr $ )

• A. $ 2980\,\,yr $
• B. $ 3070\,\,yr $
• C. $ 2966\,\,yr $
• D. $ 2770\,\,yr $

Answer 1

Answer: (C)

Here: Initial activity of wood $ ({{N}_{0}})=1; $ final activity of wood $ ({{N}_{1}})=0.70 $ and half-life $ {{t}_{1/2}}=5760\,\,yr $ . We know that disintegration constant $ (\lambda )=\frac{0.693}{{{t}_{1/2}}}=\frac{0.693}{5760} $ We also know that $ (t)=\frac{2.303}{k}\log \frac{{{N}_{o}}}{{{N}_{t}}}t=\frac{2.303}{k}.\log \frac{1}{7} $ or $ \frac{2.303\times 5760\times 0.155}{0.693}=2966\,\,yr $ .