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 $C^{14}=5760yr$ )

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

Answer 1

Answer: (C)

Here: Initial activity of wood $(N_0)=1;$ final activity of wood $(N_1)=0.70$ and half-life $t_{1/2}=5760yr$ . 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 $\frac{2.303\times 5760\times 0.155}{0.693}=2966yr$ .