Question

A wooden plant accumulates $10 𝑚𝑔 𝑘𝑔^{−1}$ of $^{14}C$ during its life span. A fossil of this plant was discovered and contains $2.5 𝑚𝑔 𝑘𝑔^{−1}$ of $^{14}C$. The age of this fossil at the time of discovery is years (rounded off to the nearest integer).
(Use 5730 years as half-life of $^{14}C$)

Answer 1

Correct Answer: 11460

Using the half-life formula:

\( t = \frac{\ln(N_0/N)}{\ln(2)} \times T_{1/2} \)

where \(N_0 = 10\), \(N = 2.5\), and \(T_{1/2} = 5730\) years. 

Substituting the values:

\( t = \frac{\ln(10/2.5)}{\ln(2)} \times 5730 = 11460 \text{ years}. \)