1. Tardigrade
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  3. Chemistry
  4. The half-life for decay of radioactive 14C is 5730 years. An archaeological artifact containing wood has only 80 % of the 14C activity as found in living trees. The age of the artifact would be: [Given: log 1.25 = 0.0969]

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Q. The half-life for decay of radioactive ${}^{14}C$ is $5730$ years. An archaeological artifact containing wood has only $80\%$ of the ${}^{14}C$ activity as found in living trees. The age of the artifact would be:
[Given: $\log 1.25 = 0.0969$]

NTA AbhyasNTA Abhyas 2022

Solution:

Radioactive decay follows first order kinetics.
Let $[A]_0=100$
$\therefore[A]=80$
Decayconstant $(k)=\frac{0.693}{t_{1 / 2}}=\frac{0.693}{5730}$
$t=\frac{2.303}{k} \log \frac{[A o]}{[A]}$
$t=\frac{2.303}{\frac{0.693}{5730}} \log \frac{100}{80} $
$t=\frac{2.303 \times 5730}{0.693} \times \log 1.25$
$t=\frac{2.303 \times 5730}{0.693} \times 0.0969=1845\, y r s$