1. Tardigrade
  2. Question
  3. Chemistry
  4. The half-life for radioactive decay of C -14 is 5730 years. An archaeological artifact containing wood had only 80 % of the C-14 found in a living tree. The age of the sample is :-

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Q. The half-life for radioactive decay of $C -14$ is $ 5730$ years. An archaeological artifact containing wood had only $80 \%$ of the $C-14$ found in a living tree. The age of the sample is :-

Chemical Kinetics

Solution:

Radioactive decay follow first order kinetics. Therefore,

$=\frac{0.693}{t_{1 / 2}}=\frac{0.693}{5730}$

Given, $R _{ o }=100 \because \Delta R =80$

and $t =\frac{2.303}{k} \log \frac{[ R ]_{0}}{[ R ]}=\frac{2.303}{\left[\frac{0.693}{5730}\right]} \log \frac{100}{80}$

$t =\frac{2.303 \times 5730}{0.693} \times 0.0969=1845$ years