The half-life for radioactive decay of ¹4}C ...

NCERT Class XII Chemistry
Chapter - Chemical Kinetics
Questions with Solutions

Question : 14 of 39

Marks: +1, -0

The half-life for radioactive decay of

^{14}

C is 5730 years. An archaeological artifact containing wood had only 80% of the

^{14}

C found in a living tree. Estimate the age of the sample.

Solution:

Radioactive decay follows first order kinetics. Therefore,

Decay constant

(\lambda) = \frac{0.693}{t_{1/2}}

= \frac{0.693}{5730} \mathrm{yr}^{-1}

Given,

[R]_0 = 100 \therefore [R] = 80

and

t = \frac{2.303}{\lambda} \log \frac{[R]_0}{[R]}

= \frac{2.303}{\left(\frac{0.693}{5730}\right)} \log \frac{100}{80}

= \frac{2.303 \times 5730}{0.693} \times 0.0969 \mathrm{yr}

=1845

years

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