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NCERT Class XII Chemistry
Chapter - Chemical Kinetics
Questions with Solutions

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Question : 14
Total: 39
The half-life for radioactive decay of ‌14C is 5730 years. An archaeological artifact containing wood had only 80% of the ‌14C found in a living tree. Estimate the age of the sample.
Solution:  
Radioactive decay follows first order kinetics. Therefore,
Decay constant (λ)=
0.693
t1∕2
‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌=
0.693
5730
 yr−1
Given, [R]0=100‌‌‌‌‌‌‌∴[R]=80
and t=
2.303
λ
‌log‌ ‌
[R]0
[R]

‌‌‌‌‌‌‌‌=
2.303
(
0.693
5730
 )
‌log‌ ‌
100
80

‌‌‌‌‌‌‌‌=
2.303×5730
0.693
×0.0969 yr
‌‌‌‌‌‌‌‌=1845 years
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