Atoms And Nuclei Question 396
Question: A piece of bone of an animal from a ruin is found to have $ ^{14}C $ activity of 12 disintegrations per minute per gm of its carbon content. The $ ^{14}C $ activity of a living animal is 16 disintegrations per minute per gm. How long ago nearly did the animal die? (Given half-life of $ ^{14}C $ is $ {t_{1/2}}=5760 $ years)
Options:
A) 1672 years
B) 2391 years
C) 3291 years
D) 4453 years
Show Answer
Answer:
Correct Answer: B
Solution:
- Given, for $ ^{14}C $ $ A_{0}=16dis{{\min }^{-1}}{{g}^{-1}} $ $ A=12dis{{\min }^{-1}}{{g}^{-1}} $ $ {t_{1/2}}=5760years $ Now, $ \lambda =\frac{0.693}{{t_{1/2}}}=\frac{0.693}{5760} $ per year Then, from, $ t=\frac{2.303}{\lambda }{\log_{10}}\frac{A_{0}}{A} $ $ =\frac{2.303\times 5760}{0.693}{\log_{10}}\frac{16}{12}\approx 2391 $ years
