SATHEE: Atoms And Nuclei Question 396

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 $^{14} C$ $A_{0} = 16 d i s {min}^{- 1} g^{- 1}$ $A = 12 d i s {min}^{- 1} g^{- 1}$ $t_{1 / 2} = 5760 y e a r s$ Now, $λ = \frac{0.693}{t_{1 / 2}} = \frac{0.693}{5760}$ per year Then, from, $t = \frac{2.303}{λ} \log_{10} \frac{A_{0}}{A}$ $= \frac{2.303 \times 5760}{0.693} \log_{10} \frac{16}{12} \approx 2391$ years

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Atoms And Nuclei Question 396

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