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JEE Main 2014 (12 Apr, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2014 (12 Apr, Shift 1)

Q95JEE Main 2014 · 12 APR · SHIFT 1Medium

Law of Radioactive Decay

A piece of bone of an animal from a ruin is found to have 14C activity of 12 disintegrations per minute per gm of its carbon content. The 14C activity of a living animal is 16 disintegrations per minute per gm. How long ago nearly did the animal die? (Given half life of 14C is t1/2 = 5760 years)

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Answer: (b)

  1. t=Tlog⁡(A0/A)log⁡2t = T \frac{\log(A_0/A)}{\log 2} with A0A=1612=43\frac{A_0}{A} = \frac{16}{12} = \frac{4}{3}.
  2. log⁡(4/3)=0.125\log(4/3) = 0.125, so t=5760×0.1250.301=5760×0.415t = 5760 \times \frac{0.125}{0.301} = 5760 \times 0.415.
  3. t≈2391t \approx 2391 years, so the answer is (b).
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