The C¹⁴ to C¹² ratio in a certain piece of wood is 25% of that in atmosphere. The half life period of C¹⁴ is 5,580 years. The age of wood piece is (in years)

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5,580

2790

1395

11,160

answer is D.

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Detailed Solution

$N = N_{0} e^{- λt} 25 = 100 e^{- λt} e^{λt} = 4 λt = \ln 4 = 2 \ln 2 t = \frac{2 \ln 2}{λ} = 2 T_{1 / 2} = 2 \times 5580 = 11, 160 (T_{1 / 2} = \frac{0.693}{λ} = \frac{\ln 2}{λ})$

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