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# CBSE Class 12-science Answered

Carbon-14(C14) decays at a constant rate in such a way that it reduces to 50% in 5568 years. Find the age of an old wooden piece in which the carbon is only 25% of the original.
Asked by rajubarman | 01 Dec, 2019, 10:03: AM
Expert Answer
We know,
Decay constant
λ= 0.693 /t1/2
t1/2 = 5568 years ... (given)
Thus,
λ= 0.693 /5568 = 1.24 × 10-4 / year

We know,
By law of radioactive decay,
N/N0 = e-λt
The number of active nuclei at t = 0,  N0 = 100%
And N = 25%
Thus,
25/100 = e-λt
or
ln(0.25) = -λt
ln(0.25) = -1.24 × 10-4 × t
t = -1.3862/ (-1.24 × 10-4 ) ≈ 11180 years

Answered by Shiwani Sawant | 03 Dec, 2019, 06:22: PM

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