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Find the age of an ancient Egyptian wooden article (in years) from the given information.
i. Activity of 1 g of carbon obtained from ancient wooden article = 7.7 counts/min/g
ii. Activity of 1 g carbon obtained from fresh wooden sample = 15.4 counts per min/g
iii. Percentage increase in level of C¹⁴ due to nuclear explosions in past 100 years is 10%
iv. $t_{1 / 2} {of}_{6} C^{14} = 5770 years$

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2488

None of these

16.87 × 10³

5.770 × 10³

answer is A.

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Detailed Solution

Corrected C^l4 content:
Let initial C¹⁴ count = A₀

$\begin{array}{l} A_{0} + A_{0} / 10 = 15 .4 .; A_{0} = 14 \\ t = \frac{1}{K} \log \frac{14}{7} = 5 .770 \times 10^{3} years; t = \frac{\ln 2}{K} = t_{1 / 2} \\ t = 5770 years = 5 .770 \times 10^{3} \end{array}$

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