The age of wine is determined by Tritium dating with half life time 12.5 yrs. If radioactivity of wine sample is found to be 3% then the age of wine is

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62.5 years

75.0 years

37.5 years

12.5 years

answer is C.

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Detailed Solution

$M = \frac{3}{100} \times M_{0}; \frac{3}{100} M_{0} = M_{0} e^{- λt}; e^{λt} = \frac{10^{2}}{3};$
Take log on both sides
$\begin{array}{l} \log_{e} e^{λt} = \log_{e} \frac{10^{2}}{3}; λt = \log_{e} 10^{2} - \log_{e} 3 \\ t = \frac{1}{λ} (3.5065) \\ = \frac{T}{0 .693} (3.5065) \\ = \frac{12 .5}{0 .693} \times 3.5065; t = 62 .5 yrs \end{array}$

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