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Q.

The radioactivity of a given sample of whisky due to tritium $(T_{1 / 2} = 12.5 y e a r s)$ was found to be only about 4% of that measured in a recently purchased bottle marked 7 years old. The sample must have been prepared about given log5=0.698

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a

58 years ago

b

100 years ago

c

420 years ago

d

300 years ago

answer is C.

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Detailed Solution

$D e c a y L a w, A = A_{o} 2^{- \frac{t}{T_{1 / 2}}} \Rightarrow \frac{A_{o}}{A} = 2^{\frac{t}{T_{1 / 2}}} T a k i n g \log \Rightarrow \frac{t \ln 2}{T_{1 / 2}} = \ln (\frac{A o}{A}) \Rightarrow \frac{\ln 2}{12.5} = \frac{1}{t} \ln (\frac{100}{4}) \Rightarrow t = \frac{12.5 \times \ln 25}{\ln 2} = 58 y e a r s$

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