Tritium (³₁H), an isotope of hydrogen with a half-life of 12.3 years, is produced in the upper atmosphere and mixed with hydrogen in air. A bottle of wine found in a cave is tested and its tritium content is found to be 6.9% of that in new wine. How old is the wine?

59.20 years
47.5 years
37.5 years
53.2 years

Correct answer: 47.5 years

Solution

Radioactive decay: N/N0 = (1/2)^(t/12.3) = 0.069. Solving: t = 12.3 * ln(1/0.069)/ln(2) = 12.3 * ln(14.49)/0.693 = 12.3 * 2.674/0.693 ~ 47.5 years.

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