The age of wine can be determined by measuring the trace amount of radioactive t

Question

The age of wine can be determined by measuring the trace amount of radioactive tritium, 3H, present in a sample. Tritium is formed from hydrogen in water vapor in the upper atmosphere by cosmic bombardment, so all naturally ocurring water contains a small amount of this isotope. Once the water is in a bottle of wine, however, the formation of additional tritium from the water is negligible, so the tritium initially present gradually diminishes by a first-order radioactive decay with a half-life of 12.5 years. If a bottle of wine is found to have a tritium concentration that is 0.100 that of freshly bottled wine (i.e. [3H]t = 0.100 [3H]0), what is the age of the wine?

Explanation / Answer

N/No = (1/2)^(t / half life) 0.100 = (1/2)^(t/12.5) ln(0.100) = - ln(2)*t/12.5 t = - ln(0.100) * 12.5 / ln(2) t = 41.524 years

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