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 0.168 that of freshly bottled wine (i.e. [3H]t = 0.168 [3H]0), what is the age of the wine?

Answer 1

.168=e^-.693t/12.5
take ln of each side
ln(.168)=-.694t/12.5
solve for time t, in years.