Tritium (³H; t₁/₂ = 12.26 yr) is continually formed in the upper troposphere by interaction of solar particles with nitrogen.As a result, natural waters contain a small amount of tritium. Two samples of wine are analyzed, one known to be made in 1941 and another made earlier. The water in the 1941 wine has 2.23 times as much tritium as the water in the other. When was the other wine produced?

Knowing the half life of a given tritium in the activity. At different times, we can find the age of a sample. To do this, we use the equation. The activity at a given time is equal to the initial activity times 1/2 t over t 1/2. So a T is the activity after a given amount of time, a zero. T is the time that's gone by or sometimes we ask for in the problems Age and t 1/2 is the half life. So if in this problem we let our initial activity be acts and we know that the activity after a certain time period is to 0.23 times X.

We also know the half life is 12.6 years for the given ice. The took that we're using so we can solve for the age or the time it's gone by 2.23 X equals x times 1/2 t over 12.26 or 2.23 equals 1/2 T divided by 12.26 to solve for T. Since it's been the exponents. We have to take the natural log of both sides.

So the natural log of 2.23 is equal to the natural log of 1/2 times T over 12.26 to solve for T. We divide both sides by the natural log of 1/2 and then multiply by 12.26 and t equals negative 14.57 years. So that means that the initial sample is 14.5 years older. So if the first sample was in 1941 that means that the previous sample had to have been in 1927.

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