Estimate the age of a bottled wine that has a tritium,³H, content 60% that of freshly bottled wine.Tritium decays by beta decay and has a half-life of 12.3 yr. H He +

Question

Quizplus · Accepted Answer

We can use the radioactive decay equation to solve the problem:

N = N0 (1/2)^(t/T)

where N is the remaining amount of tritium, N0 is the original amount of tritium (when the wine was bottled), t is the time since the wine was bottled, and T is the half-life of tritium.

Let's assume that the original amount of tritium in freshly bottled wine is 100 (arbitrary units). Then, the amount of tritium in the given wine is 60% of this value, or 60.

Using the equation with these values, we can solve for t:

60 = 100 (1/2)^(t/12.3)
0.6 = (1/2)^(t/12.3)
log(0.6) = (t/12.3) log(1/2)
t = -12.3 (log 0.6) / log 2
t ≈ 9.1 yr

Therefore, the estimated age of the wine is approximately 9.1 years. The correct answer is (C).

Estimate the Age of a Bottled Wine That Has a Tritium,