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.

Question

Quizplus · Accepted Answer

We can use the formula for radioactive decay:

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

where N0 is the initial amount, N(t) is the amount after time t, T is the half-life, and the exponent corresponds to the number of half-lives.

Let N1 be the tritium content of the freshly bottled wine, and N2 be the tritium content of the aged wine. We know that N2/N1 = 0.6, or N2 = 0.6*N1.

We also know that t = n*T, where n is the number of half-lives that have passed.

Substituting and rearranging, we have:

N2/N1 = (1/2)^(n)
0.6*N1/N1 = (1/2)^(n)
0.6 = (1/2)^(n)
n = log(0.6)/log(1/2)
n = 0.737
t = n*T
t = 0.737 * 12.3
t = 9.04

Therefore, the estimated age of the wine is 9.1 years, which is closest to choice C.

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