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. ${ }_{1}^{3} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+{ }_{-1}^{0} \mathrm{\beta}$

Question

Quizplus · Accepted Answer

We can use the formula for radioactive decay:

N = N0(e^(-λt))

Where N is the amount of tritium in the wine currently, N0 is the amount of tritium in the freshly bottled wine, λ is the decay constant (ln2/half-life), and t is the time elapsed.

First, we need to find λ:

λ = ln2 / t1/2 = ln2 / 12.3 yr = 0.0565 yr^-1

Next, we can use the fact that the current tritium content is 60% of the freshly bottled wine:

N/N0 = 0.6

Substituting in the values we have:

0.6 = e^(-0.0565t)

Taking the natural logarithm of both sides:

ln(0.6) = -0.0565t

Solving for t:

t = ln(0.6) / (-0.0565) = 9.1 yr

Therefore, the estimated age of the bottled wine is 9.1 years.

Estimate the Age of a Bottled Wine That Has a Tritium