Question

A bottle of vintage red wine has lost its label. The concentration of a radioactive isotope of hydrogen (hydrogen-3 or tritium) in the wine is 0.34 times that found in freshly bottled wines. If the half-life of tritium is 12.3 years, calculate the time elapsed since the wine was bottled. This is a first order decay.

Answer 1

Answer:

19 years

Explanation:

Tritium follows a first-order decay which can be represented by the following expression.

$ln(\frac{[H]_{t}}{[H]_{0}} )=-k.t$

where,

[H]t is the concentration of tritium at a certain time t

[H]₀ is the initial concentration of tritium

k is the rate constant

If we know the half-life (t1/2), we can calculate the rate constant.

$k=\frac{ln2}{t_{1/2}} =\frac{ln2}{12.3y} =0.0564y^{-1}$

$ln(\frac{[H]_{t}}{[H]_{0}} )=-k.t\\ln(\frac{0.34[H]_{0}}{[H]_{0}} )=-(0.0564y^{-1}).t\\t=19y$