Answer :
Answer:
24.6 years
Explanation:
Applying,
A = (A')[tex]2^{a/n}[/tex]..................... Equation 1
Where A = Original Tritium content in the wine, A' = Tritium content in the wine after decay, a = age of the old bottle, n = half life of Tritium
From the question,
Let A = X, therefore, A' = 0.25X
Given: n = 12.3 years
Substitute these values into equation 1
X = 0.25X([tex]2^{a/n}[/tex])
1 = 0.25×([tex]2^{a/12.3}[/tex])
1/0.25 =
4 = [tex]2^{a/12.3}[/tex]
[tex]2^{a/12.3}[/tex] = 2²
Equation the base,
a/12.3 = 2
a = 12.3×2
a = 24.6 years
Final answer:
The bottle of wine is approximately 24.6 years old. This is determined by considering that tritium has halved twice to reach 25% content, going through two of its half-lives (12.3 years each).
Explanation:
The age of the bottle of wine can be determined by understanding the concept of half-life in nuclear physics. Tritium, also known as hydrogen-3, has a known half-life of 12.3 years. The half-life is the time it takes for half of a sample to decay. In this case, the tritium content has reduced to 25%, which means two half-lives have passed because the tritium content has halved twice (from 100% to 50%, then from 50% to 25%). As such, if we multiply the half-life of tritium (12.3 years) by two, we get an approximate age of the wine bottle, which is 24.6 years.
Learn more about Half-life here:
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