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https://texercises.com/exercise/radioactive-dating-of-whiskey-using-tritium-decay/
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The following quantities appear in the problem: Zeit \(t\) / Halbwertszeit \(T\) / Zerfallskonstante \(\lambda\) / Anzahl \(N\) / Verhältnis / Anteil \(\eta\) /
The following formulas must be used to solve the exercise: \(\eta = \dfrac{a}{A} \quad \) \(N_t = N_0 \cdot \text{e}^{-\lambda t} \quad \) \(N_t = N_0 \cdot 2^{-\frac{t}{T}} \quad \)
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Exercise:
The age of beverages such as whiskey can be determined using the radioactive hydrogen isotope tritium isotopeH. Its content in the radioactive water cycle remains constant through new formation in the upper layers of the atmosphere and radioactive decay; however no new tritium is added to sealed liquids. FormelbuchThe content decreases with a half-life of TO. How old is a whiskey that retains only etO of its original tritium content?

Solution:
We can apply the decay law in the form al N N_ ^-fractT We need to find the time at which only N eta N_ nuclei remain. Substituting o the decay law it becomes clear that the initial amount N_ plays no role. One obtains al eta N_ N_ ^-fractT eta ^-fractT lbeta -fractT t tF -T lbet t approx taQ Note: lbx log_x denotes the binary logarithm.
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Exercise:
The age of beverages such as whiskey can be determined using the radioactive hydrogen isotope tritium isotopeH. Its content in the radioactive water cycle remains constant through new formation in the upper layers of the atmosphere and radioactive decay; however no new tritium is added to sealed liquids. FormelbuchThe content decreases with a half-life of TO. How old is a whiskey that retains only etO of its original tritium content?

Solution:
We can apply the decay law in the form al N N_ ^-fractT We need to find the time at which only N eta N_ nuclei remain. Substituting o the decay law it becomes clear that the initial amount N_ plays no role. One obtains al eta N_ N_ ^-fractT eta ^-fractT lbeta -fractT t tF -T lbet t approx taQ Note: lbx log_x denotes the binary logarithm.
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Attributes & Decorations
Tags
physik, prozentrechnen, radioaktivität, tritium, wasserstoff, zerfallsgesetz
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Difficulty
(4, default)
Points
1 (default)
Language
ENG (English)
Type
Calculative / Quantity
Decoration