Exercise
https://texercises.com/exercise/age-of-the-solar-system-determined-by-zircon-dating/
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The following quantities appear in the problem: Zeit \(t\) / Halbwertszeit \(T\) / Anzahl \(N\) /
The following formulas must be used to solve the exercise: \(t = \frac{T}{\ln 2} \cdot \ln\left(\frac{N_2}{N_1}+1\right) \quad \)
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Exercise:
The mineral ObjectNamezircon when formed is easily contaminated with uranium but never with lead. In PersonNameClair Cameron Patterson used this mineral to determine the age of our solar system. The ratio of isotopeU to isotopePb he measured was ntO. What age did he calculate from this? The half-life of uranium- is TO.

Solution:
If no lead was present initially all lead comes from the decay of uranium; the number of lead isotopes after a certain time is therefore N_t' N_ - N_t N_t ^+fractT -N_t N_t left^+fractT-right which corresponds to the difference in the number of uranium isotopes at the ning and . For the ratio of lead to uranium we therefore have fracsscNPbsscNU eta_t fracN'_tN_t fracN_t left^+fractT-rightN_t ^+fractT-. The mineral is therefore t T lblefteta_t +right T fraclneta_t +ln T lbleftnt +right t ta old. t T lblefteta_t +right T fraclneta_t +ln t taP
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Exercise:
The mineral ObjectNamezircon when formed is easily contaminated with uranium but never with lead. In PersonNameClair Cameron Patterson used this mineral to determine the age of our solar system. The ratio of isotopeU to isotopePb he measured was ntO. What age did he calculate from this? The half-life of uranium- is TO.

Solution:
If no lead was present initially all lead comes from the decay of uranium; the number of lead isotopes after a certain time is therefore N_t' N_ - N_t N_t ^+fractT -N_t N_t left^+fractT-right which corresponds to the difference in the number of uranium isotopes at the ning and . For the ratio of lead to uranium we therefore have fracsscNPbsscNU eta_t fracN'_tN_t fracN_t left^+fractT-rightN_t ^+fractT-. The mineral is therefore t T lblefteta_t +right T fraclneta_t +ln T lbleftnt +right t ta old. t T lblefteta_t +right T fraclneta_t +ln t taP
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Attributes & Decorations
Tags
alter, erde, halbwertszeit, radioaktivität, radiokarbonmethode, sonne, sonnensystem, uran, uran-blei-methode
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Difficulty
(3, default)
Points
3 (default)
Language
ENG (English)
Type
Calculative / Quantity
Decoration