Question #282442

7. The atomic ratio between Uranium isotope 238U and 234U in a mineral sample is found to be 1.8 × 104 . The half-life of 234U is 2.5 × 105 yrs. Find the hal-life of 238U.


1
Expert's answer
2021-12-28T08:44:25-0500

λ1N1=ηλ2N2,\lambda_1N_1=\eta \lambda_2N_2,

N1ln2T1=ηN2ln2T2,\frac{N_1\ln2}{T_1}=\frac{\eta N_2\ln2}{T_2},

T2=T1ηN2N2=2.51051.8104238234=4.6109 T_2=T_1\frac{\eta N_2}{N_2}=2.5\cdot 10^5\cdot 1.8\cdot 10^4\cdot\frac{238}{234}=4.6\cdot 10^9~ years.


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