Answer to Question #282442 in Atomic and Nuclear Physics for BIGIRMANA Elie

Question

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.

Answer 1

$\lambda_1N_1=\eta \lambda_2N_2,$

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

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