In nature a decay chain starts with and finally terminates at . A thorium ore sample was found to co — Nuclear Chemistry and Radioactivity Chemistry Question
Question
In nature a decay chain starts with $\text{Th}^{232}$ and finally terminates at $\text{Pb}^{208}$. A thorium ore sample was found to contain $6.72 \times 10^{-5} \text{ ml}$ of He (at 273K and 1 atm) and $4.64 \times 10^{-7} \text{ g}$ of $\text{Th}^{232}$. Find the age of the sample assuming that source of He to be only due to decay of $\text{Th}^{232}$. Also assume complete retention of He within the ore. ($t_{1/2} \text{ of } \text{Th}^{232} = 1.38 \times 10^{10} \text{ years}$, $\log 2 = 0.3$)
💡 Solution & Explanation
Each $\text{Th}^{232} \to \text{Pb}^{208}$ emits $6\alpha$. He moles = $\frac{6.72 \times 10^{-5} \text{ L}}{22.4} = 3 \times 10^{-9}$ mol. Th decayed = $0.5 \times 10^{-9}$ mol. Remaining Th moles $N = \frac{4.64 \times 10^{-7}}{232} = 2 \times 10^{-9}$. Initial Th $N_0 = 2.5 \times 10^{-9}$. $t = \frac{1.38 \times 10^{10}}{0.3} \log(2.5/2.0) \approx 4.6 \times 10^9 \text{ years}$. Therefore, correct answer is C.