A sample of pitch blend is found to contain 50% Uranium and 2.425% Lead. Of this lead, only 93% was — Nuclear Chemistry and Radioactivity Chemistry Question
Question
A sample of pitch blend is found to contain 50% Uranium and 2.425% Lead. Of this lead, only 93% was $\text{Pb}^{206}$ isotope but uranium was almost $\text{U}^{238}$ isotope. If the disintegration constant of $\text{U}^{238}$ is $1.52 \times 10^{-10} \text{ yr}^{-1}$, how old could be the pitch blend deposit?
💡 Solution & Explanation
Taking 100 g of the ore, mass of $\text{U}^{238} = 50 \text{ g}$ and mass of $\text{Pb}^{206} = 2.425 \times 0.93 = 2.255 \text{ g}$. Moles of U = $\frac{50}{238} = 0.210$. Moles of Pb = $\frac{2.255}{206} = 0.0109$. By the age formula, $t = \frac{1}{\lambda} \ln\left(1 + \frac{N_{Pb}}{N_U}\right) = \frac{1}{1.52 \times 10^{-10}} \ln\left(1 + \frac{0.0109}{0.210}\right) = \frac{\ln(1.052)}{1.52 \times 10^{-10}} \approx \frac{0.0506}{1.52 \times 10^{-10}} \approx 3.33 \times 10^8 \text{ years}$. Therefore, correct answer is A.