Question

A sample of $U^{238}$ (half-life =$4.47\times {10}^9$ years) ore is found to contain 23.8 g of $U^{238}$ and 20.6 g of $P{b}^{206}$. Calculate the age of the ore in billion years.

Answer 1

Age of rock sample = $t=\frac{1}{\lambda }ln[1+(\frac{wt\left(P{b}^{206}\right)}{M\left(P{b}^{206}\right)}\times \frac{M\left(U^{238}\right)}{wt\left(U^{238}\right)})]=\frac{t_{1/2}}{ln2}\times ln(1+\frac{20.6}{206}\times \frac{238}{23.8})=t_{1/2}=4.47\times {10}^9$ years =4.47 billion years