Problem 6.223

In a uranium ore the ratio of U $^{238}$ nuclei to $\mathrm{Pb}^{206}$ nuclei is $\eta=2.8 .$ Evaluate the age of the ore, assuming all the lead $\mathrm{Pb}^{206}$ to be a final decay product of the uranium series. The half-life of $\mathrm{U}^{238}$ nuclei is $4.5 \cdot 10^{9}$ years.