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.