The decay constant of ${}^{238}U$ is $4.9\times 10^{-18}{s}^{-1}$ (a) What is the average -life of ${}^{238}U$? (b) What is half-life of ${}^{238}U$? (c) By what factor does the activity of a ${}^{238}U$ sample decreases in $9\times 10^9$ years ?

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