${}^{238}U$ decays to ${}^{206}Pb$ with a half-life of $4.47\times 10^9$y. this happens in a number of steps.Can you justify a single half-life for this chain  of processes ? A sample of rock is found to contain 2.00 mg of ${}^{238}U$  and 0.600 mg of ${}^{206}Pb$ assuming that all the lead has come from uranium, find that life of the rock .