$$ ^{238}U $$ 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 .