A rock sample contains traces of 238U, 235U, 232Th, 208Pb, 207Pb, and 206Pb. Careful analysis shows that the ratio of the amount of 238U to 206Pb is 1.164. (a) Assume that the rock originally contained no lead, and determine the age of the rock. (b) What should be the ratios of 235U to 207Pb and of 232Th to 208Pb so that they would yield the same age for the rock? The half-lives of the isotopes are 4.47 × 109 yr for 238U, 7.04 ×108 yr for 238U, and 1.41 × 1010 yr for 232Th. allowed formula N(t)=N(0)(0.5)^t/t(1/2)