A meteor contains 0.556 g of Pb-206 to every 1.00 g of U-238. Assuming that the meteor did not contain any Pb-206 at the time of its formation, determine the age of the meteor. Uranium-238 decays to lead-206 with a half-life of 4.5 billion years.

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SORT You are given the current masses of Pb-206 and U-238 in a rock and asked to find its age. You are also given the half-life of U-238. STRATEGIZE Use the integrated rate law (Equation 21.3) to solve this problem. To do so, first determine the value of the rate constant (k) from the half-life expression (Equation 21.1). Before substituting into the integrated rate law, you need the ratio of the current amount of U-238 to the original amount (N/No). The current mass of uranium is simply 1.00 g. The initial mass includes the current mass (1.00 g) plus the mass that has decayed into lead-206, which you can deter- mine from the current mass of Pb-206. Use the value of the rate constant and the initial and current amounts of U-238 and the integrated rate law to find t. GIVEN: MU-238 = 1.00 g; mpb-206 = 0.556g; t1/2 = 4.5 x 10°yr FIND: t CONCEPTUAL PLAN 11/2 tu= g Pb-206 0.693 k k, N₁, No k 1 mol Pb 206 g Pb In- N₁ No mol Pb-206 =-kt t 1 mol U 1 mol Pb. mol U-238 238 g U 1 mol U g U-238