Measurements show that a sample of rock contains 14.90 g of ²³⁸₉₂U and 26.50 g of ²⁰⁶₈₂Pb.

[See Practice Problem 16.17 for molar masses.]

(a) To date this rock, what assumption must be made about where the ²³⁸₉₂ Pb came from?

(b) How many atoms of each isotope are present in the rock?

(c) How many atoms of ²³⁸₉₂U were present in the rock when it was new?

(d) What percentage of the original amount of  ²³⁸₉₂U remains in the rock today?

(e) How old is the rock in years? [The half-life of ²³⁸₉₂U is 4.46 × 10⁹ years.]

Data from Problem16.17

A rock from an asteroid contains 2.57 g of ²³⁸₉₂U and 3.83 g of ²⁰⁶₈₂Pb. The molar mass of ²⁰⁶₈₂Pb is 205.974 46 g/mol, the molar mass of ²³⁸₉₂U is 238.029 g/mol, and the halflife of ²³⁸₉₂U is 4.46 × 10⁹ years. Assume that all the ²⁰⁶₈₂Pb came from the radioactive decay of the ²³⁸₉₂U.