²³⁸₉₂U is known to undergo radioactive decay to form ²⁰⁶₈₂Pb by emitting alpha and beta particles. A rock initially contained 68 × 10⁻⁶ g of ²³⁸₉₂U. If the number of alpha particles that it would emit during its radioactive decay of ²³⁸₉₂U to ²⁰⁶₈₂Pb in three half-lives is Z × 10¹⁸, then what is the value of Z?