Final answer:
The amount of rock required to extract 4.7 metric tons of lead depends on the lead content in the rock and the efficiency of the extraction process, neither of which were provided. Without this information, it's not possible to calculate the precise amount of rock needed.
Step-by-step explanation:
To determine the mass of rock needed to extract 4.7 metric tons of lead, we must use the known atomic mass of lead and the percentage of lead within a typical rock ore. The atomic mass of lead is approximately 207.2 g/mol, as calculated from its isotopic abundances. One metric ton is 1,000,000 grams, so 4.7 metric tons of lead is equivalent to 4,700,000 grams of lead.
However, we are not provided with the specific percentage of lead in this rock, which would be required to accurately calculate the mass of the rock needed. Typically, the percentage of lead in ore can vary widely, and the efficiency of the extraction process must also be considered. To provide a complete answer, these additional data points are required.