Final answer:
To find the volume of a unit cell of Pb given the atomic radius, the type of crystal structure must be known. Assuming a face-centered cubic structure, the edge length is 0.495 nm and the volume is approximately 0.12 nm³, which does not match any of the provided choices.
Step-by-step explanation:
The question tasks us with finding the volume of a unit cell for lead (Pb), given the atomic radius of Pb is 0.175 nm. To find the volume of a unit cell, we first need to determine the type of unit cell (simple cubic, body-centered cubic, or face-centered cubic). Unfortunately, the type of cell is not provided in the question, making it impossible to proceed with a calculation as different cell types have different relationships between the atomic radius and the cell edge length. However, typically, for many metals, the cubic close-packed or face-centered cubic structure is common. If we assume a face-centered cubic structure for Pb (which is actually not the case for lead but serves as an example), then each edge would be equal to 4r/√2 (where r is the atomic radius).
Calculating the edge length for a face-centered cubic unit cell: edge length = 4r/√2 = 4(0.175 nm)/√2 ≈ 0.495 nm. Now, to find the volume of the unit cell, we cube the edge length: Volume = (edge length)³ = (0.495 nm)³ ≈ 0.12 nm³. This result is not an option given in the multiple-choice answers provided, indicating either the question may lack necessary details or there might have been an error in the provided radius or possible choices.