
Concept explainers
Interpretation:
The atomic radius and density of lead cubic close packing structure has to be determined.
Concept introduction:
In packing of atoms in a crystal structure, the atoms are imagined as spheres and closely packed in a regular pattern. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing. Cubic close packing structure has face-centered cubic (FCC) unit cell.
In face-centered cubic unit cell, each of the six corners is occupied by every single atom. Each face of the cube is occupied by one atom.
Each atom in the corner is shared by eight unit cells and each atom in the face is shared by two unit cells. Thus the number of atoms per unit cell in FCC unit cell is,

Answer to Problem 53E
Answer
The atomic radius of lead atom is 174 pm
Density of lead is 11.57 g/cm3
Explanation of Solution
Explanation
Calculate the atomic radius of lead.
The edge length value for the FCC unit cell is given. The edge length value is related to the radius of the atom by the equation,
Calculate the volume of the unit cell.
The edge length value for the FCC unit cell is given. Cubic value of the edge length of the unit cell gives volume of the unit cell.
Calculate the mass of the unit cell.
Each unit cell contains 4 Pb atoms. Therefore four times the average mass of one Pb atom gives mass of a unit cell.
Calculate the density of lead.
The density of lead is calculated by
Conclusion
The radius of the lead atom and its density is determined using the concept of edge length of the FCC unit cell.
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