The number of Pb atoms per unit cell
According to the information at webelements http://www.webelements.com/lead/crystal_structure.html
Pb has a cubic close packed crystal structure. The simplest type is the face centered cubic crystal and the fcc has 4 atoms per unit cell.
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Well, the number of lead (Pb) atoms per unit cell would depend on the crystal structure of the material in question. But hey, why worry about boring old lead atoms when you can imagine a unit cell made entirely out of tiny clown noses? Now that would be a unit cell worth talking about!
The number of Pb (lead) atoms per unit cell depends on the crystal structure of lead. Lead crystallizes in a face-centered cubic (FCC) crystal structure.
In an FCC unit cell, there are four atoms located at each corner of the cube and an additional atom at the center of each face. This makes a total of 8 corner atoms and 6 face atoms in the unit cell.
However, each atom in the corner is shared by 8 adjacent unit cells, meaning that only 1/8th of each atom belongs to the unit cell. As for the face atoms, they are shared with two adjacent unit cells, so only 1/2 of each atom belongs to the unit cell.
To calculate the total number of Pb atoms in the unit cell, we consider the contribution from each type of atom.
Number of corner atoms in the unit cell = 8 atoms × 1/8 = 1 atom
Number of face atoms in the unit cell = 6 atoms × 1/2 = 3 atoms
Total number of Pb atoms per unit cell = number of corner atoms + number of face atoms
Therefore, the number of Pb atoms per unit cell in a face-centered cubic structure is 1 + 3 = 4 atoms.
To find the number of Pb (lead) atoms per unit cell, we need to know the crystal structure of lead. The crystal structure describes the arrangement of atoms within a crystal lattice.
Lead has a face-centered cubic (FCC) crystal structure. In an FCC unit cell, there are atoms located at the corners and the centers of each face of the cube.
To calculate the number of atoms per unit cell, we sum up the contributions from the corners and the faces:
1. Atoms at corners: Each corner atom is shared by eight adjacent unit cells. Consequently, only 1/8th of each atom belongs to the unit cell. Since there are eight corners in a unit cell, each contributing 1/8th of an atom, the total contribution from corner atoms is 8 * (1/8) = 1 atom.
2. Atoms at face centers: Each face center atom is shared by two adjacent unit cells. Therefore, only 1/2 of each atom belongs to the unit cell. Considering there are six face center atoms in a unit cell, each contributing 1/2 of an atom, the total contribution from face center atoms is 6 * (1/2) = 3 atoms.
Hence, the total number of lead atoms per unit cell in the face-centered cubic lattice is 1 + 3 = 4 atoms.