Concept explainers
(a)
Interpretation:
The number of particles in 1 unit cell for simple cubic needs to be determined.
Concept introduction:
In simple cubic unit cell, each atom in the lattice has 6 neighboring atoms arranged in octahedral arrangement. It is an inefficient way to pack atoms in the given space. In simple cubic lattice, 52% of the total space is occupied by atoms. The example is NaCl in which each cation is surrounded by 6 anions and vice versa.
Answer to Problem 70A
8
Explanation of Solution
In simple unit cell, there are 8 atoms at corners sharing 1/8th of the original volume of the cube.
The number of atoms at centers and faces is equal to zero. Therefore, the total number of atoms per unit cell will be 8 that is present on 8 corners of the lattice.
Thus, the number of particles per unit cell is 8.
(b)
Interpretation:
The number of particles in 1 unit cell for body-centered cubic needs to be determined.
Concept introduction:
In body-centered cubic unit cell, the spheres are packed together more efficiently. There are 8 nearest neighbors in the unit cell and 68% of the volume is occupied by atoms.
Answer to Problem 70A
9
Explanation of Solution
In a simple unit cell, there are 8 atoms at the corners sharing 1/8th of the original volume of the cube.
The number of atoms at centers and faces is equal to 1 and zero respectively. Therefore, the total number of atoms per unit cell will be 9 which includes 8 atoms present at 8 corners of the lattice and 1 at the center.
Thus, the number of particles per unit cell is 9 that is one more than simple cubic.
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