
Concept explainers
(a)
Interpretation:
The unit-cell edge length of the densest diamond is to be calculated.
Concept introduction:
Crystal structure or lattice is the three-dimensional representation of atoms and molecules arranged in a particular manner. The unit cell is the smallest part of the lattice that is repeated in all directions to yield the crystal lattice. There are 3 types of cubic unit cells as follows:
1. The simple cubic unit cell
2. Body-centered unit cell
3. Face-centered unit cell
In the cubic unit cell, atom at the corner is shared by 8 adjacent cells so the contribution of an atom at the corner is
(a)

Answer to Problem 12.138P
The unit-cell edge length of the densest diamond is
Explanation of Solution
The formula to calculate the volume of one mole of carbon atom with a higher density is as follows:
Substitute the value of
Diamond has a face-centered cubic unit cell. Face-centered cubic unit cell, 8 atoms are present at the corners of the cell and 6 atoms at the face of the cell. The contribution of an atom present at the corner is
There are 4 atoms at the tetrahedral voids and therefore, the diamond has 8 carbon atoms in the lattice.
The formula to calculate the volume of the unit cell is as follows:
Substitute the value of
The formula to calculate edge length of the cube is as follows:
Substitute the value of
The unit-cell edge length of the densest diamond is
(b)
The number of C atoms present diamond unit cell with the lowest density is to be calculated.
Concept introduction:
Crystal structure or lattice is the three-dimensional representation of atoms and molecules arranged in a particular manner. The unit cell is the smallest part of the lattice that is repeated in all directions to yield the crystal lattice. There are 3 types of cubic unit cells as follows:
1. The simple cubic unit cell
2. Body-centered unit cell
3. Face-centered unit cell
In the cubic unit cell, atom at the corner is shared by 8 adjacent cells so the contribution of an atom at the corner is
(b)

Answer to Problem 12.138P
The number of C atoms present diamond unit cell with the lowest density is
Explanation of Solution
The formula to calculate the volume of one mole of carbon atom with lower density is as follows:
Substitute the value of
The formula to calculate the volume of the unit cell is as follows:
Substitute
The formula to calculate the number of C atoms with lower density is as follows:
Substitute
The number of C atoms present diamond unit cell with the lowest density is
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Chapter 12 Solutions
Loose Leaf for Chemistry: The Molecular Nature of Matter and Change
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