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Which of the following statements is not correct ?
A
The number of carbon atoms in an unit cell of diamond is 4
B
The number of Bravais lattices in which a crystal can be categorized is 14
C
The fraction of the total volume occupied by the atoms in a primitive cell is 0.48
D
Molecular solids are generally volatile
Detailed Solution
Packing fraction for a cubic unit cell: $f = \dfrac{z \times \frac{4}{3}\pi r^3}{a^3}$, where $a$ = edge length, $r$ = radius of the atom and $z$ = number of atoms per unit cell.
For a primitive (simple cubic) cell, $z = 1$ and the atoms touch along the edge, so $a = 2r$.
$f = \dfrac{1 \times \frac{4}{3}\pi r^3}{(2r)^3} = \dfrac{\pi}{6} = 0.52$
i.e. 52 percent of the unit cell is occupied by atoms and 48 percent is empty.
So the statement that the fraction of the total volume occupied by the atoms in a primitive cell is 0.48 is not correct; 0.48 is the fraction of empty space.
The number of Bravais lattices is 14, and molecular solids are generally volatile because they are held by weak intermolecular forces; these statements are correct.
Note: a diamond unit cell actually contains 8 carbon atoms (4 from the fcc positions and 4 in alternate tetrahedral voids), so the first statement is also questionable; the answer intended by the paper is the packing fraction statement.
For a primitive (simple cubic) cell, $z = 1$ and the atoms touch along the edge, so $a = 2r$.
$f = \dfrac{1 \times \frac{4}{3}\pi r^3}{(2r)^3} = \dfrac{\pi}{6} = 0.52$
i.e. 52 percent of the unit cell is occupied by atoms and 48 percent is empty.
So the statement that the fraction of the total volume occupied by the atoms in a primitive cell is 0.48 is not correct; 0.48 is the fraction of empty space.
The number of Bravais lattices is 14, and molecular solids are generally volatile because they are held by weak intermolecular forces; these statements are correct.
Note: a diamond unit cell actually contains 8 carbon atoms (4 from the fcc positions and 4 in alternate tetrahedral voids), so the first statement is also questionable; the answer intended by the paper is the packing fraction statement.