Question
Which one of the following statements is an incorrect?
A.
The fraction of the total volume occupied by the atoms in a primitive cell is 0.48
B.
Molecular solids are generally volatile
C.
The number of carbon atoms in an unit cell of diamond is 4
D.
The number of Bravais lattices in which a crystal can be categorised is 14
Answer :
The fraction of the total volume occupied by the atoms in a primitive cell is 0.48
Solution :
$$\eqalign{
& {\text{Volume of atoms in a unit cell}} \cr
& \left( V \right) = \frac{4}{3}\pi {r^3} \cr
& {\text{For primitive cell,}} \cr
& \,\,r = \frac{a}{2} \cr
& V = \frac{4}{3}\pi {\left( {\frac{a}{2}} \right)^3} \cr
& \,\,\,\,\,\, = \frac{{\pi {a^3}}}{6} \cr
& {\text{Volume of the unit cell}}\left( V \right) = {a^3} \cr} $$
Thus, total volume occupied by the atoms
$$\eqalign{
& = \frac{{{\text{Volume of the atoms in unit cell}}}}{{{\text{Volume of unit cell}}}} \cr
& = \frac{{\pi {a^3}}}{6} \times \frac{1}{{{a^3}}} \cr
& = \frac{\pi }{6} \cr
& = 0.52 \cr
& = 1.00 - 0.52 \cr
& = 0.48 \cr} $$