Solid State - Result Question 45
####45. A metallic element crystallises into a lattice containing a sequence of layers of $A B A B A B \ldots .$. Any packing of layers leaves out voids in the lattice. What percentage of this lattice is empty space?
(1996, 3M)
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Solution:
- The given arrangement : $A B A B A B \ldots . .$. represents hexagonal close-packed unit cell in which there are six atoms per unit cell. Also, volume of unit cell $=24 \sqrt{2} r^{3}$.
$\Rightarrow$ Packing fraction $=\frac{\text { Volume occupied by atoms }}{\text { Volume of unit cell }}$
$$ =6 \times \frac{4}{3} \pi r^{3} \times \frac{1}{24 \sqrt{2} r^{3}}=0.74 $$
$\Rightarrow$ Percent empty space $=100(1-0.74)=26 %$
