Question

Statement: Packing fraction of a lattice structure depends on the radius of the atom crystallizing in it.

State whether the given statement is true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Packing efficiency is the ratio of the total volume occupied by atoms to the total volume of the cube.

Packing efficiency $=\frac{n\times \frac{4}{3}\pi r^3}{V}$

For FCC, $n=4$, $r=\frac{a}{2\sqrt{2}}$, $V=a^3$

Packing fraction $=\frac{4\times \frac{4}{3}\pi \times {\left(\frac{a}{3\sqrt{2}}\right)}^3}{a^3}=\frac{\pi }{3\sqrt{2}}=0.74$

Hence, packing efficiency depends on the radius of an atom.

Hence, the given statement is $\text{true}$