Question

A solid made up of ions of A and B possess edge length of unit cell of 0.564 nm has four formula units. Among the two ions the smaller ones occupy the interstitial void and the larger ions occupy the space lattice with ccp type of arrangement. The solid has more tendency to show Frenkel defect than schottky defect. (assume anion in contact)

The packing fraction of the solid is :

• A. 79.25%
• B. 74%
• C. 80.1%
• D. 74.9%

Answer 1

The correct option is D 74.9%

APF$=\frac{4\times \frac{4}{3}\pi \left(\right(r^{-}{)}^3+\left(r^{+}{)}^3\right)}{a^3}=\frac{4\times \frac{4}{3}\pi \left(\right(r^{-}{)}^3+\left(0.225r^{-}{)}^3\right)}{a^3}=\frac{4\times \frac{4}{3}\pi \left(\right(r^{-}{)}^3+\left(0.225r^{-}{)}^3\right)}{(2\sqrt{2}{r}^{-}{)}^3}=0.749$