Question

It was found that in $30$ unit cells of $ZnS$, four atoms are of trivalent metal. How many vacant tetrahedral voids are present in $30$ unit cells of $ZnS$?

• A. $220$
• B. $126$
• C. $122$
• D. $240$

Answer 1

The correct option is C $122$

$ZnS$ forms fcc unit cell.
Total number of tetrahedral voids in $30$ unit cells $=30\times 8=240$

In ZnS, $50\%$ of terahedral voids are filled with $Z{n}^{2+}$ and $50\%$ are vacant i.e. $120$.

Four $M^{3+}$ ions can displace six $Z{n}^{2+}$ to keep the crystal electrically neutral and two tetrahedral voids will remain empty. The resulting composition of $30$ unit cells will be $114Z{n}^{2+},4M^{3+},120S^{2-}$.

Total number of vacant tetrahedral voids $=120+2=122$