Question

In the crystal $A^{2+}{B}^{2-}$, having anions in the face centred cubic packing if the radius of the anion if $1.84A^0$, ideal radius of the cation present in the tetrahedral hole will be:

• A. $0.225A^0$
• B. $0.414A^0$
• C. $0.732A^0$
• D. none of these

Answer 1

Answer: (B)

$0.414A^0$

For tetrahedral holes, ideal ratio of $\frac{r_{+}}{r_{-}}$ is $0.225$

Given: $r_{-}=1.84\mathring{A}$

Then,

$\frac{r_{+}}{1.84}=0.225$

$r_{+}=0.414\mathring{A}$