Question

An ionic solid of $XY$ type of having anions in CCP lattice and cations in the octahedral voids. Let $a$ be the edge length of the FCC cube. The radius ratio of cation $\left(R_{+}\right)$ to the anion $\left(R_{-}\right)$ is greater than $0.415$. Then which of the following is false?

• A. $R_{-}=\frac{a}{2\sqrt{2}}$
• B. $R_{+}+R_{-}=\frac{a}{2}$
• C. Anions will not be in contact with each other.
• D. Cations will not be in contact with each other.

Answer 1

The correct option is A $R_{-}=\frac{a}{2\sqrt{2}}$

For a perfect fit for octahedral void, radius ratio should be equal to $0.414$ but here cation has larger size than needed for a fit in the void. So, anions can not touch each other now. Cations, being in octahedral voids, do not touch each other. But side length,$a$ is still equal to sum of daimeter of cation in centre of the cube and twice of radius of anion, i.e., $a=2(R_{+}+R_{-})$
But to have $R_{-}=\frac{a}{2\sqrt{2}},R_{-}=\frac{2(R_{+}+R_{-})}{2\sqrt{2}}$
or, $R_{+}=0.414R_{-}$ But this is not always true.
So, (a) is incorrect.