Question

The edge length of face centered cubic unit cell is $508$ pm. If the radius of the cation is $110$ pm and it occupies the octahedral voids, then the radius of the anion is:

• A. $144\text{pm}$
• B. $398\text{pm}$
• C. $288\text{pm}$
• D. $618\text{pm}$

Answer 1

The correct option is A $144\text{pm}$

In the face centered cubic lattice, the edge length of the unit cell, $a=r+2R+r$
Since cations will ocupy the edge centers and and the anions will occupy corners and the face centers.
Where
$r=\text{Radius of cation}=110\text{pm}$
$R=\text{Radius of anion}$
$\Rightarrow 508=2\times 110+2R$
$\Rightarrow R=\frac{(508-220)}{2}=144\text{pm}$