Question

The edge length of a face centered cubic cell of an ionic substance is $508pm$. If the radius of the cation is $110pm$, the radius of the anion is:
Assume cations at octahedral voids and anoins at FCC sites.

• A. $144pm$
• B. $288pm$
• C. $398pm$
• D. $618pm$

Answer 1

The correct option is A $144pm$

In fcc latice, the distance between cation and anion:
$r_c+r_a=\frac{a}{2}$
Given: $a=508pm$
$r_c=110pm$
$\therefore$
$110+r_a=\frac{508}{2}$
$\Rightarrow r_a=144pm$