Question

$AB$ has $NaCl$ structure while $XB$ has $CsCl$ structure if $r_A|r_B=5$ and $r_X|r_B=0.75$ then what is the ratio of edge length of unit cell of $AB$ and $XB$.

• A. $1.52$
• B. $1.50$
• C. $1.40$
• D. $0.85$

Answer 1

The correct option is C $1.40$

$AB\frac{r_A}{r_B}=0.5=\frac{1}{2}$

$XB\frac{r_X}{r_B}=0.75=\frac{1.5}{2}$

$r_{B=2}$ $r_{X=1.5}$ $r_{A=1}$

$XB$ form $C_{5}Cl$ structure $50B^{-}$

takes $CCP$ porition

$4r=\sqrt{2}a$

$a=\frac{4r_B}{\sqrt{2}}=\frac{4\times 2}{\sqrt{2}}=\frac{8}{\sqrt{2}}$

As form $NaCl$ structure $50B^{-}$ takes simple cable structure

$a=2r_B=2_{X2}=4$

eape length of $A-B$: edge length of $XB$

$\frac{8}{\sqrt{2}}:4=1.4$