Question

A solid $AB$ has $NaCl$ type structure. The radius of $A^+$ is $100\, pm$. What is the radius of $B^-$ ?

• A. 190.47
• B. 540.13
• C. 525
• D. 78.12

Answer 1

Answer: (A)

190.47

Answer 2

$NaCl$ type structure is also called face centred cubic lattice. Here the radius ratio $(r_c /r_a )$ ranges from $0.414$ to $0.732$. Radius ratio $= \frac{r_{c}}{r_{a}} = \frac{\text{radius of cation}}{\text{radius of anion}}$ $\Rightarrow$ Radius of anion $\left(B^{-}\right)= \frac{\text{radius of } A^{+}}{\text{radius ratio}}$ $= \frac{100}{0.414}$ to $\frac{100}{0.732}$ $= 241.5$ to $136.6.$