Question

The arrangement of $X^{-}$ ions around $A^{+}$ ions in solid $AX$ is given in the figure (not drawn to scale ). If the radius of $X^{-}$ is $250\text{pm}$, then the maxium possible radius of $A^{+}$ is:

• A. $104\text{pm}$
• B. $125\text{pm}$
• C. $183\text{pm}$
• D. $57\text{pm}$

Answer 1

The correct option is C $183\text{pm}$

In the given diagram, $A^{+}$ is present in the octahedral void of $X^{-}$.
So the radius ratio i.e $\frac{r_{A^{+}}}{r_{X^{-}}}$
Where, $r=\frac{r_{A^{+}}}{r_{X^{-}}}$ lies in the range $0.414-0.732$
Given , $r_{X^{-}}=250\text{pm}$
So, $r_{A^{+}}=0.732\times 250=183\text{pm}$
So the maximum possible radius od $A^{+}$ is $183\text{pm}$.