Question

Which is the minimum values of $r_{+}/r_{-}$ needed to prevent anion-anion contact in $NaCl$ crystals?

• A. $0.225$
• B. $0.414$
• C. $0.342$
• D. $0.514$

Answer 1

The correct option is B $0.414$

Coordination number of each $N{a}^{+}$ and $C{l}^{-}$ is 6 in $NaCl$ structure where $N{a}^{+}$ ion occupies the void surrounded by 6$C{l}^{-}$ ions arranged on the corners of an octahedron. The minimum (limiting ) values of $r^{+}/r^{-}$ required to prevent anion-anion contact in $NaCl$ may be caliculated as follows
In $△ABC$
$\text{sin}ABC=\frac{AC}{AB}$
$\text{sin}{45}^0=\frac{2r^{-}}{2(r^{+}+r^{-})}=\frac{1}{\sqrt{2}}$
$\frac{(r^{+}+r^{-})}{r^{-}}=\sqrt{2}$
$\therefore \frac{r_{+}}{r_{-}}=0.414$

The minimum value is :
$\frac{r_{+}}{r_{-}}=0.414$