Question

KCl crystallizes in the same type of lattice as does NaCl. Given that
$\frac{r_{N{a}^{+}}}{r_{C{l}^{-}}}=0.5$ and
$\frac{r_{N{a}^{+}}}{r_{K^{+}}}=0.7$
Find the ratio of the sides of unit cell for KCl to that for NaCl :

• A. 1.143
• B. 1
• C. 2.312
• D. 4

Answer 1

The correct option is A 1.143

For NaCl type structure, $r^{+}+r^{-}=\frac{a}{2}$, where a is the edge length of the unit cell.
So, $\frac{a_{KCl}}{a_{NaCl}}=\frac{r_K^{+}+r_{Cl-}}{r_{Na}^{+}+r_{C{l}^{-}}}=\frac{\frac{r_{K^{+}}}{r_{C{l}^{-}}}+1}{\frac{r_{N{a}^{+}}}{r_{C{l}^{-}}}+1}=\frac{\frac{0.5}{0.7}+1}{0.5+1}=1.143$