The ratio of the side of the unit cell for to that for is — Solid State Chemistry Question

💡 Solution & Explanation

For $NaCl$: a_NaCl = 2 * (r_Na+ + r_Cl-). Given r_Na+/r_Cl- = 0.5 => r_Cl- = 2 * r_Na+ => a_NaCl = 6 * r_Na+. For $KCl$: a_KCl = 2 * (r_K+ + r_Cl-). Given r_Na+/r_K+ = 0.7 => r_K+ = r_Na+/0.7. a_KCl = 2 * (r_Na+/0.7 + 2 * r_Na+) = 2 * r_Na+ * (10/7 + 2) = (48/7) * r_Na+. The ratio of cell edges is a_KCl / a_NaCl = (48/7) / 6 = 8/7 \u2248 1.143.