[Single-digit Integer] KF crystallizes in the type structure. If the radius of K+ ion is 186/sqrt(2) — Solid State Chemistry Question

💡 Solution & Explanation

In the $NaCl$ structure, the shortest distance between two similar ions (like K+ to K+) is along the face diagonal, which is equal to a / sqrt(2). We know that along the edge of the unit cell: a = 2 * (r_K+ + r_F-) = 2 * (186/sqrt(2) + 214/sqrt(2)) = 2 * (400 / sqrt(2)) = 800 / sqrt(2) pm. The shortest distance between K+ and K+ is: d = a / sqrt(2) = (800 / sqrt(2)) / sqrt(2) = 400 pm = 4 A.