Calcium fluoride, CaF₂, has a unit cell with the Ca²⁺ ions in a face-centered cubic arrangement. How many fluoride ions are present in the unit cell?

Question

Quizplus · Accepted Answer

In a face-centered cubic unit cell, each corner ion is shared by 8 adjacent unit cells and each face-centered ion is shared by 2 adjacent unit cells. Therefore, there are 8 corner ions (CaS1U1P12+) and 6 face-centered ions (FS1U1B12S1U1B0) in each unit cell. However, since each fluoride ion (FS1U1B12S1U1B0) is located at the center of an edge shared by 4 adjacent face-centered ions, each unit cell contains only 1/4 of a fluoride ion. Thus, the total number of fluoride ions in one unit cell is 6 x (1/4) = 1.5. Since we can't have a fraction of an ion, we round up to the nearest whole number, giving us a final answer of 2 fluoride ions in the unit cell. Therefore, the best choice is C.

Calcium Fluoride, CaF2, Has a Unit Cell with the Ca2+

Calcium Fluoride, CaF₂, Has a Unit Cell with the Ca²⁺