Solved Homework StatementMetal Fluoride Crystallizes in a Cubic Structure

[susan__t]

Homework Statement

A metal fluoride crystallizes in a cubic structure such that the fluoride ions occupy lattice positions at the corners and on the faces while 4 metal atoms occupy positions within the body of the unit cells. The formula of the metal fluoride is?



I don't know where to start or what equations are relevant. all i know is that I'm pretty sure this is a face centered cubic structure

 

[Borek]

How many atoms of each element per unit cell? Note that atoms lying on the border have only their part in unit cell, so you have to sum fractions.

 

[Blueshift5]

I can provide some insights to help you solve this homework problem.

Firstly, you are correct in identifying the crystal structure as a face-centered cubic (FCC) structure. This means that each unit cell of the metal fluoride crystal has fluoride ions at the corners and on the faces, and 4 metal atoms in the center of each unit cell.

To determine the formula of the metal fluoride, we need to know the number of fluoride ions and metal atoms in each unit cell. In an FCC structure, there are 8 corner atoms and 6 face atoms, but each atom is shared by multiple unit cells. Therefore, we need to divide the number of atoms by the number of unit cells it is shared by.

For the fluoride ions, there are 8 corners and each one is shared by 8 unit cells, so there are a total of 1 fluoride ion per unit cell (8/8 = 1).

For the metal atoms, there are 4 atoms in the center of each unit cell, but each one is shared by 2 unit cells (one on the top half and one on the bottom half of the unit cell). So there are a total of 2 metal atoms per unit cell (4/2 = 2).

Therefore, the formula of the metal fluoride is MF2 (1 fluoride ion and 2 metal atoms per unit cell).

I hope this helps you solve the problem. Remember to always consider the crystal structure and the number of atoms shared by each unit cell when determining the formula of a compound.