If an ionic compound were composed of a4+ and b−, which unit cell structure would give a neutral compound?

To achieve a neutral ionic compound, the charges on the cations and anions in the unit cell must balance out. In this case, you have a4+ cations and b− anions. The unit cell structure that would give a neutral compound involves arranging these ions in a way that ensures electrical neutrality.

The formula for the ionic compound indicates that you need four b− ions for every a4+ ion to achieve electrical neutrality. The most common unit cell structure for achieving this balance is a face-centered cubic (FCC) unit cell.

In an FCC unit cell, each lattice point is shared among eight neighboring unit cells. The arrangement allows for efficient packing of ions while maintaining electrical neutrality. In this scenario, the a4+ ions can be placed at the corners of the cube, and the b− ions can be placed at the face centers. This arrangement ensures that each a4+ ion is surrounded by four b− ions, resulting in a 1:1 ratio and achieving electrical neutrality.

So, the unit cell structure that would give a neutral compound with a4+ and b− ions is a face-centered cubic (FCC) unit cell.