A solid with a formula AB has the rock-salt type of structure. If all the atoms touching one body-diagonal plane are removed, then what would the formula of the compound be?

Explanation

If the unit cell of AB contains A atoms at its corners and face centres, the B atoms will be situated at its edge centres and body centres. A body-diagonal plane of the unit cell is associated with four A atoms at four corners, two A atoms at the centres of the opposite faces, two B atoms at the edge centres of the diagonally opposite edges and one B atom at the body centre.
Removing four A atoms from the four corners and two A atoms from face centres leaves a total of `4xx1/8+4xx1/2=5/2` A atoms in the unit cell. On the other hand, removal of two B atoms from two edge centres and body centre leaves a total of two `10xx1/4=5/2` B atoms in the unit cell. Thus the ratio of A to B atoms per unit cell will become
`A:B=5/2:5/2=1:1`
So, the formula of the compound remains as AB.
If the locations of A and B atoms are considered to be the other way around, that is, B atoms are at the corners and face centres, and A atoms at the edge centres and body centre, then the formula of the compound will also remain as AB.