[kimxx972]

Hi~

Can anybody tell me how to solve the following problem?

A substance containing A, B and C ions crystallizes in a unit cell. A ions are at each of the corners, B ions are at the center of each face and C ions are at the centers of each edge. What is the empirical formula of the substance?

(A) ABC
(B) AB3C3
(C) A3B3C3
(D) A4B3C6
(E) A8B6C12

I do not understand why the answer is (B), not (D).

Thanks for your help in advance.

[Squirmy]

Answer D sounds like you just took the # of corners, faces and edges and divided each by 2, which is only works for the faces. The reason you divide by 2 for the faces is that half of each atom on a face is in the unit cell, half is part of another cell that abuts the original one.

So, the question becomes how many unit cells are the atoms on the corners and edges in? Divide accordingly.

[kimxx972]

Thanks for your explanation.

I got you.