[vanderwaals]

Problem: The cubic unit cell of a perovskite structure containing atoms of types A, B, and C is illustrated below. What is the empirical formula of this substance?

(A) ABC  (B) ABC₃  (C)AB₄C₆  (D)AB₈C₁₂

The correct answer is (B). I initially did this problem by counting how many of each type of atom there was in the cubic unit cell, so I got (D), which was obviously wrong. I do not understand how the answer could possibly be (B), because it seems like there are far more B atoms than A atoms, while the answer choice says that they are equal. I think I do not fundamentally understand what the unit cell says about the empirical formula...could someone explain why the answer is (B)?

[Vidya]

You should calculate the number of atoms per unit cell...you can not predict it just by looking at it...
I walk you through how to do it ...
How many A's in one unit cell...it is body centered
How many C's ---it is edge centered
How many B's --it is on the corners of the unit cell ...
now check how are they shared by different immediate neighboring unit cells which are touching this cell...
You will get the answer ...work on it ..

[AWK]

And remember about cubic symmetry. I mean triple axis. This may verify your counting.

[vanderwaals]

I completely understand the problem now...I'm not sure why I didn't think about this before. Thanks!