Question

A compound made of elements A and B, has a cubic unit cell. There is an A atom at each corner of the cube and an A atom at the center of each face of the cube. There are four B atoms that lie entirely within the unit cell. Based on this information, the empirical formula for the compound is:

Answer 1

A₅B₄

Step-by-step explanation:

Since we have one atom of element A at the center of each face of the unit cell, since the unit cell is a cubic cell, we have 6 faces. Since the atom on the face of the unit cell is shared with another cell, we have half of it in the unit cell is shared So, the number of atoms per face is 1/2 atom/face × 6 faces = 4 atoms on the faces of the unit cell.

Also, we have 1 atom at each corner of the cubic unit cell. Since there are 8 corner in the cubic unit cell. Also, each atom at the corner is shared with 8 unit cells, so we have 1/8 atom per corner. So, the number of atoms per unit cell is 1/8 atom/corner × 8 corners = 1 atoms at the corners of the unit cell.

So, in total we have 4 + 1 = 5 atoms of element A in the unit cell.

Also, there are 4 atoms of element B in the unit cell.

So, the ratio of atoms of element A to element B is 5 : 4.

A:B = 5:4

So, the empirical formula of the compound containing elements A and B is A₅B₄