Q12.79 P - Chemistry: Molecular Nature Of Matter And Change

Question

What specific difference in the positioning of spheres gives a crystal structure based on the face-centered cubic unit cell less empty space than one based on the body-centered cubic unit cell?

Step-by-Step Solution

Answer

As the number of atoms contributing in the face-centered cubic unit cell (FCC) is 4 and that in the body-centered cubic unit cell (BCC) is 2, FCC has less empty space than BCC.

Step 1: Different types of the cubic unit cell

In the face-centered cubic unit cell (FCC), atoms are present in the corners of the cell along with the center of the faces of the cell. In the body-centered cubic unit cell (BCC), atoms are present in the corner plus one atom is present in the center of the body of the cell.

Step 2: Number of atoms in FCC and BCC

As per the above explanation, thus the total number of atoms in FCC is 4 and in BCC is 2. Thus, considering this information, the FCC has less empty space than one based on BCC.