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Chapter 12: Q12.79 P (page 496)

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?

Short Answer

Expert verified

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 by step solution

01

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.

02

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.

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