Question

Atomic packing factor of a body centered cubic structure is closest to:

• A. 0.34
• B. 0.52
• C. 0.68
• D. 0.74

Hint:

In crystallography, the atomic packing factor (APF) helps determine how efficiently atoms are packed in a crystal structure. For BCC structures, the APF is approximately 0.68, meaning that about 68% of the unit cell is filled with atoms.

Answer 1

The Correct Option is C

The atomic packing factor (APF) is a measure of how efficiently atoms are packed in a crystal structure. It is defined as the ratio of the volume occupied by atoms to the total volume of the unit cell. The higher the APF, the more efficiently the atoms are packed. For different types of crystal structures, the APF varies. For a body-centered cubic (BCC) structure, the APF can be calculated by considering the geometry of the unit cell. In a BCC structure: 
- There are 2 atoms per unit cell: one atom at the center of the cube and eight atoms at the corners of the cube, with each corner atom contributing \( \frac{1}{8} \) of an atom to the unit cell. 
- Therefore, the total number of atoms in a BCC unit cell is \( 2 \). 
- The volume occupied by these atoms can be expressed as \( 2 \times \frac{4}{3} \pi r^3 \), where \( r \) is the atomic radius. The total volume of the unit cell is \( a^3 \), where \( a \) is the edge length of the cube. Using geometric relationships for the BCC structure, the APF is calculated to be approximately \( 0.68 \). This value means that approximately 68% of the volume of the unit cell is occupied by atoms, while the remaining 32% is empty space. 
Thus, the atomic packing factor for a body-centered cubic structure is closest to \( 0.68 \), which corresponds to option (C).