Which of the following has least value of 'packing efficiency' ?

Question

Accepted Answer

Packing efficiency is a measure of how tightly the constituent particles (atoms, ions, or molecules) are packed in a crystal lattice. It is defined as the fraction of volume in a crystal structure that is occupied by the constituent particles.

1. **Simple Cube (Option 4):**  
   - In a simple cubic structure, each corner atom is shared by eight adjacent unit cells. The packing efficiency of a simple cubic structure is approximately 52%. This is because the atoms in a simple cubic lattice touch along the edges of the cube, leaving a significant amount of empty space within the structure. This results in the least efficient packing among the common crystal structures.

2. **Body-Centred Cube (Option 1):**  
   - In a body-centred cubic (BCC) structure, there is an additional atom at the center of the cube, which increases the packing efficiency compared to a simple cubic structure. The packing efficiency of a BCC structure is approximately 68%. This is higher than that of a simple cubic structure because the central atom helps fill some of the empty space.

3. **Face-Centred Cube (Option 2):**  
   - A face-centred cubic (FCC) structure has atoms at each corner and at the center of each face of the cube. The packing efficiency of an FCC structure is about 74%, which is significantly higher than that of a simple cubic structure. This is because the face-centered arrangement allows for a more compact packing of atoms.

4. **Closed Packed Hexagonal (Option 3):**  
   - The hexagonal close-packed (HCP) structure is another highly efficient packing arrangement, with a packing efficiency of approximately 74%, similar to that of the FCC structure. The HCP structure is characterized by layers of atoms arranged in a hexagonal pattern, which maximizes the use of space.

In conclusion, the simple cubic structure (Option 4) has the least packing efficiency at approximately 52%, making it the correct answer. The other structures—BCC, FCC, and HCP—have higher packing efficiencies due to their more compact arrangements of atoms.