Question

Vacant Space in a body centered cubic lattice unit cell is about

• A. 23%
• B. 32%
• C. 46%
• D. 10%

Answer 1

The Correct Option is B

"To determine the vacant space in a BCC lattice unit cell, we need to consider the arrangement of atoms or ions and the spaces left between them. 
In a BCC lattice, each lattice point is occupied by an atom or ion, and there is a vacant space in the center of the unit cell. This vacant space is often referred to as an octahedral void. 
The volume of the octahedral void is equal to the volume of one atom or ion. In a BCC lattice, the volume occupied by the atoms or ions is equal to the volume of the eight atoms or ions at the corners plus the volume of the one atom or ion at the center. 
Therefore, the vacant space in a BCC lattice unit cell is given by: Vacant space = (Volume of octahedral void) / (Total volume of the unit cell) * 100 
Since the volume of the octahedral void is equal to the volume of one atom or ion, and the total volume of the unit cell is the sum of the volumes of the atoms or ions at the corners and the center, we can calculate the vacant space. 
The vacant space in a BCC lattice unit cell is approximately 32% (option B)."

Answer 2

Vacant Space in a Body Centered Cubic (BCC) Lattice 

In a Body Centered Cubic (BCC) unit cell, atoms are arranged such that:

• There is one atom at each corner of the cube (8 corners × 1/8 = 1 atom)
• One atom is at the center of the cube (1 atom)

Total atoms per unit cell = 2

 

The packing efficiency (the percentage of volume occupied by atoms) in a BCC structure is approximately 68%.

Therefore, the vacant space = 100% − 68% = 32%

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Correct Answer: 32%