Question

What is the number of unit particles present in a Body-Centered Cubic (BCC) unit cell?

• A. \(1\)
• B. \(2\)
• C. \(4\)
• D. \(6\)

Hint:

Number of atoms in common cubic unit cells:
• Simple Cubic (SC): \(1\)
• Body-Centered Cubic (BCC): \(2\)
• Face-Centered Cubic (FCC): \(4\)

Answer 1

The Correct Option is B

Topic: Solid State - Crystal Lattices
Step 1: Understanding the Question:
We need to calculate the effective number of atoms (rank) within a Body-Centered Cubic (BCC) unit cell based on atom contributions.
Step 2: Detailed Explanation:
1. Corner Atoms: There are \(8\) corners in a cube. Each atom at a corner is shared by \(8\) adjacent unit cells.
Contribution = \(8 \times \frac{1}{8} = 1\) atom.
2. Body Center Atom: There is \(1\) atom located exactly in the center of the cube. This atom is not shared with any other unit cell.
Contribution = \(1 \times 1 = 1\) atom.
3. Total Calculation:
Total atoms = (Contribution from corners) + (Contribution from center)
Total atoms = \(1 + 1 = 2\).
Step 3: Final Answer:
The number of unit particles in a BCC unit cell is \(2\).