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

Concept: A Body-Centered Cubic (BCC) unit cell has atoms located at:
• The eight corners of the cube
• One atom at the center of the cube However, atoms located at corners are shared among neighboring unit cells.

Step 1: Contribution of corner atoms. Each corner atom is shared by \(8\) unit cells. Contribution of one corner atom: \[ \frac{1}{8} \] Total contribution from \(8\) corners: \[ 8 \times \frac{1}{8} = 1 \]

Step 2: Contribution of body-centered atom. The atom at the center belongs completely to the unit cell. Contribution: \[ 1 \]

Step 3: Total number of atoms. \[ 1 + 1 = 2 \] Therefore, the number of unit particles in a BCC unit cell is \[ \boxed{2} \]