Question

How many lattice points are there in a Body-Centered Cubic (BCC) structure?

• A. \( 1 \)
• B. \( 2 \)
• C. \( 3 \)
• D. \( 4 \)

Hint:

In a BCC structure, the atoms at the corners each contribute \( \frac{1}{8} \) of an atom, and the atom at the center contributes \( 1 \) atom. The total number of lattice points in a BCC unit cell is \( 2 \).

Answer 1

The Correct Option is B

A Body-Centered Cubic (BCC) structure is a crystal lattice arrangement with atoms at specific points in a cubic unit cell.

Step 1: Lattice Points in a BCC Structure.
Atoms in a BCC structure are arranged thusly:
- 8 atoms are located at the corners of the cube.
- 1 atom is situated at the center of the cube.

Step 2: Contribution of Each Lattice Point.
- Corner atoms are shared by 8 adjacent unit cells, meaning each corner atom contributes \( \frac{1}{8} \) of an atom to a unit cell.
- The center atom is entirely within the unit cell, contributing 1 atom.

Step 3: Calculate the Total Number of Lattice Points.
The total number of lattice points per unit cell is calculated as:
\[\text{Total number of lattice points} = 8 \cdot \frac{1}{8} + 1 = 1 + 1 = 2.\]

Conclusion:
The Body-Centered Cubic (BCC) structure has \( \mathbf{2} \) lattice points per unit cell.

Therefore, the correct answer is \( \mathbf{(B)} \).