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 type of crystal lattice arrangement that consists of atoms positioned at specific points within a cubic unit cell.
Step 1: Lattice Points in a BCC Structure. In a BCC structure, atoms are arranged as follows: - There are 8 atoms at the corners of the cube. - There is 1 atom at the center of the cube.
Step 2: Contribution of Each Lattice Point. - The atoms located at the corners of the cube are shared by 8 adjacent unit cells, so each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell. - The center atom is entirely contained within the unit cell and contributes 1 atom to the unit cell.
Step 3: Calculate the Total Number of Lattice Points. To calculate the total number of lattice points in the unit cell: \[ \text{Total number of lattice points} = 8 \cdot \frac{1}{8} + 1 = 1 + 1 = 2. \]
Conclusion: The Body-Centered Cubic (BCC) structure contains \( \mathbf{2} \) lattice points per unit cell. Thus, the correct answer is \( \mathbf{(B)} \).