Question

The ratio of effective number of atoms in a unit cell of fcc and bcc lattices is

• A. 1:2
• B. 4:1
• C. 1:4
• D. 2:1

Hint:

For FCC: Effective atoms = 4
For BCC: Effective atoms = 2
Use contributions of atoms at different lattice positions

Answer 1

The Correct Option is D

In an FCC (Face Centered Cubic) lattice: - 8 corner atoms contribute \( \frac{1}{8} \) each: \( 8 \times \frac{1}{8} = 1 \) - 6 face atoms contribute \( \frac{1}{2} \) each: \( 6 \times \frac{1}{2} = 3 \) - Total = 1 + 3 = 4 atoms In a BCC (Body Centered Cubic) lattice: - 8 corner atoms contribute \( \frac{1}{8} \) each: \( 8 \times \frac{1}{8} = 1 \) - 1 atom at center = 1 - Total = 1 + 1 = 2 atoms Hence, the ratio is \( 4:2 = 2:1 \)