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:

Remember the number of atoms per unit cell: \[ \text{Simple Cubic (SC)} = 1 \] \[ \text{Body Centered Cubic (BCC)} = 2 \] \[ \text{Face Centered Cubic (FCC)} = 4 \] These values are frequently used in solid-state chemistry problems.

Answer 1

The Correct Option is D

Step 1: Count effective atoms in FCC.
FCC: 8 corners \( imes rac{1}{8}\) + 6 faces \( imes rac{1}{2}\) = 1 + 3 = 4 atoms.

Step 2: Count effective atoms in BCC and find ratio.
BCC: 8 corners \( imes rac{1}{8}\) + 1 body center = 1 + 1 = 2 atoms. Ratio FCC:BCC = 4:2 = 2:1. \[ oxed{2:1} \]