Question

The effective number of atoms in a body-centered cubic (BCC) unit cell is

• A. 1
• B. 2
• C. 4
• D. 8

Hint:

Remember the effective number of atoms for common cubic lattices:
- Simple Cubic (SC) = 1
- Body-Centered Cubic (BCC) = 2
- Face-Centered Cubic (FCC) = 4

Answer 1

The Correct Option is B

Step 1: Locate the atoms in the cell.
A BCC cell has one atom sitting at each of the 8 corners and one atom sitting fully inside at the body centre.

Step 2: Share out the corner atoms.
Each corner atom is shared among 8 neighbouring cells, so only \( \frac{1}{8} \) of each belongs to this cell: \( 8 \times \frac{1}{8} = 1 \) atom contributed by the corners.

Step 3: Add the body centre atom.
The centre atom belongs entirely to this one cell, adding a full atom, so the total works out to \( 1 + 1 = 2 \).
\[ \boxed{2} \]
This matches option (B).