Question

What is the total number of unit cells shared by each corner particle of bcc unit cell?

• A. 4
• B. 2
• C. 8
• D. 1

Hint:

Memorize the sharing fractions for solid state packing:
- Corner particle = Shared by 8 (Contribution = $1/8$)
- Face-centered particle = Shared by 2 (Contribution = $1/2$)
- Body-centered particle = Shared by 1 (Contribution = 1, entirely inside)
- Edge-centered particle = Shared by 4 (Contribution = $1/4$)

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In any cubic lattice (simple cubic, bcc, or fcc), a corner atom is located at the intersection of three perpendicular planes.

Step 2: Formula Application:
Contribution of a corner atom to one unit cell $= 1/8$.

Step 3: Explanation:
A corner particle is common to 4 unit cells in the same layer and 4 unit cells in the layer above (or below) it. Therefore, every corner atom is shared by 8 adjacent unit cells. This rule applies to all cubic systems, regardless of whether there is an atom in the center (bcc) or on the faces (fcc).

Step 4: Final Answer:
The total number of unit cells shared is 8.