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 Question:
The question asks how many adjacent unit cells share a single particle located exactly at the corner of a body-centered cubic (bcc) unit cell in a continuous 3D crystal lattice.

Step 2: Detailed Explanation:
In a regular three-dimensional crystalline solid lattice, any specific corner point represents the vertex where multiple cubic units meet.
Geometrically, a corner is formed by the intersection of 8 distinct cubic unit cells: 4 unit cells meet at a corner on a single plane (one layer), and another 4 unit cells meet at that exact same point from the layer directly above or below it.
Because the atom sits exactly on that 3D intersection point, its total volume is divided equally into eight pieces.
Therefore, only $\frac{1}{8}$th of the corner particle actually belongs to any one specific unit cell, because the particle is shared completely among 8 cells.
This property is entirely independent of whether the lattice is simple cubic, bcc, or fcc.

Step 3: Final Answer:
A corner particle is shared by 8 unit cells, making option (c) correct.