Question

What is the total number of adjacent unit cells shared by each face particle of fcc unit cell ?

• A. \(1\)
• B. \(2\)
• C. \(4\)
• D. \(8\)

Hint:

A particle in the centre of a face is shared between two adjacent unit cells.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In a face-centred cubic (fcc) unit cell, atoms sit at the 8 corners and at the centres of the 6 faces. Each type of position is shared with neighbouring cells.

Step 2: Key Formula or Approach:
A corner atom is shared by 8 unit cells, so it contributes 1/8. A face-centre atom lies on a face that belongs to exactly two cubes, so it is shared by 2 unit cells and contributes 1/2.

Step 3: Detailed Explanation:
Place one fcc cell. The atom in the middle of its front face is also in the middle of the back face of the cell placed right in front. No other cell touches that point.
So each face particle is shared by 2 unit cells.
Total atoms in fcc: \(8\times\frac{1}{8} + 6\times\frac{1}{2} = 1 + 3 = 4\).
Option (D) 8 refers to a corner particle. Option (C) 4 is the number of atoms per fcc cell, which is a different quantity.

Final Answer:
Each face-centre particle is shared by 2 unit cells, option (B). \[ \boxed{2 \text{ (B)}} \]