Question

Identify the type of unit cell that has particles at the centre of each face in addition to the particles at eight corners of a cube?

• A. Face centred cubic unit cell
• B. Hexagonal unit cell
• C. Simple cubic unit cell
• D. Body centred cubic unit cell

Hint:

Associate the terms directly with their literal names: "particles at the centre of each face" translates directly to a Face-centred unit cell.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The problem describes the positional arrangement of constituent particles (atoms, molecules, or ions) within a crystal lattice framework and asks us to name the specific cubic unit cell type.

Step 2: Key Formula or Approach:
Cubic unit cells are fundamentally classified based on lattice point locations: Primitive / Simple Cubic (scc): Corners only. Body-Centred Cubic (bcc): Corners + center of the body. Face-Centred Cubic (fcc): Corners + centers of all six faces.

Step 3: Detailed Explanation:
The question explicitly states that the particles are located at: 1. The eight corners of the cube structure. 2. The center of each of the six faces. This arrangement fits the definition of a Face-Centred Cubic (fcc) unit cell. In this arrangement, each corner particle contributes $\frac{1}{8}$ to the unit cell, and each face particle contributes $\frac{1}{2}$, making the total number of effective atoms per unit cell equal to: $$\left(8 \times \frac{1}{8}\right) + \left(6 \times \frac{1}{2}\right) = 1 + 3 = 4$$

Step 4: Final Answer:
The unit cell described is the face-centred cubic unit cell, corresponding to option (A).