Question

How many particles per unit cell are present in BCC structure?

• A. 1
• B. 4
• C. 3
• D. 2

Hint:

Keep a simple memory checklist for cubic unit cells: Simple Cubic (SCC) = 1 atom, Body-Centered Cubic (BCC) = 2 atoms, and Face-Centered Cubic (FCC) = 4 atoms.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The problem asks for the effective number of atoms (or particles) contained inside a single Body-Centered Cubic (BCC) unit cell.

Step 2: Key Formula or Approach:
The total number of atoms per unit cell ($Z$) is calculated by summing the fractional contributions of all atoms based on their lattice positions: $$Z = \frac{N_{\text{corner}}}{8} + \frac{N_{\text{face}}}{2} + N_{\text{center}}$$

Step 3: Detailed Explanation:
In a body-centered cubic (BCC) arrangement: 1. There are 8 atoms located at the 8 corners of the cube. Each corner atom is shared equally among 8 adjacent unit cells, contributing only $\frac{1}{8}$ of its volume to a single cell.
$$\text{Contribution from corners} = 8 \times \frac{1}{8} = 1\text{ atom}$$ 2. There is 1 atom completely localized at the center of the body of the cube. This atom belongs entirely to this single unit cell and is not shared with any neighboring cells.
$$\text{Contribution from center} = 1 \times 1 = 1\text{ atom}$$ Adding the shared corner contributions and the unshared central contribution together: $$Z = 1 + 1 = 2\text{ atoms}$$

Step 4: Final Answer:
There are 2 particles present per unit cell in a BCC structure, matching option (D).