Question

How many lattice points are present in a face centred cubic unit cell?

• A. 8
• B. 17
• C. 14
• D. 9

Hint:

Always read solid-state questions carefully to differentiate between these two terms: Lattice Points: The total number of coordinate positions defining the shape ($8 \text{ corners} + 6 \text{ faces} = 14$). Effective Atoms ($Z$): The actual material net count after adjusting for shared boundary fractions ($1 + 3 = 4$).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the total number of individual lattice points that define the geometry of a single face-centered cubic (fcc) unit cell.

Step 2: Key Formula or Approach:
A lattice point refers to any specific geometric position in a space lattice where an atom, ion, or molecule can reside. It represents the position itself, regardless of how much of that atom is shared with surrounding cells.

Step 3: Detailed Explanation:
Let's systematically locate all the structural lattice positions within an fcc unit cell configuration: 1. There is a lattice point situated at each of the 8 corners of the cube. This gives 8 corner lattice points. 2. There is an additional lattice point located at the exact center of each of the 6 faces of the cube. This gives 6 face-centered lattice points. Summing all of these separate spatial positions together: $$\text{Total lattice points} = 8\text{ (corners)} + 6\text{ (faces)} = 14\text{ lattice points}$$ (Note: Do not confuse this with the effective number of atoms belonging to the unit cell, which would be $8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 4$. The total number of independent geometric sites is exactly 14).

Step 4: Final Answer:
The total number of lattice points present in a face-centered cubic unit cell is 14, which corresponds to option (C).