Question

What is the number of neighbouring spheres for any particle in the fcc crystal lattice ?

• A. \(6\)
• B. \(8\)
• C. \(10\)
• D. \(12\)

Hint:

Each sphere in an fcc (ccp) lattice touches 12 others.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The number of neighbouring spheres touching a given sphere is called its coordination number.

Step 2: Count in fcc:
In a face-centred cubic (cubic close packed) structure, a sphere touches 6 spheres in its own close-packed layer, 3 in the layer above and 3 in the layer below. So \(6 + 3 + 3 = 12\).

Step 3: Why the other options are wrong.
6 is the value for simple cubic. 8 is the value for body-centred cubic. 10 does not occur in any of these standard packings.

Final Answer:
Each sphere in an fcc lattice has 12 neighbours. \[ \boxed{\text{(D) }12} \]