How many total numbers of voids are present in a CCP lattice?

12

The correct answer is option 3. 12.

In a cubic close packing (CCP) lattice, also known as a face-centered cubic (FCC) lattice, there are two types of voids present: octahedral voids and tetrahedral voids.

Octahedral Voids:

Each octahedral void is surrounded by 6 close-packed spheres (atoms). In a CCP lattice, there is one octahedral void centered at the body center of each unit cell. Since there is one octahedral void per close-packed atom, the number of octahedral voids in a CCP lattice is equal to the number of close-packed atoms, which is 4 per unit cell. Therefore, the total number of octahedral voids in a CCP lattice is \(4 \times 1 = 4\).

Tetrahedral Voids:

Each tetrahedral void is surrounded by 4 close-packed spheres (atoms). In a CCP lattice, there are two tetrahedral voids associated with each close-packed atom. Since there are 4 close-packed atoms per unit cell, there are \(4 \times 2 = 8\) tetrahedral voids per unit cell.

Total Number of Voids:

Octahedral Voids: 4

Tetrahedral Voids: 8

So, the total number of voids in a CCP lattice is \(4 + 8 = 12\).

Therefore, the correct answer is 12.