How many total numbers of atoms are present per unit cell in FCC unit cell?

4

The correct answer is option 4. 4.

In a face-centered cubic (FCC) unit cell, the total number of atoms per unit cell can be determined by considering the atoms located at the corners, as well as those at the face centers.

Atoms at Corners:

There are 8 corner positions in a cubic unit cell. Each corner atom is shared among 8 adjacent unit cells. Therefore, each corner atom contributes \( \frac{1}{8} \) to the unit cell it belongs to.

Total contribution from corner atoms = \( 8 \times \frac{1}{8} = 1 \) atom.

Atoms at Face Centers:

There are 6 face centers in a cubic unit cell. Each face-centered atom is shared among 2 adjacent unit cells. Therefore, each face-centered atom contributes \( \frac{1}{2} \) to the unit cell it belongs to.

Total contribution from face-centered atoms = \( 6 \times \frac{1}{2} = 3 \) atoms.

Total Number of Atoms per Unit Cell:

Contribution from corner atoms: 1 atom

Contribution from face-centered atoms: 3 atoms

Therefore, the total number of atoms per unit cell in an FCC unit cell is \( 1 + 3 = 4 \).

So, the correct answer is 4.