Question

The number of atoms in body-centred and face-centred cubic unit cell respectively are

• A. 2 and 4
• B. 4 and 3
• C. 1 and 2
• D. 4 and 6

Answer 1

The Correct Option is A

In a unit cell, the number of atoms can be determined based on the arrangement of atoms in the lattice.

1. Body-Centered Cubic (BCC): - In a body-centered cubic unit cell, there is 1 atom at each corner of the cube (8 corners in total) and 1 atom at the center of the cube. 
- The atoms at the corners are shared among 8 unit cells, so each corner atom contributes 1/8 of an atom to the unit cell. 
- Therefore, the total number of atoms in a body-centered cubic unit cell is: 
(8 × 1/8) + 1 = 2 atoms.

 2. Face-Centered Cubic (FCC): - In a face-centered cubic unit cell, there is 1 atom at each corner of the cube (8 corners) and 1 atom at the center of each face (6 faces in total). 
- The atoms at the corners are shared among 8 unit cells, so each corner atom contributes 1/8 of an atom. 
- The atoms at the faces are shared between 2 unit cells, so each face-centered atom contributes 1/2 of an atom. 
- Therefore, the total number of atoms in a face-centered cubic unit cell is: 
(8 × 1/8) + (6 × 1/2) = 1 + 3 = 4 atoms. 

Answer: 2 and 4