The Solid State

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

For a body-centred cubic (BCC) crystal, the relationship between the edge length and the atomic radius is:

Given:

Substituting the value:

Therefore, the edge length of the unit cell is 173.2 pm.

Correct option: (D) 173.2 pm