The cell content (Z) of the unit cell of a h.c.p. space lattice is

Options

A. 2
B. 6
C. 12
D. 17

Explanation

To determine the cell content (Z) of the unit cell of a hexagonal close-packed (h.c.p.) space lattice, we follow these steps:

### Step-by-Step Solution:

1. **Understanding the Unit Cell**:
- The hexagonal close-packed (h.c.p.) structure is one of the most efficient ways to pack spheres in three-dimensional space. It consists of two layers of atoms arranged in a hexagonal pattern.

2. **Counting Atoms in the Unit Cell**:
- In an h.c.p. unit cell, there are 2 complete atoms in the unit cell, plus additional contributions from the atoms located at the corners and the face centers.
- Each corner atom is shared by 6 unit cells, contributing \( \frac{1}{6} \) of an atom to the unit cell. There are 12 corners in a hexagonal unit cell.
- Each face-centered atom (there are 2 in the h.c.p. structure) is shared by 2 unit cells, contributing \( \frac{1}{2} \) of an atom to the unit cell.

3. **Calculating Total Contribution**:
- Contribution from corner atoms: \( 12 \times \frac{1}{6} = 2 \) atoms.
- Contribution from face-centered atoms: \( 2 \times \frac{1}{2} = 1 \) atom.
- Total number of atoms (Z) in the unit cell = Contribution from corners + Contribution from faces = \( 2 + 1 = 3 \).

4. **Considering the Additional Atoms**:
- In addition to the above, there are 2 complete atoms located within the unit cell itself (one at the top and one at the bottom).
- Therefore, the total number of atoms per unit cell (Z) in h.c.p. is \( 3 + 3 = 6 \).

### Final Answer:
- The cell content (Z) of the unit cell of a hexagonal close-packed (h.c.p.) space lattice is **6**.