The problem asks for the total number of atoms in a hexagonal close-packed (HCP) unit cell. To find this, we need to consider the atoms at different positions within the unit cell and their respective contributions.

The HCP unit cell is a hexagonal prism with atoms at the following positions:

1. At the corners: There are two hexagonal faces (top and bottom), and each hexagon has 6 corners. This gives a total of $6 \times 2 = 12$ corner atoms.
2. At the face centers: There is one atom at the center of each of the two hexagonal faces. This gives a total of 2 face-centered atoms.
3. Inside the body: There are 3 atoms located entirely within the body of the hexagonal prism, sandwiched between the top and bottom layers.

Now, we calculate the effective number of atoms (Z) by summing the contributions from each position:

Step 1: Contribution of corner atoms An atom at a corner of the hexagonal prism is shared by 6 adjacent unit cells. Therefore, the contribution of each corner atom to one unit cell is $1/6$. Total contribution from 12 corner atoms = $12 \times \frac{1}{6} = 2$ atoms.

Step 2: Contribution of face-centered atoms An atom at the center of a hexagonal face is shared by 2 adjacent unit cells (the one above and the one below). Therefore, the contribution of each face-centered atom is $1/2$. Total contribution from 2 face-centered atoms = $2 \times \frac{1}{2} = 1$ atom.

Step 3: Contribution of atoms inside the body The 3 atoms located inside the body of the prism belong entirely to that single unit cell. They are not shared with any other unit cell. Total contribution from 3 body-centered atoms = $3 \times 1 = 3$ atoms.

Step 4: Total number of atoms per unit cell The total number of atoms (Z) per HCP unit cell is the sum of all these contributions. $Z = (\text{Contribution from corners}) + (\text{Contribution from face centers}) + (\text{Contribution from body})$ $Z = (12 \times \frac{1}{6}) + (2 \times \frac{1}{2}) + (3 \times 1)$ $Z = 2 + 1 + 3 = 6$

Thus, the number of atoms in an HCP unit cell is 6.

Comparing this result with the given options: A: 4 (This is for FCC/CCP) B: 6 C: 12 (This is the coordination number for HCP) D: 17

The correct option is B.