The number of atoms per unit cell, coordination number, and atomic packing factor, for a FCC crystal are……………a.4, 12, and 0.74b.1, 6, and 0.52c.2, 8, and 0.68d.6, 12, and 0.74

The correct answer is a.4, 12, and 0.74.

Here's why:

1. Number of atoms per unit cell for a Face-Centered Cubic (FCC) crystal: In a FCC structure, there are atoms at each of the eight corners and one at the center of each of the six faces. Each corner atom is shared by eight adjacent unit cells, and each face-centered atom is shared by two adjacent unit cells. Therefore, the number of atoms per unit cell is (81/8) + (61/2) = 4.

2. Coordination number for a FCC crystal: The coordination number is the number of nearest neighbors an atom has. In a FCC structure, each atom has 12 nearest neighbors (4 atoms in the same plane, 4 atoms below, and 4 atoms above), so the coordination number is 12.

3. Atomic packing factor (APF) for a FCC crystal: The APF is the fraction of the total crystal volume that is occupied by atoms. For a FCC structure, the APF is approximately 0.74, which means 74% of the total volume is occupied by atoms. This is the highest packing density possible and is the reason why many metals crystallize in the FCC system.