Final answer:
The face-centered cubic (FCC) or cubic close-packed (CCP) structure is the most compact arrangement for packing equal-sized spheres, with a coordination number of 12 and occupying about 74% of the volume.
Step-by-step explanation:
The face-centered cubic (FCC) lattice, also known as the cubic close-packed (CCP) structure, is the most compact way to pack spheres of equal size together. In the FCC or CCP structures, the spheres (atoms) are arranged in a pattern that repeats in three alternating layers, known as the ABCABC... pattern. This arrangement allows the atoms to occupy approximately 74% of the volume, with each atom contacting 12 near neighbors, giving it a coordination number of 12.
The other arrangements mentioned, such as hexagonal closest packed (HCP), body-centered cubic (BCC), and simple cubic, do not achieve the same level of closeness in packing. The BCC structure has a coordination number of 8 and the simple cubic has a much lower density of packed atoms. Therefore, the correct answer is B. Face-centered cubic.