Final answer:
Osteoblasts are responsible for appositional bone growth within the periosteum by forming new bone through the synthesis and secretion of the bone matrix.
Step-by-step explanation:
The cell primarily responsible for appositional bone growth within the periosteum is the osteoblast. Osteoblasts are bone-forming cells that synthesize and secrete the collagen matrix and calcium salts. They become trapped within this matrix as it calcifies, and subsequently they mature into osteocytes, which are the main cells in bony connective tissue and are responsible for maintaining the bone matrix. Osteocytes reside in spaces called lacunae and cannot divide. Therefore, the correct answer to which cell is primarily responsible for appositional bone growth within the periosteum is (b) osteoblasts.