An important difference between cellular respiration and photosynthesis is that when cellular respiration begins, glucose molecules are split. However, when photosynthesis begins

The answer is water molecules are split.

Cellular respiration and photosynthesis are complement reactions to each other. These are reverse reactions. In cellular respiration glucose and oxygen yield water and carbon dioxide. So, when respiration begins, glucose molecules are split. In the opposite reaction - in photosynthesis, carbon dioxide and water yield glucose and oxygen. Thus, when respiration begins, water molecules are split.