During photosynthesis, O₂ of the atmosphere is fixed with the help of H₂O and sunlight to synthesize carbohydrate and O₂ is evolved by the splitting of

In photosynthesis, the oxygen (O₂) released into the atmosphere is derived from the photolysis (splitting) of water (H₂O). This reaction occurs during the light-dependent phase in the thylakoid membranes of chloroplasts, where light energy is used to split water molecules into hydrogen ions (protons), electrons, and oxygen gas. This mechanism was experimentally confirmed by Ruben and Kamen using the ¹⁸O isotope, showing that the evolved oxygen comes from water and not from carbon dioxide.

Although the question text contains a common technical error (it is actually carbon dioxide, CO₂, that is "fixed" from the atmosphere to synthesize carbohydrates during the Calvin cycle), the specific process that evolves oxygen is the splitting of H₂O. CO₂ provides the carbon and oxygen atoms that are incorporated into the glucose molecule.