Step 1: Peter Mitchell proposed the chemiosmotic theory to explain how ATP is generated using a proton gradient across a membrane.
Step 2: In mitochondria, electron transport pumps protons across the inner membrane, and their flow back through ATP synthase drives ATP formation, this is oxidative phosphorylation.
Step 3: The C3 cycle, pentose phosphate pathway and mineral uptake do not rely on this proton motive force mechanism for ATP synthesis in the way oxidative phosphorylation does, so oxidative phosphorylation is the correct match among the options given.