The immediate energy source that drives atp synthesis by atp synthase during oxidative phosphorylation is the

Electrochemical gradients of protons, driven by Proton Motive Force.

Explanation:

NADH and FADH2 are the two coenzymes that ferry Hydrogen atoms into the mitochondria matrix.The Hydrogen  atoms is splits into H+/protons and electrons.

The protons is continuously  pumped across the matrix into the intramembrane of the mitochondria setting up an electrochemical gradient.

The influx of protons down the electrochemical gradients into the matrix  generated the energy needed by the enzyme ATPase synthase to phosphorylate ADP  with inorganic phosphate ion(Pi)  to give ATPs.

Thus the influx of protons down their electrochemical gradients is the immediate source of energy.

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