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How do NADH and FADH2 help mitochondria make ATP?

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Fluorescent confocal image of HeLa cells with green microtubules outlining cell shapes, red mitochondria, and blue nuclei. — mitochondrion Mitochondria (red) are found throughout the cytoplasm of almost all eukaryotic cells (cell nucleus is shown in blue; cytoskeleton is shown in yellow).

NADH and FADH $_{2}$ are essential electron donors that facilitate the production of ATP in the mitochondrion through a process known as oxidative phosphorylation.123

The process functions as follows:

Electron Donation: NADH and FADH $_{2}$ donate high-energy electrons to the electron-transport chain, a series of protein complexes embedded in the inner mitochondrial membrane (cristae).14
Proton Pumping: As electrons are transferred through these complexes, the energy released is used to pump protons (H $^{+}$ ions) from the mitochondrial matrix into the intermembrane space.13
Gradient Formation: This pumping action creates an electrochemical gradient—a high concentration of protons outside the membrane relative to the matrix—which stores potential energy.13
ATP Synthesis: Because the inner membrane is impermeable to protons, they must flow back into the matrix through a specialized enzyme complex called ATP synthase. The energy released by this flow drives the conversion of ADP and inorganic phosphate into ATP.13

Ultimately, the electrons are transferred to oxygen, which combines with protons to form water, completing the cycle.13