The energy given up by electrons as they move through the electron transport chain is used to pump protons (H+) across the inner mitochondrial membrane, creating a proton gradient. This proton gradient is then used to drive the synthesis of ATP, the primary energy currency of the cell, through a process called oxidative phosphorylation.

Here's a breakdown:

1. Electron Transport Chain: Electrons from NADH and FADH2, produced during glycolysis and the citric acid cycle, enter the electron transport chain.

2. Energy Transfer: As electrons move through the chain, they lose energy. This energy is harnessed by specific protein complexes within the chain.

3. Proton Pumping: The energy released by the electrons is used to pump protons from the mitochondrial matrix across the inner mitochondrial membrane into the intermembrane space. This creates a concentration gradient of protons, with a higher concentration in the intermembrane space.

4. Proton Motive Force: The proton gradient across the membrane creates an electrochemical potential, also known as the proton motive force.

5. ATP Synthase: This force drives the movement of protons back across the membrane through ATP synthase, a protein complex embedded in the membrane.

6. ATP Synthesis: As protons flow through ATP synthase, it catalyzes the synthesis of ATP from ADP and inorganic phosphate.

In summary, the energy released by electrons in the electron transport chain is ultimately used to create the proton gradient that powers ATP synthesis, providing the cell with its primary energy source.