Final answer:
The generation of ATP by the movement of protons down their concentration gradient occurs in mitochondria and chloroplasts.
Step-by-step explanation:
The generation of ATP by the movement of protons down their concentration gradient occurs in mitochondria and chloroplasts. In mitochondria, the movement of protons (H+) occurs across the inner membrane, while in chloroplasts, it occurs across the thylakoid membrane. This movement of protons is facilitated by a membrane-bound enzyme complex called ATP synthase. The flow of hydrogen ions through ATP synthase powers the synthesis of ATP from ADP and inorganic phosphate (P₁).