binding energy per nucleon

If you spread a nucleus's total binding energy evenly over all its nucleons, you get the binding energy per nucleon, B/A, where A is the mass number. It answers a simple but powerful question: on average, how tightly is each nucleon held? Plotting this number against A traces the single most important curve in nuclear physics, the one that tells you which nuclei are the most stable and which way energy flows in every fusion and fission process.

The curve rises steeply from hydrogen, climbs through helium-4 (a sharp local spike near 7.07 MeV per nucleon), and reaches a broad maximum of about 8.8 MeV per nucleon in the iron-nickel region before declining gently toward the heaviest nuclei. Quantitatively B/A = [Z m_p + N m_n - M(Z,N)] c^2 / A. The peak exists because of two competing effects: the attractive nuclear force saturates and favours more nucleons (volume term), while long-range Coulomb repulsion between protons grows and penalises large, heavy nuclei. The balance is optimal around A = 56 to 62.

This shape is why the universe has a preferred fuel. Light nuclei to the left of the peak release energy by fusing (climbing toward iron); heavy nuclei to the right release energy by fissioning (also moving toward iron). Nothing is gained by fusing or splitting nuclei that already sit at the peak, which is why iron-group elements are the ash of stellar burning and cannot be pushed further by energy-releasing fusion.