Nuclear Binding Energy

A nucleus weighs slightly less than the sum of its separate protons and neutrons. That missing mass didn't disappear — it became the binding energy holding the nucleus together. Iron's nucleus is bound the tightest of any element, which is why fusing light nuclei together or splitting heavy nuclei apart both release energy as they move toward iron.

E = Δm · c²

  • E — binding energy (J): the energy released or needed to hold the nucleus together
  • Δm — mass defect (kg): the mass missing compared to the separate protons and neutrons
  • c — speed of light (m/s): a huge constant, about three times ten to the eighth meters per second

A nucleus is missing 0.01 kilograms of mass compared to its separate protons and neutrons. How much binding energy does that missing mass represent?

  • Δm = 0.01 kg
  • c = 3×10⁸ m/s
  1. E = Δm · c²
  2. E = 0.01 kg · (3×10⁸ m/s)²

E = 9×10¹⁴ J

A different nucleus is missing 0.02 kilograms of mass instead. How much binding energy does that represent?

  • 1.8×10¹⁵ J
  • 4.5×10¹⁴ J
  • 1.8×10¹⁶ J

Iron sits at the very top of the binding energy curve. What does that mean for fusion and fission?

  • Only fusion releases energy; fission near iron absorbs it
  • Only fission releases energy; fusion near iron absorbs it
  • Both fusion and fission release energy as they move toward iron