Mass Defect Energy

Weigh the parts of a uranium-235 nucleus separately (92 protons, 143 neutrons) and they total more than the assembled nucleus. The "missing" mass is not lost. It was converted into the binding energy holding the nucleus together, following E = mc². That tiny mass difference, multiplied by the speed of light squared, is the reason a single uranium fuel pellet contains as much energy as a ton of coal.

The mass defect is the difference between the total mass of individual nucleons and the mass of the assembled nucleus. When nucleons bind together, some mass converts to energy (released during formation) and must be resupplied to break the nucleus apart. For fission, splitting a heavy nucleus into lighter fragments releases energy because the products are more tightly bound (lower total mass) than the original.

The speed of light squared (c² = 9 x 10^16 m²/s²) is an enormous conversion factor. Even a tiny mass difference, measured in atomic mass units, corresponds to millions of electron volts of energy per atom, billions of joules per kilogram.

Worked Example

One fission event of U-235 converts about 0.215 atomic mass units (u) of mass into energy. 1 u = 1.66 x 10^-27 kg.

• Convert mass to kg. 0.215 x 1.66 x 10^-27 = 3.57 x 10^-28 kg.
• Apply E = mc². E = 3.57 x 10^-28 x (3 x 10^8)² = 3.21 x 10^-11 J, or about 200 MeV.

How does this compare to the energy from burning one molecule of methane (~9.3 eV)?

200 MeV / 9.3 eV = about 21.5 million times more energy per reaction. This is the fundamental reason nuclear fuel is millions of times more energy-dense than chemical fuel: mass-to-energy conversion via E = mc² versus electron rearrangement.

The mass defect is the physical origin of nuclear energy density, and the reason a reactor's fuel load fits in a room while a coal plant's fuel fills a trainyard.

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