Formulas & tables/Physics/Atomic and nuclear physics/Nuclear binding energy

Nuclear binding energy

E=Δm c2E=\Delta m\,c^2

Result unit: J (often MeV)

What it describes

The energy needed to separate a nucleus into its nucleons; equivalent to the mass defect of the nucleus.

Symbols

EE
binding energy
[J]
Δm\Delta m
mass defect
[kg]
cc
speed of light
[m/s]

Where it comes from

The mass of a nucleus is smaller than the sum of the masses of its nucleons — this mass defect corresponds to the energy that "binds" the nucleus together. The greater the binding energy per nucleon, the more stable the nucleus.

When to use it

Stability of nuclei, energy of nuclear reactions (fission, fusion).

Example

The mass defect of a nucleus is Δm=5⋅10−29\Delta m=5\cdot10^{-29} kg. Calculate the binding energy.
SubstitutionΔm=5⋅10−29\Delta m=5\cdot10^{-29}, c=3⋅108c=3\cdot10^{8}.
ResultE≈5⋅10−29⋅9⋅1016≈4.5⋅10−12E\approx5\cdot10^{-29}\cdot9\cdot10^{16}\approx4.5\cdot10^{-12} J (≈28\approx28 MeV).

Related formulas

Mass–energy equivalence Law of radioactive decay

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