Result

Nuclear binding energy

E_{b} = Δ m c^{2} = [Z m_{p} + N m_{n} - M_{nucleus}] c^{2}

Statement

The energy that would be required to separate a nucleus into its individual protons and neutrons, from the mass defect Δm.

Symbols and units

$E_{b}$	nuclear binding energy	J
$Z, N$	proton, neutron number	—
$m_{p}, m_{n}$	proton, neutron mass	kg
$Δ m$	mass defect	kg
$c$	speed of light	2.998×10⁸ m/s
$M_{nucleus}$	measured mass of the nucleus	kg

When it applies

Any nucleus, given its measured mass and the masses of its constituent protons and neutrons.

Don't use when

Computed from the mass defect of the nucleus as a whole — it does not by itself indicate how tightly any single nucleon is bound; binding energy per nucleon is the relevant quantity for comparing stability across nuclei.

Derivation

A nucleus's mass is measurably less than the sum of its separate proton and neutron masses; that missing mass, via E = mc², corresponds to the energy holding the nucleus together:

E_{b} = Δ m c^{2}

Watch out for

Binding energy PER NUCLEON, not total binding energy, determines nuclear stability — it peaks near iron (A ≈ 56), which is why both fission of heavy nuclei and fusion of light nuclei release energy, moving toward that peak from opposite directions.

Connects to

Mass-energy equivalence