Nuclear Binding Energy Calculator

Calculate binding energy, mass defect, and nuclear stability

Supported formats: Element-Mass (U-238), MassElement (238U), Element Mass (Uranium 238)
Calculation Results
56Fe
Binding Energy
492.3
MeV
Per Nucleon
8.79
MeV/nucleon
Mass Defect
0.528
u (atomic mass units)
Binding Energy Curve

Common Isotopes Binding Energy Data

Binding energy per nucleon varies across the periodic table, peaking around iron-56 which is the most stable nucleus.

Isotope Protons (Z) Neutrons (N) Binding Energy (MeV) Per Nucleon (MeV) Stability
⁴He 2 2 28.3 7.07 High
¹²C 6 6 92.2 7.68 High
¹⁶O 8 8 127.6 7.98 High
⁵⁶Fe 26 30 492.3 8.79 Highest
¹⁰⁷Ag 47 60 915.2 8.55 High
¹⁹⁷Au 79 118 1559.3 7.92 Medium
²³⁸U 92 146 1801.7 7.57 Low (Radioactive)

Nuclear Binding Energy Explained

Nuclear binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It represents the energy equivalent of the mass defect - the difference between the mass of the separated nucleons and the mass of the nucleus.

Mass-Energy Equivalence: According to Einstein's equation E=mc², the binding energy is related to the mass defect by ΔE = Δm × c², where c is the speed of light.

Understanding Nuclear Binding Energy

Mass Defect

The difference between the mass of the separated nucleons and the actual mass of the nucleus.

Δm = (Z × mₚ + N × mₙ) - mnucleus

This "missing mass" is converted to energy according to E = mc².

Binding Energy

The energy equivalent of the mass defect.

BE = Δm × c²

Typically measured in MeV (mega-electronvolts).

Binding Energy per Nucleon

BE/A = Binding Energy / Mass Number

Measures nuclear stability:

  • Higher BE/A = More stable nucleus
  • Peaks at iron-56 (8.79 MeV/nucleon)
Nuclear Stability

Nuclei with intermediate mass numbers (A ≈ 50-60) are most stable.

Light nuclei gain stability through fusion.

Heavy nuclei gain stability through fission.

Mass defect is the difference between the mass of an atom and the sum of the masses of its individual protons, neutrons, and electrons. This "missing" mass is converted to energy (binding energy) that holds the nucleus together.

For example, a helium-4 nucleus has a mass about 0.7% less than the combined mass of two free protons and two free neutrons. This mass defect corresponds to the binding energy of 28.3 MeV.

Binding energy per nucleon indicates nuclear stability:

  • Higher values mean more stable nuclei
  • Iron-56 has the highest binding energy per nucleon (8.79 MeV)
  • Elements lighter than iron can release energy through fusion
  • Elements heavier than iron can release energy through fission

This explains why stars fuse hydrogen into helium and why nuclear reactors fission uranium.

Binding energy is calculated using the formula:

BE = [Z × mₚ + N × mₙ - mₙᵤ꜀] × c²

Where:

  • Z = number of protons
  • N = number of neutrons
  • mₚ = mass of a proton (1.007825 u)
  • mₙ = mass of a neutron (1.008665 u)
  • mₙᵤ꜀ = measured mass of the nucleus
  • c = speed of light (931.494 MeV/u)

Our calculator uses precise mass data from nuclear databases to compute binding energies.

Nuclear stability depends on:

  • Neutron-Proton Ratio: Stable nuclei have N/Z ratios between 1 (for light elements) and 1.5 (for heavy elements)
  • Binding Energy per Nucleon: Higher values indicate greater stability
  • Magic Numbers: Nuclei with 2, 8, 20, 28, 50, 82, or 126 protons/neutrons are exceptionally stable
  • Even-Even Nuclei: Nuclei with even numbers of both protons and neutrons are generally more stable

Unstable nuclei undergo radioactive decay to achieve more stable configurations.