Nuclear Binding Energy Calculator
Calculate the nuclear binding energy and mass defect of an atomic nucleus from proton and neutron counts using Einstein mass-energy equivalence.
Nuclear Binding Energy
The nuclear binding energy is the energy required to completely disassemble an atomic nucleus into its constituent protons and neutrons. It arises from the strong nuclear force that holds nucleons (protons and neutrons) together — one of the four fundamental forces of nature.
Mass Defect and E = mc²
When protons and neutrons come together to form a nucleus, the resulting nucleus is actually slightly lighter than the sum of its parts. This difference in mass is called the mass defect (Δm).
Einstein’s famous equation connects mass and energy:
E = Δm × c²
Where:
- E = binding energy in Joules
- Δm = mass defect in kilograms
- c = speed of light = 2.998 × 10⁸ m/s
The Mass Defect Calculation
Δm = Z × m_p + N × m_n − M_nucleus
Where:
- Z = number of protons (atomic number)
- N = number of neutrons
- m_p = proton mass = 1.007276 u
- m_n = neutron mass = 1.008665 u
- M_nucleus = actual nuclear mass in atomic mass units (u)
1 u (atomic mass unit) = 1.66054 × 10⁻²⁷ kg
Binding Energy per Nucleon
The binding energy per nucleon (BE/A) is one of the most important quantities in nuclear physics. It tells you how tightly each nucleon is bound on average.
| Nuclide | BE/Nucleon (MeV) |
|---|---|
| Deuterium (²H) | 1.11 |
| Iron-56 (⁵⁶Fe) | 8.79 (maximum — most stable nucleus) |
| Uranium-238 (²³⁸U) | 7.57 |
Iron-56 has the highest binding energy per nucleon — it is the most tightly bound nucleus. Nuclei lighter than iron can release energy by fusion; heavier nuclei release energy by fission.
Conversion: eV and MeV
- 1 MeV = 10⁶ eV = 1.602 × 10⁻¹³ J
- 1 u of mass defect = 931.5 MeV of energy
This convenient conversion (931.5 MeV/u) makes nuclear energy calculations straightforward.