What Is Nuclear Binding Energy?
Nuclear binding energy is the energy required to separate a nucleus into its individual protons and neutrons. It is also the energy released when the nucleus is formed from separated nucleons.
A higher binding energy per nucleon generally means a more tightly bound and stable nucleus. Binding energy is central to nuclear physics, fission, fusion, radioactive decay, and stellar energy production.
Binding Energy Formula
Binding energy is calculated from the mass defect:
where Δm is the mass defect in atomic mass units.
Atomic Mass Formula
Most isotope tables give the mass of the neutral atom, not the bare nucleus. When using atomic mass, use:
where:
- Z = number of protons
- N = A - Z = number of neutrons
- mH = mass of hydrogen atom
- mn = mass of neutron
- Matom = neutral atomic mass
Nuclear Mass Formula
If you are using the mass of the bare nucleus only, use:
where mp is the proton mass and Mnucleus is the nuclear mass without electrons.
Binding Energy Per Nucleon
Binding energy per nucleon is:
This value is useful for comparing nuclear stability across different isotopes.
How to Use the Calculator
- Choose custom data or select an isotope from the list.
- If entering custom data, choose whether your mass is atomic mass or nuclear mass.
- Enter atomic number Z, mass number A, and mass in atomic mass units.
- Click calculate to get mass defect, total binding energy, and binding energy per nucleon.
Example: Iron-56
Iron-56 has Z = 26 and A = 56. Using atomic mass data, the calculator applies:
The total binding energy is then:
Dividing by 56 gives the binding energy per nucleon.
Typical Binding Energy Per Nucleon
| Region | Typical Behavior |
|---|---|
| Light nuclei | Binding energy per nucleon generally rises as nuclei become heavier. |
| Iron/nickel region | Among the highest binding energy per nucleon values. |
| Very heavy nuclei | Binding energy per nucleon slowly decreases. |
Important Assumptions
- Masses are treated using atomic mass units.
- The energy equivalent used is approximately 931.494 MeV/u.
- Electron binding energies are very small compared with nuclear binding energies and are ignored in the atomic-mass method.
- Isotope list values are neutral atomic masses.
- For high-precision nuclear data, use official evaluated atomic mass tables.
Frequently Asked Questions
What is binding energy?
Binding energy is the energy required to separate a nucleus into its protons and neutrons.
What is mass defect?
Mass defect is the difference between the mass of separated nucleons and the measured mass of the bound atom or nucleus.
Why is binding energy per nucleon important?
Binding energy per nucleon helps compare nuclear stability. Higher values generally mean the nucleus is more tightly bound.
Why does the calculator ask for atomic mass or nuclear mass?
Atomic mass includes electrons, while nuclear mass does not. The correct mass-defect formula depends on which type of mass you enter.
How is binding energy related to fission and fusion?
Fission and fusion release energy when the products have a higher total binding energy per nucleon than the reactants.