Nuclear Binding Energy Calculator
Calculate the mass defect and binding energy of an atomic nucleus.
Inputs
Results
Mass Defect ($\Delta m$)
Binding Energy ($E_b$)
Binding Energy per Nucleon ($E_b/A$)
Physics Formulas
1. Mass Defect ($\Delta m$):
$$\Delta m = Z m_p + N m_n – m_{\text{nucleus}}$$Where $m_p = 1.007276\,\text{u}$ (Proton Mass) and $m_n = 1.008665\,\text{u}$ (Neutron Mass).
2. Binding Energy ($E_b$):
$$E_b = \Delta m \times 931.5 \, \text{MeV}$$The conversion factor $931.5\,\text{MeV}/\text{u}$ is derived from $E=mc^2$.
3. Binding Energy per Nucleon ($E_b/A$):
$$\frac{E_b}{A} = \frac{E_b}{Z+N}$$What is Nuclear Binding Energy?
Nuclear binding energy ($E_b$) is the energy required to completely separate an atomic nucleus into its constituent particles, protons ($Z$) and neutrons ($N$), collectively called nucleons. This energy is released when the nucleus is formed from its individual components.
The existence of binding energy is a direct consequence of Mass Defect ($\Delta m$): the actual mass of a nucleus ($m_{\text{nucleus}}$) is always less than the sum of the masses of its individual nucleons ($Z m_p + N m_n$). This “missing” mass is converted into binding energy according to Einstein’s famous equation $E=mc^2$.
Binding Energy per Nucleon ($E_b/A$) is the key factor determining the stability of a nucleus. Nuclei with higher binding energy per nucleon (e.g., Iron-56) are the most stable. This concept explains why energy is released during nuclear fusion and nuclear fission processes.
How to Use the Calculator
- Enter Protons ($Z$): Input the number of protons (the atomic number) in the nucleus.
- Enter Neutrons ($N$): Input the number of neutrons in the nucleus. (The total mass number is $A = Z+N$).
- Enter Nuclear Mass ($m_{\text{nucleus}}$): Input the precise measured mass of the nucleus in atomic mass units ($\text{u}$). This value must be highly accurate to show the mass defect.
- View Results: Click “Calculate Energy” to trigger the calculation and view the results.
- Review Steps: The “Step-by-Step Calculation” section dynamically shows the formula substitution based on your inputs.
