Binding Energy per Nucleon Calculator Formula

Understand the math behind the binding energy per nucleon calculator. Each variable explained with a worked example.

Formulas Used

Total Binding Energy

be_mev = mass_defect * 931.494

Binding Energy per Nucleon

be_per_nucleon = mass_defect * 931.494 / nucleons

Variables

VariableDescriptionDefault
mass_defectMass Defect (delta m)(u)0.5284
nucleonsNumber of Nucleons (A)56

How It Works

Nuclear Binding Energy

The binding energy is the energy required to disassemble a nucleus into free protons and neutrons. Higher binding energy per nucleon means greater nuclear stability.

Formula

BE = delta_m × 931.494 MeV/u

BE per nucleon = BE / A

where delta_m is the mass defect (in atomic mass units) and 931.494 MeV/u is the energy equivalent of one atomic mass unit. Iron-56 has the highest BE/nucleon at about 8.79 MeV.

Worked Example

Fe-56 with mass defect 0.5284 u and A = 56 nucleons.

mass_defect = 0.5284nucleons = 56
  1. 01BE = 0.5284 × 931.494 = 492.3 MeV
  2. 02BE/A = 492.3 / 56 = 8.79 MeV/nucleon

Frequently Asked Questions

Why is iron-56 the most stable nucleus?

Fe-56 has the highest binding energy per nucleon (~8.79 MeV). Elements lighter than iron release energy through fusion (moving toward higher BE/A), while heavier elements release energy through fission.

What is the mass defect?

The mass defect is the difference between the sum of individual nucleon masses and the actual nuclear mass: delta_m = Z×m_p + N×m_n - M_nucleus. This "missing" mass has been converted to binding energy via E=mc².

How does binding energy relate to nuclear power?

In fission, heavy nuclei split into fragments with higher BE/A, releasing the difference as energy. In fusion, light nuclei combine into products with higher BE/A. Both processes release energy by moving toward the iron peak.