Mass Defect Calculator Formula

Understand the math behind the mass defect calculator. Each variable explained with a worked example.

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Formulas Used

Mass Defect

mass_defect = expected_mass - atomic_mass

Binding Energy

binding_energy = (expected_mass - atomic_mass) * 931.494

Packing Fraction

packing_fraction = (atomic_mass - (protons + neutrons)) / (protons + neutrons) * 10000

Variables

VariableDescriptionDefault
protonsNumber of Protons (Z)26
neutronsNumber of Neutrons (N)30
atomic_massMeasured Atomic Mass(u)55.9349
expected_massDerived value= protons * 1.007276 + neutrons * 1.008665calculated

How It Works

Nuclear Mass Defect

The mass defect is the difference between the total mass of individual nucleons and the actual mass of the assembled nucleus.

Formula

delta_m = (Z × m_p + N × m_n) - M_atom

where m_p = 1.007276 u (proton), m_n = 1.008665 u (neutron), and M_atom is the measured atomic mass. The mass defect is converted to binding energy via E = delta_m × 931.494 MeV/u.

Worked Example

Fe-56: Z=26, N=30, measured mass = 55.9349 u.

protons = 26neutrons = 30atomic_mass = 55.9349
  1. 01Expected mass = 26 × 1.007276 + 30 × 1.008665
  2. 02Expected = 26.1891 + 30.2600 = 56.4491 u
  3. 03Mass defect = 56.4491 - 55.9349 = 0.5142 u
  4. 04BE = 0.5142 × 931.494 = 479.1 MeV

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