Mass Defect Calculator Formula
Understand the math behind the mass defect calculator. Each variable explained with a worked example.
Formulas Used
Mass Defect
mass_defect = expected_mass - atomic_massBinding Energy
binding_energy = (expected_mass - atomic_mass) * 931.494Packing Fraction
packing_fraction = (atomic_mass - (protons + neutrons)) / (protons + neutrons) * 10000Variables
| Variable | Description | Default |
|---|---|---|
protons | Number of Protons (Z) | 26 |
neutrons | Number of Neutrons (N) | 30 |
atomic_mass | Measured Atomic Mass(u) | 55.9349 |
expected_mass | Derived value= protons * 1.007276 + neutrons * 1.008665 | calculated |
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.
- 01Expected mass = 26 × 1.007276 + 30 × 1.008665
- 02Expected = 26.1891 + 30.2600 = 56.4491 u
- 03Mass defect = 56.4491 - 55.9349 = 0.5142 u
- 04BE = 0.5142 × 931.494 = 479.1 MeV
Frequently Asked Questions
Why is the mass defect positive?
The nucleus weighs less than its parts. The missing mass has been converted to binding energy that holds the nucleus together. More stable nuclei have larger mass defects per nucleon.
Should I use proton mass or hydrogen atom mass?
If using nuclear masses, use proton mass (1.007276 u). If using atomic masses (which include electrons), use hydrogen mass (1.007825 u) and the electron masses cancel approximately.
What is packing fraction?
Packing fraction = (M - A) / A × 10⁴, where A is the mass number. It measures deviation from whole-number atomic mass. Negative values indicate tighter binding. Fe-56 has the most negative packing fraction.
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