Mass Defect & Binding Energy Calculator Physics

Mass defect: --- u
Binding energy: --- MeV
Mass defect: -- Binding energy: -- BE per nucleon: --

What is Mass Defect & Binding Energy Calculator?

Quick Answer: An interactive tool that calculates the mass defect (difference between mass of nucleons and actual nuclear mass) and the binding energy using Einstein's equation E = mc². Enter atomic number, mass number, and actual nuclear mass to obtain binding energy in MeV and per nucleon. A visual nucleus diagram shows protons and neutrons.

Theory of Mass Defect and Binding Energy

The mass defect (Δm) is the difference between the sum of the masses of free nucleons (protons and neutrons) and the actual mass of the nucleus. When nucleons bind together, some mass is converted into energy (binding energy) that holds the nucleus together. Einstein's mass-energy relation:
EB = Δm c²
Using atomic mass units (u), where 1 u = 931.494 MeV/c², the binding energy in MeV is simply Δm × 931.494 MeV.
Mass of proton = 1.007276 u, mass of neutron = 1.008665 u.
The binding energy per nucleon = EB / A, a measure of nuclear stability. The iron‑56 nucleus has the highest binding energy per nucleon.

Step-by-Step Examples

Example 1: Helium‑4 (²He⁴)

  1. Set Z = 2, A = 4, actual mass = 4.002603 u. Click Calculate.
  2. Mass of nucleons = 2×1.007276 + 2×1.008665 = 4.031882 u.
  3. Mass defect = 4.031882 - 4.002603 = 0.029279 u.
  4. Binding energy = 0.029279 × 931.494 = 27.27 MeV. Per nucleon = 6.82 MeV.

Example 2: Iron‑56 (Fe-56)

  1. Use preset "Fe-56": Z=26, A=56, mass=55.934942 u.
  2. BE per nucleon ~ 8.79 MeV (highest stability).

Example 3: Uranium‑238

  1. Preset "U-238": Z=92, A=238, mass=238.050788 u.
  2. Binding energy per nucleon ~ 7.57 MeV (less stable than iron, can undergo fission).

Frequently Asked Questions

What is mass defect?

It is the difference between the total mass of individual protons and neutrons and the actual mass of the nucleus. This "missing" mass is converted into binding energy.

Why is binding energy per nucleon important?

It indicates nuclear stability. Iron-56 has the maximum (~8.8 MeV), so nuclei heavier than iron can release energy by fission, and lighter ones by fusion.

What are the masses of proton and neutron used?

Proton mass = 1.007276 u, neutron mass = 1.008665 u. These are standard values in atomic mass units.

How is the conversion from u to MeV done?

Using 1 u = 931.494 MeV/c². So binding energy (MeV) = mass defect (u) × 931.494.

Can I use this for any nucleus?

Yes, as long as you know the actual nuclear mass. The calculator works for all nuclides. Presets provide known values for a few common ones.