Mass defect and nuclear binding energy

Physics A2 · Nuclear physics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

Test this topic freeAll Physics A2 topics

The idea

Mass and energy are equivalent: E = mc2. A nucleus has less mass than its protons and neutrons have when they are separate. This difference is the mass defect. The energy equal to it is the binding energy, the energy needed to separate the nucleus completely into its nucleons.

Binding energy per nucleon shows how stable a nucleus is. Plotted against nucleon number, it rises steeply for light nuclei, reaches a peak of about 8.8 MeV near iron-56, then falls slowly.

Fusion joins light nuclei and fission splits a heavy nucleus. Both move towards the peak, so the binding energy per nucleon increases and energy is released.

Rules to remember

Common mistake

Students think a large binding energy means the nucleus holds a lot of energy. It is energy the nucleus has lost; compare stability using binding energy per nucleon, not total binding energy.

Worked example

A carbon-12 nucleus has mass 11.996706 u. Proton mass = 1.007276 u, neutron mass = 1.008665 u. What is its binding energy per nucleon?

  1. Mass of 6 protons and 6 neutrons = 6 × 1.007276 + 6 × 1.008665 = 12.095646 u.
  2. Mass defect = 12.095646 − 11.996706 = 0.098940 u = 0.098940 × 1.66 × 10−27 = 1.64 × 10−28 kg.
  3. Binding energy = c2Δm = (3.00 × 108)2 × 1.64 × 10−28 = 1.48 × 10−11 J = 92.4 MeV.
  4. Per nucleon: 92.4 ÷ 12 = 7.7 MeV.

Answer: About 7.7 MeV per nucleon (1.2 × 10−12 J).

Ask about this

Type what you are stuck on. The helper finds the explanation, worked examples and the notes to read, free and instant.

Read the full notes

Keep going

← Energy levels in atoms and line spectraRadioactive decay →Take a Physics A2 test