A level-readyAll subjects · Physics · WPH15 (Unit 5)
Mass deficit and nuclear binding energy
A nucleus has less mass than the protons and neutrons it is made from. The missing mass is the binding energy that holds it together.
Mass deficit and binding energy
- Mass deficit Δm: (total mass of the separate nucleons) - (mass of the nucleus).
- Binding energy: the energy needed to separate a nucleus completely into its individual protons and neutrons. It equals the energy released when the nucleus forms.
- They are linked by ΔE = c2Δm.
The atomic mass unit
Nuclear masses are given in unified atomic mass units: 1 u = 1.66 x 10-27 kg (data list value). To use ΔE = c2Δm, convert Δm from u to kg first, then convert the energy from J to MeV by dividing by 1.60 x 10-13. Useful masses: proton 1.007276 u, neutron 1.008665 u.
Binding energy per nucleon
To compare stability, divide the binding energy by the nucleon number A. A larger binding energy per nucleon means a more stable nucleus. It rises steeply for light nuclei, peaks near iron-56 (about 8.8 MeV per nucleon), then falls slowly for heavier nuclei.
Worked example
A helium-4 nucleus has mass 4.001506 u. Find its binding energy per nucleon. (m_p = 1.007276 u, m_n = 1.008665 u)
- Δm = 2(1.007276) + 2(1.008665) - 4.001506 = 0.030376 u
- Δm = 0.030376 x 1.66 x 10-27 = 5.04 x 10-29 kg
- ΔE = c2Δm = 9.00 x 1016 x 5.04 x 10-29 = 4.54 x 10-12 J = 28.4 MeV
- Per nucleon: 28.4 / 4
Answer: About 7.1 MeV per nucleon
Check yourself
- Convert a mass deficit of 0.0300 u into kg, in units of 10-29 kg.
Show answer
4.98 x 10-29 kg. 0.0300 x 1.66 x 10-27 = 4.98 x 10-29 kg.
- A nucleus has a mass deficit of 3.0 x 10-29 kg. Find its binding energy, in units of 10-12 J.
Show answer
2.7 x 10-12 J. ΔE = c2Δm = 9.00 x 1016 x 3.0 x 10-29 = 2.7 x 10-12 J.
- Convert a binding energy of 2.7 x 10-12 J into MeV, to 3 s.f.
Show answer
16.9 MeV. 2.7 x 10-12 / 1.60 x 10-13 = 16.875, which is 16.9 MeV to 3 s.f.
- A deuterium nucleus (1 proton, 1 neutron) has mass 2.013553 u. Find its binding energy in MeV, to 3 s.f. (m_p = 1.007276 u, m_n = 1.008665 u)
Show answer
2.23 MeV. Δm = 2.015941 - 2.013553 = 0.002388 u = 3.96 x 10-30 kg; ΔE = 9.00 x 1016 x 3.96 x 10-30 = 3.57 x 10-13 J = 2.23 MeV.
- Iron-56 has a total binding energy of 492 MeV. Find its binding energy per nucleon in MeV, to 3 s.f.
Show answer
8.79 MeV. 492 / 56 = 8.79 MeV per nucleon.
- What is the binding energy of a nucleus?
- The energy holding electrons in the atom
- The kinetic energy of its nucleons
- The energy released when it decays
- The energy needed to separate it completely into individual nucleons
Show answer
The energy needed to separate it completely into individual nucleons. That is the definition; it equals c2 times the mass deficit.
- How does the mass of a nucleus compare with the total mass of its separate protons and neutrons?
- It is larger
- It is smaller
- It is the same
- It depends on the temperature
Show answer
It is smaller. Energy is released when the nucleus forms, so its mass is less (the mass deficit).
Sources
- Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
- Pearson qualifications: International Advanced Levels Physics (2018)
- Pearson Edexcel IAL Physics Unit 5 (WPH15) question paper, June 2023: list of data, formulae and relationships
Last updated 7 November 2026. Spotted a mistake? Tell us.