Physics HL · Chapter 23: Nuclear Physics
23.1 Nuclear Notation, Mass Defect, and Binding Energy
Build the language of nuclides, then compute how missing mass becomes nuclear binding energy.
Estimated time: 42 minutes
Nuclear Notation and Isotope Structure
A nuclide is specified by proton number (Z) and nucleon number (A). Neutron number is (N=A-Z). Isotopes share the same (Z) but have different (N), so they are chemically similar (same electron count for neutral atoms) but can have very different nuclear stability. This is the basic bookkeeping language for every nuclear reaction you will write in this chapter.
Notation explicitly separates element identity (Z) from isotope identity (A and N).
When you read a decay equation, first inspect how (A) and (Z) change. That immediately tells you which particle was emitted and whether nucleons were lost or only converted (for example neutron to proton in beta minus decay). Treat this as a conservation check before doing any energy calculation.
Mass Defect: Why Nuclei Weigh Less Than Separated Nucleons
If you add the masses of (Z) free hydrogen atoms and (N) free neutrons, that total is larger than the measured atomic mass of the nuclide. The difference is the mass defect. Physically, the nucleus has lower total energy than fully separated nucleons, and relativity connects this energy reduction to lower mass.
Binding energy Eb is the minimum energy required to separate the nucleus into free nucleons.
The key idea is that the missing mass is not lost matter; it is released binding energy. In formation, that energy leaves as radiation or kinetic energy. In breakup, the same amount must be supplied back. This is why mass-defect calculations are really energy-accounting problems written in mass units.
Binding Energy Per Nucleon and What It Measures
Total binding energy grows with nucleon count, so comparing nuclei by total (E_b) is misleading. Divide by (A) to get binding energy per nucleon, a better measure of average nuclear tightness. Higher (E_b/A) means nucleons are held more strongly on average and more energy is needed per nucleon to dismantle the nucleus.
Simulation: Mass Defect and Binding-Energy Curve Explorer
Select benchmark isotopes and compare free-nucleon mass, measured mass, mass defect, total binding energy, and position on a binding-energy trend curve.
Link nucleus composition, binding-energy trends, decay statistics, and strong-force evidence in one chapter workspace.
Mass defect
0.5285 u
Binding energy
492.3 MeV
Binding per nucleon
8.790 MeV
Atomic mass
55.934936 u
Test Yourself
Using atomic-mass data, iron-56 has mass defect about 0.528 u. Enter its binding energy per nucleon.
Hint: Use Eb = mu x 931.5 MeV and divide by A = 56.