Mass Defect & Binding Energy
Weigh the separate protons and neutrons against the bound nucleus of specific isotopes. Convert the missing mass defect into nuclear strong force binding energy using E=mc².
WHAT IS MASS DEFECT?
Mass defect is the difference between the mass of a completely assembled atomic nucleus and the sum of the masses of its individual constituent nucleons (protons and neutrons). Surprisingly, the nucleus always weighs **less** than its parts. This "missing" mass is not actually gone—it has been converted into the **binding energy** that holds the nucleus together, according to Einstein's equation .
NUCLEAR BINDING ENERGY
Binding energy is the energy required to disassemble a nucleus into its separate protons and neutrons. The higher the binding energy per nucleon, the more stable the nucleus. Iron-56 is one of the most stable isotopes. Elements lighter than iron can release energy through **fusion**, while elements heavier than iron can release energy through **fission** as they move toward more stable configurations.
HOW TO USE THIS VISUALIZATION
1. **Build an Atom**: Drag protons and neutrons into the nucleus. Watch the mass scale. 2. **Observe the Deficit**: Compare the "Sum of Parts" vs. "Actual Mass". See the energy equivalent calculated live. 3. **Fusion vs Fission**: Combine small nuclei or split large ones to see how energy is released in different regions of the binding energy curve.
CORE FORMULAS
AP EXAM CONNECTION
Unit: Unit 7: Fluids and Modern Physics (Topic 7.3)
Learning Objective: MOD-1.A
COMMON MISCONCEPTIONS
- Thinking mass is always conserved in nuclear reactions (only mass-energy is).
- Confusing binding energy with the energy of the electrons.
- Believing mass defect only happens in fission reactions.
KEY TAKEAWAYS
- Nuclei are lighter than the sum of their parts.
- Missing mass = Binding Energy ().
- Binding energy per nucleon determines stability.
PRACTICE QUESTIONS
Q1 (QUANTITATIVE): If a nucleus has a mass defect of 0.02 atomic mass units (u), what is its binding energy in MeV?
Show Answer & Explanation
Answer: 18.63 MeV
Explanation: .
Q2 (CONCEPTUAL): Which is heavier: a Helium-4 nucleus, or two protons and two neutrons measured separately?
Show Answer & Explanation
Answer: The separate protons and neutrons.
Explanation: Energy must be added to the Helium nucleus to break it apart. This energy adds mass to the separate components.
