Mass Defect and Binding Energy
For a nucleus with Z protons and N neutrons, mass defect is the free-nucleon mass sum minus nuclear mass, and binding energy is Delta m c^2. With atomic masses, hydrogen-atom masses must be used consistently so electron masses cancel.
Why this shows up in the exam
Calculating total binding energy · Finding missing nuclear mass · Computing photodisintegration energy
Learn the idea
Binding energy is the rest-energy equivalent of the mass missing when free nucleons form a bound nucleus. A bound nucleus has less mass than its separated protons and neutrons because energy was released during assembly. Supplying the same binding energy can separate it back into free nucleons.
🧠 Memory hook: Free pieces weigh more; the missing mass is binding energy.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Delta m = Z m_p + N m_n - M_nucleus — mass defect when nuclear masses are used
- Delta m = Z m_H + N m_n - M_atom — mass defect using neutral atomic masses, neglecting small electron binding energies
- B = Delta m c² — total nuclear binding energy
How to approach it
- 1Decide whether the data are atomic or nuclear masses
- 2Compute N = A - Z
- 3Check that a bound nucleus gives positive mass defect
Common slip-ups that cost marks
- •Mixing proton mass with neutral atomic mass inconsistently
- •Reversing the mass-defect subtraction
- •Reporting total binding energy as binding energy per nucleon
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
In hydrogen, an electron transitions from n = 2 to n = 1. Using E_n = -13.6/n^2 eV, find the emitted photon energy.
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