Nuclear binding, particle families and Hall carriers
| English | 中文 | Pinyin |
|---|---|---|
| binding energy per nucleon/ˈbaɪndɪŋ ˈenədʒi pɜː ˈnjuːklɪən/ | 平均核子结合能 | píng jūn hé zǐ jié hé néng |
| Hall coefficient | 霍尔系数 | huò ěr xì shù |
A decision before an answer
- Measuring conductivity alone does not tell you whether electrons or holes dominate transport. A magnetic Hall measurement provides a sign-sensitive test.
- Your goal: Compare binding energy per nucleon and reaction energy.
Read the relationship
- Binding energy B is the energy needed to separate a nucleus into its constituent free nucleons, equal to the corresponding mass deficit times c². Binding energy per nucleon B/A is the relevant comparison across different mass numbers; a heavier nucleus can have greater total B but lower B/A. The broad B/A maximum is near the iron/nickel region. Light-nucleus fusion and very-heavy-nucleus fission can release energy when products have greater total binding. For a reaction, Q=(initial rest mass−final rest mass)c²; positive Q means released energy. Always compare the actual specified isotopes and final products, not just their element names.
- Distinguish leptons, mesons and baryons with conservation constraints.
Which ordinary constituent description is correct?
Leptons are not constituent-quark composites; ordinary baryons contain three quarks.
Use the defining rule
- Leptons such as electrons, muons and neutrinos are not made of constituent quarks in the Standard Model. A negative muon has charge −e and spin 1/2, like an electron, but has a different mass and belongs to a different flavour family; it is not a meson despite its historical name. Hadrons contain quarks: ordinary mesons have one quark and one antiquark, and ordinary baryons have three quarks. Corresponding antibaryons have three antiquarks. These elementary classification models do not imply every composite particle is a simple baryon or meson.
- Infer dominant carrier sign from the one-carrier Hall model.
Under R_H=1/(nq) for a single carrier, a negative coefficient identifies:
Density is positive, so coefficient sign follows charge sign.
Check the conditions
- Check charge, energy, momentum, baryon number and relevant lepton numbers in a proposed process. A proton’s uud quarks sum to charge +e; neutron udd sums to zero. Beta-minus decay n→p+e−+antineutrino conserves electric charge and includes the antineutrino to balance lepton number and kinematics. A particle’s mass alone does not classify it as a quark, lepton or hadron. Reaction thresholds may require kinetic energy beyond an exothermic rest-mass difference when other constraints apply.
- Infer dominant carrier sign from the one-carrier Hall model.
If nucleus A has B=24 MeV and A=4, its B/A is 6 MeV; if nucleus B has B=80 MeV and A=10, its B/A is 8 MeV despite both having positive binding. Quark charges uud add to +e, udd to 0. In a one-carrier sample with density n and charge −e, R_H=−1/(ne); a raw Hall-voltage sign is meaningful only with fixed lead/field directions.
A nucleus has binding energy 72 MeV and mass number 9. B/A is ____ MeV.
Divide total binding by nucleon count: 72/9=8.
Apply the task format
- In a simple one-carrier conductor, transverse magnetic Lorentz force builds a Hall electric field until transverse carrier force balances. With a stated tensor/sign convention, Hall coefficient is R_H=1/(nq); negative q gives electron-like negative coefficient, positive q gives hole-like positive coefficient. Resistivity magnitude alone does not reveal this sign. Set current, magnetic field and voltage directions consistently before reading raw polarity. Semiconductors with electrons and holes both contributing require a mobility-weighted two-carrier model; the simple coefficient need not equal the inverse total carrier density.
- Infer dominant carrier sign from the one-carrier Hall model.
Compare binding per nucleon, not just total binding. A muon is a lepton, and Hall sign requires the declared measurement convention and carrier model.
Which answer fits this case?
Compare binding energy per nucleon and reaction energy
A negative muon is a meson because its name contains the syllable mu.
A muon is a charged lepton; names do not establish quark composition.
Keep the distinctions
- binding energy per nucleon 平均核子结合能 — Nuclear binding energy divided by nucleon count.
- Hall coefficient 霍尔系数 — Signed proportionality relating transverse Hall field to current density and magnetic field under a stated convention.
- Compare binding energy per nucleon and reaction energy.
- Distinguish leptons, mesons and baryons with conservation constraints.
- Infer dominant carrier sign from the one-carrier Hall model.
Match each term with its precise meaning in this lesson.
Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
The order follows the stated process; check each stage before the next.