Solid-state, nuclear and particle models
| English | 中文 | Pinyin |
|---|---|---|
| band gap/bænd ɡæp/ | 带隙 | dài xì |
| half-life/hɑːf laɪf/ | 半衰期 | bàn shuāi qī |
A decision before an answer
- A semiconductor’s conductivity depends on available states and carriers, not merely on the number of electrons in the material.
- Your goal: Use band and carrier descriptions.
Read the relationship
- Filled bands cannot carry ordinary current without accessible nearby states. Metals have partially filled or overlapping bands; semiconductors have a small band gap. Donor and acceptor doping change carrier populations.
- Apply radioactive decay and binding-energy ideas.
After two half-lives, the remaining fraction is:
Two successive halvings give one quarter.
Use the defining rule
- Fermi–Dirac occupancy is 1/[exp((E−μ)/(kT))+1]. At zero temperature it becomes a step at the Fermi energy; thermal broadening does not make every state half occupied.
- Check conservation laws in particle reactions.
Donor doping commonly supplies:
Donor levels facilitate electron excitation into conducting states.
Check the conditions
- Radioactive populations obey N=N0e^(−λt), activity λN and half-life ln2/λ. Binding energy comes from a mass deficit multiplied by c²; compare binding energy per nucleon when discussing stability.
- Check conservation laws in particle reactions.
After three half-lives, N/N0=(1/2)^3=1/8, so activity is also one eighth if λ is unchanged. A mass defect of 0.010 u corresponds to about 9.315 MeV using 1 u c²=931.5 MeV.
After four half-lives, one part in ____ remains.
2^4=16.
Apply the task format
- Nuclear and particle processes must conserve charge, energy, momentum and the applicable quantum numbers. Beta decay includes a neutrino or antineutrino; a two-body electron-only story cannot explain its continuous energy spectrum.
- Check conservation laws in particle reactions.
Activity and surviving population both decay, but their units differ: activity is transitions per second.
Which answer fits this case?
Use band and carrier descriptions
Charge conservation alone is sufficient to validate any particle reaction.
Energy, momentum and other applicable conservation laws also matter.
Keep the distinctions
- band gap 带隙 — An energy interval with no allowed bulk electronic states in the band model.
- half-life 半衰期 — Time for a radioactive population to halve.
- Use band and carrier descriptions.
- Apply radioactive decay and binding-energy ideas.
- Check conservation laws in particle reactions.
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.