Atomic spectra and selection rules
| English | 中文 | Pinyin |
|---|---|---|
| selection rule/sɪˈlekʃn ruːl/ | 选择定则 | xuǎn zé dìng zé |
| Zeeman splitting/ˈziːmən ˈsplɪtɪŋ/ | 塞曼分裂 | sāi màn fēn liè |
A decision before an answer
- Not every energy difference produces a strong electric-dipole line.
- Your goal: Relate atomic energies to spectral lines.
Read the relationship
- For hydrogen-like one-electron ions, the bound energies scale as −13.6 Z²/n² eV in the simplest nonrelativistic model. Emission requires a downward transition and positive photon energy.
- Apply angular-momentum quantum numbers.
Hydrogen n=3 has energy about:
Divide −13.6 by 9.
Use the defining rule
- Orbital angular momentum has l=0,…,n−1 and m_l=−l,…,l. Electron spin adds s=1/2; total angular momentum combines orbital and spin contributions.
- Distinguish allowed and forbidden electric-dipole transitions.
Which Δl is electric-dipole allowed?
The orbital rule is Δl=±1.
Check the conditions
- Electric-dipole selection rules include Δl=±1 and Δm=0,±1. These rules concern a specific transition mechanism; forbidden does not mean impossible by every mechanism.
- Distinguish allowed and forbidden electric-dipole transitions.
In hydrogen, E1=−13.6 eV and E2=−3.4 eV. A 2p→1s emission releases 10.2 eV and satisfies Δl=−1. A 2s→1s transition has Δl=0, so it is electric-dipole forbidden even though the same energy difference exists.
For hydrogen 2→1, the photon energy is ____ eV.
Subtract −13.6 from −3.4.
Apply the task format
- Fine structure, spin–orbit effects and Zeeman splitting refine the simplest hydrogen picture. In many-electron atoms, shielding and electron interactions invalidate direct hydrogen-energy substitution.
- Distinguish allowed and forbidden electric-dipole transitions.
Do not make the final-state energy minus initial-state energy negative for an emitted photon.
Which answer fits this case?
Relate atomic energies to spectral lines
Electric-dipole forbidden means no emission mechanism can ever exist.
Other mechanisms, such as two-photon emission, can occur.
Keep the distinctions
- selection rule 选择定则 — A restriction on transitions for a specified interaction mechanism.
- Zeeman splitting 塞曼分裂 — Magnetic-field splitting of atomic energy levels.
- Relate atomic energies to spectral lines.
- Apply angular-momentum quantum numbers.
- Distinguish allowed and forbidden electric-dipole transitions.
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.