Atomic spectra and selection rules · 原子光谱与选择定则
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| 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.
答案前的判断
- 并非所有能级差都会产生强的电偶极子谱线。
- 你的目标：将原子能级与光谱线联系起来。
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.
阅读关系
- 在 simplest nonrelativistic model（最简单的非相对论模型）中，类氢单电子离子的束缚能标度为 −13.6 Z²/n² eV。发射过程要求向下跃迁且具有正光子能量。
- 应用角动量量子数。
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.
运用定义规则
- 轨道角动量量子数为 l=0,…,n−1，磁量子数 m_l=−l,…,l。电子自旋贡献 s=1/2；总角动量由轨道和自旋部分共同组成。
- 区分允许与禁止的电偶极跃迁。
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.
检查条件
- 电偶极选择定则包括 Δl=±1 和 Δm=0,±1。这些规则针对特定的跃迁机制；“禁止”并不意味着通过其他所有机制都绝对不可能发生。
- 区分允许与禁止的电偶极跃迁。
在氢原子中，E1=−13.6 eV 且 E2=−3.4 eV。一次 2p→1s 发射释放 10.2 eV 能量，并满足 Δl=−1。而一次 2s→1s 跃迁的 Δl=0，因此属于电偶极禁戒跃迁，尽管其能级差相同。
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.
应用题目格式
- 精细结构、自旋-轨道耦合效应及塞曼分裂完善了最简单的氢原子图像。在多电子原子中，屏蔽效应和电子间相互作用使得直接套用氢原子能级公式不再适用。
- 区分允许与禁止的电偶极跃迁。
计算发射光子时，切勿使末态能量减去初态能量为负值。
Which answer fits this case? · 哪个答案符合此案例？
Relate atomic energies to spectral lines · 将原子能级与光谱线相关联
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.
保持区别
- selection rule 选择定则 — 对特定相互作用机制下可能发生的跃迁所施加的限制条件。
- Zeeman splitting 塞曼分裂 — 原子能级在外加磁场作用下的分裂现象。
- 将原子能级与光谱线联系起来。
- 应用角动量量子数。
- 区分允许与禁止的电偶极跃迁。
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.