Not every energy difference produces a strong electric-dipole 电偶极 line.
Prerequisites: 23, 40, 41.
- Relate atomic energies to spectral lines
- Apply angular-momentum quantum numbers
- Distinguish allowed and forbidden electric-dipole transitions
AT · Atomic spectra and selection rules
GRE · GRE Subject Test · GRE 物理 · 知识点 7
7.1
原子光谱与选择定则
词汇
训练
| English | 中文 | 拼音 |
|---|---|---|
| electric-dipole | 电偶极 | diàn ǒu jí |
7.2
Choose the system and model
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.
7.3
Use the governing relation
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.
7.4
Apply 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.
7.5
Check the conclusion
Fine structure, spin–orbit effects and Zeeman splitting 塞曼分裂 refine the simplest hydrogen picture. In many-electron atoms, shielding and electron interactions invalidate direct hydrogen-energy substitution.
词汇
训练
| English | 中文 | 拼音 |
|---|---|---|
| Zeeman splitting/ˈziːmən ˈsplɪtɪŋ/ | 塞曼分裂 | sāi màn fēn liè |
7.6
Worked method
For a nonrelativistic one-electron ion, neglecting fine structure,
$$E_n=-13.6\,\mathrm{eV}\,Z^2/n^2.$$
For Z = 2, an emission from n = 3 to n = 2 gives positive photon energy:
$$E_\gamma=E_3-E_2=(13.6\,\mathrm{eV})(2^2)(1/2^2-1/3^2)=7.56\,\mathrm{eV}.$$
$$\lambda=hc/E_\gamma=(1240\,\mathrm{eV\,nm})/(7.56\,\mathrm{eV})=164\,\mathrm{nm}.$$
An energy difference alone does not guarantee an electric-dipole transition;
the participating orbital states must satisfy the selection rules.
7.7
Check conditions and vocabulary
Do not make the final-state energy minus initial-state energy negative for an emitted photon.
selection rule 选择定则: A restriction on transitions for a specified interaction mechanism.
Zeeman splitting: Magnetic-field splitting of atomic energy levels.
词汇
训练
| English | 中文 | 拼音 |
|---|---|---|
| selection rule/sɪˈlekʃn ruːl/ | 选择定则 | xuǎn zé dìng zé |
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